1############################################################################# 2## 3#W ctomisc1.tbl GAP table library Thomas Breuer 4## 5#Y Copyright (C) 1997, Lehrstuhl D fuer Mathematik, RWTH Aachen, Germany 6## 7## This file contains the ordinary character tables of miscellaneous 8## CAS tables (alphabetical order, up to 'e') 9## 10#H ctbllib history 11#H --------------- 12#H $Log: ctomisc1.tbl,v $ 13#H Revision 4.38 2012/04/23 16:16:14 gap 14#H next step of consolidation: 15#H 16#H - removed a few unnecessary duplicate tables, 17#H and changed some related fusions, names of maxes, table constructions 18#H - make sure that duplicate tables arise only via `ConstructPermuted' 19#H constructions 20#H - added some relative names 21#H - added fusions A11.2 -> A12.2, L2(11).2 -> A12.2, D8x2F4(2)'.2 -> B, 22#H L2(41) -> M, (A5xA12):2 -> A17, 23#H - added maxes of A12.2, L6(2), 2.M22.2 24#H - added table of QD16.2, 25#H - fixed the syntax of two `ALN' calls 26#H TB 27#H 28#H Revision 4.37 2012/01/30 08:31:57 gap 29#H removed #H entries from the headers 30#H TB 31#H 32#H Revision 4.36 2011/09/28 13:23:58 gap 33#H - removed revision entry and SET_TABLEFILENAME call, 34#H - added fusions 2.2^8.f20 -> 2.[2^9]:5:4, 2^2.2^8:s3 -> 2^2.[2^9]:S3, 35#H c3d2 -> Co3 36#H TB 37#H 38#H Revision 4.35 2010/12/01 17:47:57 gap 39#H renamed "Sym(4)" to "Symm(4)"; 40#H note that the table constructed with `CharacterTable( "Symmetric", 4 )' 41#H gets the identifier `"Sym(4)"', and this table is sorted differently 42#H TB 43#H 44#H Revision 4.34 2010/05/05 13:20:07 gap 45#H - added many class fusions, 46#H - changed several class fusions according to consistency conditions, 47#H after systematic checks of consistency 48#H - with Brauer tables w.r.t. the restriction of characters, 49#H - of subgroup fusions with the corresponding subgroup fusions between 50#H proper factors where the factor fusions are stored, 51#H - of subgroup fusions from maximal subgroups with subgroup fusions of 52#H extensions inside automorphic extensions 53#H 54#H TB 55#H 56#H Revision 4.33 2010/01/19 17:05:34 gap 57#H added several tables of maximal subgroups of central extensions of 58#H simple groups (many of them were contributed by S. Dany) 59#H TB 60#H 61#H Revision 4.32 2009/07/29 14:00:41 gap 62#H added two tables of maxes of 2F4(2) 63#H TB 64#H 65#H Revision 4.31 2009/03/02 16:44:38 gap 66#H moved the tables of A15, A16 from ctomisc1.tbl to ctoalter.tbl 67#H TB 68#H 69#H Revision 4.30 2007/07/03 08:27:32 gap 70#H renamed table `"d60"' to `"D120"' 71#H (the name goes back to CAS times; it does not fit to the programmatic use 72#H of names such as `"C<n>"', `"D<n>"', `"S<n>"' etc.) 73#H TB 74#H 75#H Revision 4.29 2004/02/17 17:33:14 gap 76#H added certain tables of isoclinic groups of ATLAS groups 77#H (which are available in atlasrep), 78#H added missing maxes of U5(2) 79#H TB 80#H 81#H Revision 4.28 2004/01/20 10:26:13 gap 82#H added several names of the forms `<name>C<class>', `<name>N<class>' 83#H TB 84#H 85#H Revision 4.27 2003/06/20 15:03:09 gap 86#H added several fusions 87#H TB 88#H 89#H Revision 4.26 2003/06/10 16:19:09 gap 90#H store in several fusions between character tables to which subgroup number 91#H in the table of marks of the supergroup the subgroup belongs 92#H (in order to make the commutative diagrams testable) 93#H TB 94#H 95#H Revision 4.25 2003/05/15 17:38:17 gap 96#H next step towards the closer connection to the library of tables of marks: 97#H added fusions tbl -> tom, adjusted fusions between character tables 98#H in order to make the diagrams commute, adjusted orderings of maxes 99#H TB 100#H 101#H Revision 4.24 2003/03/07 15:53:40 gap 102#H added tables of `Isoclinic(2.A5.2)' and `L2(125)', 103#H and many `tomidentifier' components (still several are missing) 104#H TB 105#H 106#H Revision 4.23 2003/01/24 15:57:34 gap 107#H replaced several fusions by ones that are compatible with Brauer tables 108#H TB 109#H 110#H Revision 4.22 2003/01/21 16:25:32 gap 111#H further standardizations of `InfoText' strings, 112#H added and corrected `Maxes' infos, 113#H added some fusions 114#H TB 115#H 116#H Revision 4.21 2003/01/14 17:28:50 gap 117#H changed `InfoText' values (for a better programmatic access) 118#H and replaced `ConstructDirectProduct' by `ConstructPermuted' where 119#H there is only one factor (again better programmatic handling) 120#H TB 121#H 122#H Revision 4.20 2002/10/22 12:44:11 gap 123#H added 215 factor fusions for cases <tbl> -> <tbl> / O_{<p>}(<tbl>) 124#H (they make it possible to construct <p>-modular Brauer tables 125#H for tables of the type [p^n].<fact> where the <p>-modular Brauer table 126#H of <fact> is in the library) 127#H TB 128#H 129#H Revision 4.19 2002/09/23 15:00:11 gap 130#H changed 2x3.A7.2 into a ``construction'' table, 131#H corrected fusion A11Syl2 -> A11, 132#H changed the name `c2m24' to `M24C2B' 133#H TB 134#H 135#H Revision 4.18 2002/09/18 15:22:01 gap 136#H changed the `text' components of many fusions, 137#H in order to use them as a status information (for evaluation) 138#H TB 139#H 140#H Revision 4.17 2002/08/21 13:53:50 gap 141#H removed names of the form `c1m<n>', `c2m<n>', `c3m<n>' 142#H TB 143#H 144#H Revision 4.16 2002/07/26 16:58:05 gap 145#H added more missing table automorphisms, 146#H removed a few inconvenient names such as `c2' for `Co2' 147#H (note that `c2' is used for the cyclic group of order 2, 148#H which occurs in direct product constructions ...) 149#H TB 150#H 151#H Revision 4.15 2002/07/12 06:45:55 gap 152#H further tidying up: removed `irredinfo' stuff, rearranged constructions 153#H TB 154#H 155#H Revision 4.14 2001/05/04 16:48:49 gap 156#H first revision for ctbllib 157#H 158#H 159#H tbl history (GAP 4) 160#H ------------------- 161#H (Rev. 4.14 of ctbllib coincides with Rev. 4.13 of tbl in GAP 4) 162#H 163#H RCS file: /gap/CVS/GAP/4.0/tbl/ctomisc1.tbl,v 164#H Working file: ctomisc1.tbl 165#H head: 4.13 166#H branch: 167#H locks: strict 168#H access list: 169#H symbolic names: 170#H GAP4R2: 4.13.0.6 171#H GAP4R2PRE2: 4.13.0.4 172#H GAP4R2PRE1: 4.13.0.2 173#H GAP4R1: 4.10.0.2 174#H keyword substitution: kv 175#H total revisions: 15; selected revisions: 15 176#H description: 177#H ---------------------------- 178#H revision 4.13 179#H date: 2000/01/06 14:47:53; author: gap; state: Exp; lines: +2 -2174 180#H removed tables with name `2.cenc1' 181#H (a relic from old CAS times that is inconsistent; 182#H time to get rid of it, before someone finds it interesting ...) 183#H 184#H TB 185#H ---------------------------- 186#H revision 4.12 187#H date: 1999/10/04 15:57:15; author: gap; state: Exp; lines: +6 -2 188#H added and corrected several fusions from character tables 189#H to their tables of marks, 190#H unified two instances of the table of (A6xA6):2^2, 191#H corrected the name of the table of marks of 2F4(2). 192#H 193#H TB 194#H ---------------------------- 195#H revision 4.11 196#H date: 1999/09/14 13:28:19; author: gap; state: Exp; lines: +2 -484 197#H really removed corrupted tables (had only been commented out before) 198#H 199#H TB 200#H ---------------------------- 201#H revision 4.10 202#H date: 1999/07/21 11:11:30; author: gap; state: Exp; lines: +12 -20 203#H renamed `a15' and `a16' to `A15' and `A16', respectively 204#H (just for unified treatment of tables via names) 205#H 206#H TB 207#H ---------------------------- 208#H revision 4.9 209#H date: 1999/07/19 16:00:31; author: gap; state: Exp; lines: +20 -12 210#H added fusion A16 -> S16 211#H 212#H TB 213#H ---------------------------- 214#H revision 4.8 215#H date: 1999/07/16 10:53:37; author: gap; state: Exp; lines: +58 -45 216#H changed `classtext' components of tables of alternating and symmetric 217#H groups to `ClassParameters' values (same format as computed from 218#H generic tables) 219#H 220#H TB 221#H ---------------------------- 222#H revision 4.7 223#H date: 1999/07/14 15:18:38; author: gap; state: Exp; lines: +483 -483 224#H removed incomplete CAS table of `D2MJ4' 225#H 226#H TB 227#H ---------------------------- 228#H revision 4.6 229#H date: 1999/07/14 11:39:40; author: gap; state: Exp; lines: +4 -3 230#H cosmetic changes for the release ... 231#H 232#H TB 233#H ---------------------------- 234#H revision 4.5 235#H date: 1999/06/11 14:35:34; author: gap; state: Exp; lines: +17 -2 236#H added fusions A15 -> S15, A16 -> S16 237#H 238#H TB 239#H ---------------------------- 240#H revision 4.4 241#H date: 1997/11/25 15:45:25; author: gap; state: Exp; lines: +7 -5 242#H first attempt to link the library of character tables and the 243#H library of tables of marks 244#H TB 245#H ---------------------------- 246#H revision 4.3 247#H date: 1997/08/05 15:03:47; author: gap; state: Exp; lines: +5 -5 248#H removed unnecessary (and ugly) `return' statements in the calls of 249#H `ConstructPermuted' and `ConstructSubdirect' 250#H ---------------------------- 251#H revision 4.2 252#H date: 1997/08/01 15:43:06; author: gap; state: Exp; lines: +2 -40 253#H added table of 2^7:S6(2) 254#H (subgroup of Fi22.2; stored using Clifford matrices); 255#H added tables of A14 mod p for p = 2, 11, 13 256#H (moved ordinary table from `ctomisc1.tbl' to `ctoalter.tbl' for that); 257#H added maxes of 2.M12; 258#H updated the ``table of contents''. 259#H ---------------------------- 260#H revision 4.1 261#H date: 1997/07/17 15:43:37; author: fceller; state: Exp; lines: +2 -2 262#H for version 4 263#H ---------------------------- 264#H revision 1.2 265#H date: 1997/04/04 12:20:17; author: sam; state: Exp; lines: +59 -96 266#H added 'ConstructPermuted', 'ConstructSubdirect', 267#H changed table constructions involving 'CharTable', 'RecFields' 268#H 'Sort...' up to now 269#H ---------------------------- 270#H revision 1.1 271#H date: 1996/10/21 16:00:19; author: sam; state: Exp; 272#H first proposal of the table library 273#H ========================================================================== 274## 275 276MOT("2..11.m23", 277[ 278"origin: CAS library,\n", 279"names:= 2..11.m23\n", 280" order: 2^18.3^2.5.7.11.23 = 20,891,566,080\n", 281" number of classes: 56\n", 282" source:gabrysch, thomas\n", 283" ein computerprogramm zur berechnung\n", 284" von charakterentafeln und einige anwendungen,\n", 285" diplomarbeit, univ. of bielefeld [1977]\n", 286" comments:non-split extension of m23 with an\n", 287" elementar-abelian group of order 2..11.m23 \n", 288" test: 1. o.r., sym 2 decompose correctly \n", 289"2nd power map determined by subgroup fusion into Fi23\n", 290"tests: 1.o.r., pow[2,3,5,7,11,23]" 291], 292[20891566080,908328960,82575360,11796480,344064,49152,43008,6144,12288,12288, 293512,512,256,128,128,128,32,32,32,32,5760,1152,576,576,1152,5760,96,96,96,96, 29448,48,120,40,40,120,30,30,30,30,56,28,56,56,28,56,28,28,28,28,22,22,22,22,23, 29523], 296[,[1,1,1,1,1,1,3,3,4,4,6,6,5,9,9,10,12,11,16,16,21,21,21,21,21,21,21,21,25,25, 29723,23,33,33,33,33,37,37,39,39,41,41,41,44,44,44,41,43,44,46,53,53,51,51,55, 29856],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,1,2,3,4,4,4,5,6,9,10, 2997,8,33,34,35,36,33,36,33,36,44,45,46,41,42,43,49,50,47,48,51,52,53,54,55, 30056],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,20,19,21,22,23,24,25,26,27, 30128,29,30,31,32,1,2,3,4,21,26,21,26,44,45,46,41,42,43,49,50,47,48,51,52,53,54, 30256,55],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,20,19,21,22,23,24,25,26, 30327,28,29,30,31,32,33,34,35,36,39,40,37,38,1,2,3,1,2,3,5,7,5,7,53,54,51,52,56, 30455],,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26, 30527,28,29,30,31,32,33,34,35,36,39,40,37,38,41,42,43,44,45,46,47,48,49,50,1,2,1, 3062,56,55],,,,,,,,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,20,19,21,22, 30723,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48, 30849,50,51,52,53,54,1,1]], 309[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, 3101,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[22,22,22,22,6,6,6,6,6,6,2,2,2,2,2,2,0,0, 3110,0,4,4,4,4,4,4,0,0,0,0,0,0,2,2,2,2,-1,-1,-1,-1,1,1,1,1,1,1,-1,-1,-1,-1,0,0,0, 3120,-1,-1],[230,230,230,230,22,22,22,22,22,22,2,2,2,2,2,2,0,0,0,0,5,5,5,5,5,5,1, 3131,1,1,1,1,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,0,0],[231,231, 314231,231,7,7,7,7,7,7,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,6,6,6,6,6,6,-2,-2,-2,-2,-2, 315-2,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1],[45,45,45,45,-3,-3,-3,-3, 316-3,-3,1,1,1,1,1,1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 317E(7)^3+E(7)^5+E(7)^6,E(7)^3+E(7)^5+E(7)^6,E(7)^3+E(7)^5+E(7)^6, 318E(7)+E(7)^2+E(7)^4,E(7)+E(7)^2+E(7)^4,E(7)+E(7)^2+E(7)^4,-E(7)^3-E(7)^5-E(7)^6 319 ,-E(7)^3-E(7)^5-E(7)^6,-E(7)-E(7)^2-E(7)^4,-E(7)-E(7)^2-E(7)^4,1,1,1,1,-1, 320-1], 321[GALOIS,[5,3]],[231,231,231,231,7,7,7,7,7,7,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-3, 322-3,-3,-3,-3,-3,1,1,1,1,1,1,1,1,1,1,-E(15)^7-E(15)^11-E(15)^13-E(15)^14, 323-E(15)^7-E(15)^11-E(15)^13-E(15)^14,-E(15)-E(15)^2-E(15)^4-E(15)^8, 324-E(15)-E(15)^2-E(15)^4-E(15)^8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1], 325[GALOIS,[7,7]],[253,253,253,253,13,13,13,13,13,13,1,1,1,1,1,1,-1,-1,-1,-1,1,1, 3261,1,1,1,1,1,1,1,1,1,-2,-2,-2,-2,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,0,0,0,0,0,0],[ 327770,770,770,770,-14,-14,-14,-14,-14,-14,-2,-2,-2,-2,-2,-2,0,0,0,0,5,5,5,5,5,5, 3281,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,E(23)+E(23)^2+E(23)^3 329 +E(23)^4+E(23)^6+E(23)^8+E(23)^9+E(23)^12+E(23)^13+E(23)^16+E(23)^18, 330E(23)^5+E(23)^7+E(23)^10+E(23)^11+E(23)^14+E(23)^15+E(23)^17+E(23)^19+E(23)^20 331 +E(23)^21+E(23)^22], 332[GALOIS,[10,5]],[896,896,896,896,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-4,-4,-4,-4, 333-4,-4,0,0,0,0,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,E(11)+E(11)^3+E(11)^4 334 +E(11)^5+E(11)^9,E(11)+E(11)^3+E(11)^4+E(11)^5+E(11)^9, 335E(11)^2+E(11)^6+E(11)^7+E(11)^8+E(11)^10,E(11)^2+E(11)^6+E(11)^7+E(11)^8 336 +E(11)^10,-1,-1], 337[GALOIS,[12,2]],[990,990,990,990,-18,-18,-18,-18,-18,-18,2,2,2,2,2,2,0,0,0,0, 3380,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,E(7)+E(7)^2+E(7)^4,E(7)+E(7)^2+E(7)^4, 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401[GALOIS,[45,2]],[12880,-560,-560,80,-112,16,0,0,16,-16,0,0,0,0,0,0,0,0, 402-2*E(8)-2*E(8)^3,2*E(8)+2*E(8)^3,10,-2,-2,2,2,-10,2,-2,-2,2,0,0,0,0,0,0,0,0,0, 4030,0,0,0,0,0,0,0,0,0,0,-1,1,-1,1,0,0], 404[GALOIS,[47,5]],[2530,-990,290,-30,-46,18,18,-14,2,18,-2,-2,-2,2,2,-2,0,0,0,0, 40510,0,2,0,-6,0,2,0,2,0,0,-2,0,0,0,0,0,0,0,0,E(7)+E(7)^2+E(7)^4, 406-E(7)-E(7)^2-E(7)^4,E(7)+E(7)^2+E(7)^4,E(7)^3+E(7)^5+E(7)^6, 407-E(7)^3-E(7)^5-E(7)^6,E(7)^3+E(7)^5+E(7)^6,E(7)+E(7)^2+E(7)^4, 408-E(7)-E(7)^2-E(7)^4,E(7)^3+E(7)^5+E(7)^6,-E(7)^3-E(7)^5-E(7)^6,0,0,0,0,0,0], 409[GALOIS,[49,3]],[11385,-4455,1305,-135,-87,9,45,-3,-15,9,-3,5,1,1,-3,1,-1,-1, 4101,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,E(7)^3+E(7)^5+E(7)^6, 411-E(7)^3-E(7)^5-E(7)^6,E(7)^3+E(7)^5+E(7)^6,E(7)+E(7)^2+E(7)^4, 412-E(7)-E(7)^2-E(7)^4,E(7)+E(7)^2+E(7)^4,-E(7)^3-E(7)^5-E(7)^6, 413E(7)^3+E(7)^5+E(7)^6,-E(7)-E(7)^2-E(7)^4,E(7)+E(7)^2+E(7)^4,0,0,0,0,0,0], 414[GALOIS,[51,3]],[22770,6930,1170,-270,-126,-30,-42,6,-6,18,-2,6,2,-2,2,-2,0,0, 4150,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2*E(7)^3+2*E(7)^5+2*E(7)^6,0, 416-2*E(7)^3-2*E(7)^5-2*E(7)^6,2*E(7)+2*E(7)^2+2*E(7)^4,0,-2*E(7)-2*E(7)^2 417 -2*E(7)^4,0,0,0,0,0,0,0,0,0,0], 418[GALOIS,[53,3]],[10626,3234,546,-126,-14,-46,14,-2,10,2,6,-2,2,2,-2,-2,0,0,0, 4190,-3,3,-3,3,-3,3,1,-1,1,-1,-1,1,1,-1,1,-1,-E(15)^7-E(15)^11-E(15)^13-E(15)^14, 420E(15)^7+E(15)^11+E(15)^13+E(15)^14,-E(15)-E(15)^2-E(15)^4-E(15)^8, 421E(15)+E(15)^2+E(15)^4+E(15)^8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], 422[GALOIS,[55,7]]], 423[(55,56),(51,53)(52,54),(41,44)(42,45)(43,46)(47,49)(48,50),(37,39)(38,40), 424(19,20)]); 425ALF("2..11.m23","Fi23",[1,2,3,4,3,4,9,11,10,12,12,10,11,31,30,32,31,32,63, 42664,7,18,24,26,25,20,24,26,49,53,51,55,13,38,39,40,62,91,62,91,29,59,60,29, 42759,60,60,88,60,88,41,78,41,79,80,81],[ 428"fusion is unique up to table automorphisms,\n", 429"the representative is equal to the fusion map on the CAS table" 430]); 431ALF("2..11.m23","M23",[1,1,1,1,2,2,2,2,2,2,4,4,4,4,4,4,9,9,9,9,3,3,3,3,3, 4323,6,6,6,6,6,6,5,5,5,5,14,14,15,15,7,7,7,8,8,8,12,12,13,13,10,10,11,11,16, 43317]); 434ALN("2..11.m23",["f23m6"]); 435 436MOT("2.2^8.f20", 437[ 438"origin: CAS library,\n", 439"maximal subgroup of 2F4(2)',\n", 440" centralizer of 2a-element\n", 441" structure:= 2*[2^8]:f20 [f20: frobenius group of order 20]\n", 442" 1st & 2nd orthogonality relations are satisfied\n", 443" symmetric squares decompose properly\n", 444" created August 1984,\n", 445" test: 1. o.r., sym 2 decompose correctly,\n", 446"tests: 1.o.r., pow[2,5]" 447], 448[10240,10240,1024,128,512,128,128,64,32,32,128,64,64,32,32,32,10,32,16,32,16, 44916,16,10,16,16,16,16], 450[,[1,1,1,1,1,1,1,5,7,7,2,3,5,5,7,7,17,11,12,11,12,13,13,17,18,20,20,18],,,[1, 4512,3,4,5,6,7,8,9,10,11,12,13,14,15,16,1,18,19,20,21,22,23,2,28,27,26,25]], 452[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1, 453-1,-1,1,1,1,1,-1,-1,1,1,-1,1,-1,1,1,1,-1,-1,-1,-1],[1,1,1,-1,1,1,-1,1,-E(4), 454E(4),1,-1,1,-1,-E(4),E(4),1,-1,-E(4),-1,E(4),-1,-1,1,E(4),-E(4),-E(4),E(4)], 455[TENSOR,[2,3]],[4,4,4,0,4,4,0,4,0,0,4,0,4,0,0,0,-1,0,0,0,0,0,0,-1,0,0,0,0],[5, 4565,5,1,5,-3,1,1,1,1,-3,1,1,1,1,1,0,1,1,1,1,-1,-1,0,-1,-1,-1,-1], 457[TENSOR,[6,2]], 458[TENSOR,[6,3]], 459[TENSOR,[6,4]],[10,10,10,2,10,2,2,-2,0,0,2,2,-2,2,0,0,0,-2,0,-2,0,0,0,0,0,0,0, 4600], 461[TENSOR,[10,3]],[10,10,-6,-2,2,2,-2,-2,0,0,-2,-2,2,2,0,0,0,0,0,0,0,0,0,0, 462E(8)+E(8)^3,-E(8)-E(8)^3,E(8)+E(8)^3,-E(8)-E(8)^3], 463[TENSOR,[12,2]],[10,10,-6,0,2,2,0,2,1-E(4),1+E(4),-2,0,-2,0,1-E(4),1+E(4),0, 4642*E(4),-1+E(4),-2*E(4),-1-E(4),0,0,0,0,0,0,0], 465[TENSOR,[14,4]], 466[TENSOR,[12,3]], 467[TENSOR,[12,4]], 468[TENSOR,[14,2]], 469[TENSOR,[14,3]],[16,-16,0,-4,0,0,4,0,-2,-2,0,0,0,0,2,2,1,0,0,0,0,0,0,-1,0,0,0, 4700], 471[TENSOR,[20,2]], 472[TENSOR,[20,3]], 473[TENSOR,[20,4]],[20,20,-12,0,4,-4,0,0,0,0,4,0,0,0,0,0,0,0,0,0,0,2,-2,0,0,0,0, 4740], 475[TENSOR,[24,3]],[40,40,8,4,-8,0,4,0,0,0,0,-4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], 476[TENSOR,[26,3]],[64,-64,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,1,0,0,0, 4770]], 478[(25,28)(26,27),(22,23),( 9,10)(15,16)(18,20)(19,21)(25,26)(27,28),( 9,10) 479(15,16)(18,20)(19,21)(25,27)(26,28),( 9,15)(10,16)]); 480ARC("2.2^8.f20","tomfusion",rec(name:="2.[2^8]:5:4",map:=[1,2,3,6,4,5,7, 48126,36,36,18,23,24,35,37,37,38,108,115,108,115,89,90,119,243,243,243,243], 482text:=[ 483"fusion map is unique up to table autom." 484])); 485ALF("2.2^8.f20","2F4(2)'",[1,2,2,2,3,3,3,5,5,5,6,6,7,7,7,7,8,10,10,11,11, 48612,13,14,19,20,22,21],[ 487"fusion is unique up to table automorphisms,\n", 488"the representative is equal to the fusion map on the CAS table" 489]); 490ALF("2.2^8.f20","2.[2^9]:5:4",[1,2,3,19,4,7,20,11,36,37,8,24,12,26,38,39, 49115,28,42,27,43,31,31,16,47,46,46,47]); 492ALN("2.2^8.f20",["2F4(2)'C2a","2F4(2)'N2a"]); 493 494MOT("2^10:(2^5:s5)", 495[ 496"origin: CAS library,\n", 497"One intersection between a Co2M8 and a Co2M2, has index 3 in Co2M8.\n", 498"Computed using Clifford matrices and lots of information from Co2M2.\n", 499"Test: 1.OR, JAMES, JAMES,n=3,\n", 500"and restricted characters from Co2M2 (and Co2) decompose properly.\n", 501"tests: 1.o.r., pow[2,3,5]" 502], 503[3932160,786432,393216,98304,98304,32768,32768,49152,122880,40960,24576,12288, 504256,256,256,256,128,128,128,128,128,128,4096,4096,4096,4096,2048,2048,2048, 5052048,2048,2048,2048,2048,1024,1024,1024,512,512,512,512,128,128,128,128,64,64, 50648,48,48,48,192,192,192,192,96,96,96,96,48,6144,6144,6144,6144,2048,2048,2048, 5072048,512,512,512,512,64,64,32,1024,1024,512,512,512,128,16384,16384,16384, 50816384,8192,8192,8192,8192,4096,2048,2048,1024,1024,512,512,512,512,256,256, 509128,128,20,20,40,40,20,20480,4096,2048,1280,49152,49152,24576,4096,4096,4096, 5103072,3072,2048,1536,12288,12288,12288,12288,4096,4096,4096,4096,1536,1536, 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903[TENSOR,[122,52]],[240,-144,48,0,0,16,-16,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 9040,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,12,0, 905-12,0,0,4,-4,0,4,0,-4,0,0,0,0,8,-8,0,0,0,0,16,-16,16,-16,0,0,0,0,0,0,0,0,0,4, 906-4,4,-4,0,0,0,0,0,0,0,0,0,0,0,0,0,48,-48,0,0,8,-8,0,0,0,0,24,0,0,-24,0,8,-8,0, 9070,0,8,-8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 9080,0,0,0,0,0,8,8,-8,0,0,0,0,0,0,0,0,0,0,0], 909[TENSOR,[172,2]], 910[TENSOR,[172,3]],[240,-144,48,0,0,16,-16,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 9110,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-12,0, 91212,0,0,-4,4,0,-4,0,4,0,0,0,0,-8,8,0,0,0,0,16,-16,16,-16,0,0,0,0,0,0,0,0,0,4, 913-4,4,-4,0,0,0,0,0,0,0,0,0,0,0,0,0,48,-48,0,0,8,-8,0,0,0,0,0,24,-24,0,-8,0,0,8, 9140,0,0,0,0,0,-8,8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 9150,0,0,0,0,0,-8,-8,8,0,0,0,0,0,0,0,0,0,0,0], 916[TENSOR,[172,4]], 917[TENSOR,[175,2]], 918[TENSOR,[175,3]], 919[TENSOR,[175,4]],[480,-288,96,0,0,32,-32,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 9200,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,24,0, 921-24,8,0,0,-8,0,-8,0,8,0,0,0,0,0,0,0,0,0,-32,32,-32,32,0,0,0,0,0,0,0,0,0,0,0,0, 9220,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 9230,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 9240,0,0,0,0,0,0,0,0,0,0,0], 925[TENSOR,[180,3]],[320,64,-64,-32,-32,0,0,32,0,0,0,0,0,0,0,0,0,0,0,0,0,0,16, 926-16,16,-16,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,-2,-2,2,2,0,0, 927-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 9280,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,32,-32,-16,16,0,-16,0,16,0, 9290,0,0,0,0,0,0,0,2,-2,2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 9300,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[320,64,-64,-32,-32,0,0,32,0,0,0,0,0,0, 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945(112,113)(116,117)(118,119)(122,123)(124,125)(126,128)(127,129)(132,137) 946(133,136)(134,135)(139,142)(140,141)(150,151)(153,156)(154,155)(159,161) 947(160,162)(163,166)(164,165)(168,169)(171,173)]); 948ALF("2^10:(2^5:s5)","2^10:m22:2",[1,2,3,2,3,4,3,4,2,4,3,4,57,58,60,60,59, 94960,62,61,61,62,5,9,11,10,8,12,6,6,11,7,9,7,7,8,6,7,6,7,6,24,25,27,26,28, 95028,32,34,34,33,13,17,14,17,16,16,15,15,17,5,12,12,10,11,8,9,8,6,6,7,7,69, 95170,71,18,19,20,21,22,23,5,10,11,9,12,8,11,9,8,7,6,7,6,18,21,21,19,22,20, 95223,23,72,73,29,30,31,49,50,51,52,43,48,47,47,45,46,46,45,44,44,43,48,46, 95345,47,46,47,45,44,47,44,46,46,45,45,44,44,63,65,66,64,67,68,24,25,26,27, 95428,39,40,41,63,65,66,64,67,68,57,59,58,59,62,62,61,61,60,57,58,59,62,60, 95561,49,50,51,50,51,51,52,52,53,54,56,55,56,55],[ 956"fusion is unique up to table automorphisms,\n", 957"the representative is equal to the fusion map on the CAS table" 958]); 959ALF("2^10:(2^5:s5)","Co2",[1,2,3,2,3,4,3,4,2,4,3,4,8,11,23,23,12,23,27,24, 96024,27,3,4,10,7,9,8,12,12,10,11,4,11,11,9,12,11,12,11,12,11,25,13,23,28,28, 96120,39,39,36,6,20,19,20,21,21,18,18,20,3,8,8,7,10,9,4,9,12,12,11,11,24,28, 96249,9,11,25,12,26,27,3,7,10,4,8,9,10,4,9,11,12,11,12,9,12,12,11,26,25,27, 96327,32,52,15,32,31,4,10,12,13,2,3,4,4,9,8,8,9,12,12,2,3,8,9,4,8,4,9,12,4, 96412,8,8,9,9,12,12,19,37,39,20,21,41,11,25,23,13,28,27,28,48,19,37,39,20,21, 96541,8,12,11,12,27,27,24,24,23,8,11,12,27,23,24,4,10,12,10,12,12,13,13,12, 96623,26,13,26,13],[ 967"fusion is unique up to table automorphisms,\n", 968"the representative is equal to the fusion map on the CAS table" 969]); 970ALF("2^10:(2^5:s5)","A5.2",[1,1,1,1,1,1,1,1,1,1,1,1,6,6,6,6,6,6,6,6,6,6,2, 9712,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,6,6,6,6,6,6,7,7,7,7,3,3,3,3,3,3,3,3,3, 9725,5,5,5,5,5,5,5,5,5,5,5,6,6,6,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,5,5,5, 9735,5,5,5,5,4,4,4,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,5,5,5,5,5,5,5,5,5,5,5,5,5, 9745,5,5,5,7,7,7,7,7,7,2,2,2,2,2,6,6,6,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,2,2,2,2, 9752,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]); 976 977MOT("2^2.2^8:s3", 978[ 979"origin: CAS library,\n", 980"maximal subgroup of 2F4(2)',\n", 981" normalizer of klein four group contained in class 2b\n", 982" structure:= 2^2.[2^8]:s3 [s3: symmetric group on 3 elements]\n", 983" 1st & 2nd orthogonality relations are satisfied\n", 984" symmetric squares decompose properly\n", 985" created august 1984\n", 986"tests: 1.o.r., pow[2,3]" 987], 988[6144,2048,256,1536,256,256,32,12,32,192,32,128,32,64,32,32,12,32,32,16,16,12, 98912,16,16,16,16], 990[,[1,1,1,1,1,1,1,8,5,4,6,2,2,4,5,6,8,12,12,14,14,17,17,18,19,19,18],[1,2,3,4, 9915,6,7,1,9,10,11,12,13,14,15,16,4,19,18,20,21,10,10,26,27,24,25]], 992[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,-1,1,1, 9931,-1,1,-1,1,1,-1,1,1,1,-1,-1,1,1,-1,-1,-1,-1],[2,2,2,2,2,2,0,-1,2,2,0,2,0,2,2, 9940,-1,2,2,0,0,-1,-1,0,0,0,0],[2,2,-2,2,-2,2,0,-1,0,-2,0,-2,0,2,0,0,-1,0,0,0,0, 9951,1,E(8)+E(8)^3,-E(8)-E(8)^3,E(8)+E(8)^3,-E(8)-E(8)^3], 996[TENSOR,[4,2]],[3,3,3,3,3,3,-1,0,-1,3,-1,3,-1,3,-1,-1,0,-1,-1,-1,-1,0,0,1,1,1, 9971], 998[TENSOR,[6,2]],[3,3,-1,3,-1,3,1,0,1,3,1,-1,1,-1,1,1,0,-1+2*E(4),-1-2*E(4),-1, 999-1,0,0,-E(4),E(4),E(4),-E(4)], 1000[TENSOR,[8,2]], 1001[GALOIS,[8,3]], 1002[TENSOR,[10,2]],[4,4,-4,4,-4,4,0,1,0,-4,0,-4,0,4,0,0,1,0,0,0,0,-1,-1,0,0,0, 10030],[6,6,-2,6,-2,6,0,0,-2,6,0,-2,0,-2,-2,0,0,2,2,0,0,0,0,0,0,0,0],[6,6,2,6,2,6, 10040,0,0,-6,0,2,0,-2,0,0,0,0,0,0,0,0,0,E(8)-E(8)^3,E(8)-E(8)^3,-E(8)+E(8)^3, 1005-E(8)+E(8)^3], 1006[TENSOR,[14,2]],[12,12,-4,12,-4,-4,0,0,0,0,0,4,0,0,0,0,0,0,0,2,-2,0,0,0,0,0, 10070],[12,12,4,12,4,-4,-2,0,0,0,2,-4,-2,0,0,2,0,0,0,0,0,0,0,0,0,0,0], 1008[TENSOR,[16,2]], 1009[TENSOR,[17,2]],[16,16,0,-16,0,0,0,-2,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0],[ 101016,16,0,-16,0,0,0,1,0,0,0,0,0,0,0,0,-1,0,0,0,0,-E(12)^7+E(12)^11, 1011E(12)^7-E(12)^11,0,0,0,0], 1012[GALOIS,[21,5]],[24,-8,-4,0,4,0,2,0,-2,0,-2,0,-2,0,2,2,0,0,0,0,0,0,0,0,0,0, 10130],[24,-8,-4,0,4,0,2,0,2,0,2,0,-2,0,-2,-2,0,0,0,0,0,0,0,0,0,0,0], 1014[TENSOR,[23,2]], 1015[TENSOR,[24,2]],[48,-16,8,0,-8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]], 1016[(24,27)(25,26),(22,23),(20,21),(18,19)(24,25)(26,27),(18,19)(24,26)(25,27), 1017(18,19)(22,23)(24,25)(26,27),(18,19)(22,23)(24,26)(25,27),( 9,15)(11,16)]); 1018ARC("2^2.2^8:s3","tomfusion",rec(name:="2^2.[2^8]:S3",map:=[1,2,5,3,4,6,7, 10198,29,14,43,18,44,27,35,42,47,131,131,111,128,152,152,321,321,321,321],text:=[ 1020"fusion map is unique up to table autom." 1021])); 1022ALF("2^2.2^8:s3","2F4(2)'",[1,2,2,3,3,3,3,4,5,5,5,6,6,7,7,7,9,10,11,12,13, 102315,16,19,20,22,21],[ 1024"fusion is unique up to table automorphisms,\n", 1025"the representative is equal to the fusion map on the CAS table" 1026]); 1027ALF("2^2.2^8:s3","2^2.[2^9]:S3",[1,2,7,3,8,4,28,23,18,5,35,9,33,12,19,34, 102824,20,21,37,37,25,25,42,41,41,42]); 1029 1030MOT("2.[2^9]:5:4", 1031[ 1032"origin: Dixon's Algorithm" 1033], 1034[20480,20480,2048,1024,1280,1280,256,256,256,256,128,128,128,128,20,20,20,20, 1035256,256,256,256,128,128,64,64,64,64,32,16,16,64,64,64,64,64,64,64,64,32,32,32, 103632,16,16,16,16], 1037[,[1,1,1,1,2,2,1,2,3,3,4,4,3,3,15,15,16,16,1,1,3,3,2,3,4,4,8,8,8,11,12,19,19, 103819,19,20,20,20,20,24,24,24,24,27,28,27,28],,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14 1039,1,2,6,5,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41, 104042,43,44,45,46,47]], 1041[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, 10421,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, 10431,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[1,1,1,1,1,1,1,1,1,1,1,1, 10441,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-E(4),E(4),-E(4),E(4),E(4), 1045-E(4),E(4),-E(4),-E(4),E(4),E(4),-E(4),-E(4),E(4),E(4),-E(4)], 1046[TENSOR,[2,3]],[4,4,4,4,4,4,4,4,4,4,4,4,4,4,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0 1047,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[5,5,5,5,5,5,-3,-3,1,1,1,1,-3,1,0,0,0,0, 10481,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1], 1049[TENSOR,[6,2]], 1050[TENSOR,[6,4]], 1051[TENSOR,[6,3]],[10,10,10,10,10,10,2,2,-2,-2,-2,-2,2,-2,0,0,0,0,-2,-2,-2,-2,-2 1052,-2,-2,-2,2,2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], 1053[TENSOR,[10,3]],[1,1,1,1,-1,-1,1,1,-1,-1,1,1,-1,-1,1,1,-1,-1,1,1,-1,-1,-1,1, 1054-1,1,1,1,-1,-1,1,-1,-1,-1,-1,1,1,1,1,-1,-1,1,1,-1,-1,1,1], 1055[TENSOR,[2,12]], 1056[TENSOR,[3,13]], 1057[TENSOR,[2,14]], 1058[TENSOR,[5,12]], 1059[TENSOR,[6,13]], 1060[TENSOR,[6,12]], 1061[TENSOR,[6,15]], 1062[TENSOR,[6,14]], 1063[TENSOR,[10,12]], 1064[TENSOR,[10,14]],[10,10,-6,2,0,0,2,-2,-4*E(4),4*E(4),2,-2,0,0,0,0,0,0,0,0,2,2 1065,2,0,-2,0,-2*E(4),2*E(4),0,0,0,-1+E(4),-1-E(4),-1+E(4),-1-E(4),-1+E(4),-1-E(4) 1066,-1+E(4),-1-E(4),1-E(4),1+E(4),1-E(4),1+E(4),0,0,0,0], 1067[TENSOR,[23,15]], 1068[TENSOR,[23,2]], 1069[TENSOR,[23,14]], 1070[TENSOR,[23,13]], 1071[TENSOR,[23,4]], 1072[TENSOR,[23,12]], 1073[TENSOR,[23,3]],[20,20,-12,4,0,0,4,-4,0,0,-4,4,0,0,0,0,0,0,-4,-4,0,0,0,-4,0,4 1074,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], 1075[TENSOR,[31,3]],[40,40,8,-8,0,0,0,0,4,4,0,0,0,-4,0,0,0,0,-4,-4,-4,-4,4,4,0,0, 10760,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], 1077[TENSOR,[33,14]], 1078[TENSOR,[33,12]], 1079[TENSOR,[33,3]],[40,40,-24,8,0,0,-8,8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 1080,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[16,-16,0,0,-4*E(4),4*E(4),0,0,0,0,0,0 1081,0,0,1,-1,-E(4),E(4),-4,4,-4*E(4),4*E(4),0,0,0,0,0,0,0,0,0,-2*E(4),2*E(4), 10822*E(4),-2*E(4),-2,-2,2,2,0,0,0,0,0,0,0,0], 1083[TENSOR,[38,12]], 1084[TENSOR,[38,2]], 1085[TENSOR,[38,13]], 1086[TENSOR,[38,14]], 1087[TENSOR,[38,3]], 1088[TENSOR,[38,15]], 1089[TENSOR,[38,4]],[64,-64,0,0,-16*E(4),16*E(4),0,0,0,0,0,0,0,0,-1,1,E(4),-E(4), 10900,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], 1091[TENSOR,[46,12]]], 1092[(32,34)(33,35)(36,38)(37,39), 1093(19,20)(21,22)(32,36)(33,37)(34,38)(35,39)(40,42)(41,43)(44,46)(45,47), 1094( 9,10)(27,28)(32,33)(34,35)(36,39)(37,38)(40,41)(42,43)(44,45)(46,47), 1095( 5, 6)(17,18)(21,22)(36,38)(37,39)]); 1096ALF("2.[2^9]:5:4","2F4(2)'.2",[1,2,2,3,18,19,3,6,18,19,5,7,21,21,8,13,29, 109728,2,3,18,19,21,6,20,7,10,11,22,23,12,18,19,21,21,7,7,5,5,22,22,11,10,26, 109827,16,17]); 1099 1100MOT("2^2.[2^9]:S3", 1101[ 1102"origin: Dixon's Algorithm" 1103], 1104[12288,4096,3072,512,384,192,512,512,256,256,256,128,128,128,128,128,128,64,64 1105,64,64,32,24,24,12,12,12,64,128,128,128,128,64,64,64,32,16,16,16,16,16,16], 1106[,[1,1,1,1,3,3,1,1,2,2,2,3,2,7,7,7,7,8,8,9,9,9,23,23,24,24,24,1,7,7,7,7,2,4,4, 11077,12,5,20,21,21,20],[1,2,3,4,5,6,7,8,9,11,10,12,13,15,14,17,16,18,19,21,20,22, 11081,3,5,6,6,28,30,29,32,31,33,34,35,36,37,38,40,39,42,41]], 1109[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, 11101,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1 1111,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2, 1112-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[3,3,3,3,3,3,3,3,3,3,3,3,3,-1,-1 1113,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1], 1114[TENSOR,[4,2]],[3,3,3,3,3,3,-1,-1,-1,-1,-1,-1,-1,-1-2*E(4),-1+2*E(4), 1115-1-2*E(4),-1+2*E(4),1,1,-1+2*E(4),-1-2*E(4),1,0,0,0,0,0,-1,1,1,1,1,-1,-1,-1,1, 11161,-1,E(4),-E(4),-E(4),E(4)], 1117[GALOIS,[6,3]], 1118[TENSOR,[6,2]], 1119[TENSOR,[7,2]],[6,6,6,6,6,6,-2,-2,-2,-2,-2,-2,-2,2,2,2,2,-2,-2,2,2,-2,0,0,0,0 1120,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[1,1,1,1,1,-1,1,1,1,-1,-1,1,-1,-1,-1,-1,-1,1 1121,1,1,1,-1,1,1,1,-1,-1,-1,1,1,1,1,-1,-1,-1,1,-1,1,1,1,-1,-1], 1122[TENSOR,[2,11]], 1123[TENSOR,[3,11]], 1124[TENSOR,[4,12]], 1125[TENSOR,[4,11]], 1126[TENSOR,[7,12]], 1127[TENSOR,[6,12]], 1128[TENSOR,[7,11]], 1129[TENSOR,[6,11]], 1130[TENSOR,[10,11]],[4,4,4,4,-4,0,-4,-4,-4,0,0,4,0,0,0,0,0,0,0,0,0,0,-2,-2,2,0,0 1131,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[4,4,4,4,-4,0,-4,-4,-4,0,0,4,0,0,0,0,0,0,0,0,0 1132,0,1,1,-1,-E(3)+E(3)^2,E(3)-E(3)^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], 1133[TENSOR,[22,11]],[12,12,12,12,-12,0,4,4,4,0,0,-4,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 11340,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[12,12,12,-4,0,0,4,4,-4,4,4,0,-4,0,0,0,0,0,0, 11350,0,0,0,0,0,0,0,-2,2,2,2,2,-2,2,2,-2,0,0,0,0,0,0], 1136[TENSOR,[25,2]], 1137[TENSOR,[25,12]], 1138[TENSOR,[25,11]],[24,24,24,-8,0,0,-8,-8,8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 1139,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[16,16,-16,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 1140,0,-2,2,0,0,0,0,-4,-4,4,4,0,0,0,0,0,0,0,0,0,0], 1141[TENSOR,[30,2]],[32,32,-32,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,-2,0,0,0,0 1142,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[24,-8,0,0,0,0,-4,4,0,4*E(4),-4*E(4),0,0,-2*E(4) 1143,2*E(4),2*E(4),-2*E(4),-2,2,0,0,0,0,0,0,0,0,-2,4*E(4),-4*E(4),0,0,2,-2,2,0,0,0 1144,0,0,0,0], 1145[TENSOR,[33,12]], 1146[TENSOR,[33,2]], 1147[TENSOR,[33,11]],[24,-8,0,0,0,0,-4,4,0,-4*E(4),4*E(4),0,0,-2*E(4),2*E(4), 11482*E(4),-2*E(4),2,-2,0,0,0,0,0,0,0,0,-2,0,0,-4*E(4),4*E(4),2,2,-2,0,0,0,0,0,0,0 1149], 1150[TENSOR,[37,12]], 1151[TENSOR,[37,2]], 1152[TENSOR,[37,11]],[48,-16,0,0,0,0,8,-8,0,0,0,0,0,-4,-4,4,4,0,0,0,0,0,0,0,0,0,0 1153,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], 1154[TENSOR,[41,11]]], 1155[(26,27),(14,17)(15,16)(20,21)(39,40)(41,42), 1156(10,11)(14,16)(15,17)(29,30)(31,32),(14,16)(15,17)(18,19)(29,31)(30,32)(34,35) 1157]); 1158ALF("2^2.[2^9]:S3","2F4(2)'.2",[1,2,3,3,5,20,2,3,6,18,19,7,21,18,19,21,21, 11595,7,10,11,22,4,9,14,24,25,3,21,21,19,18,6,7,5,21,12,23,26,27,17,16],[ 1160"fusion map is unique up to table automorphisms" 1161]); 1162 1163MOT("2^6:u3(3)", 1164[ 1165"origin: CAS library,\n", 1166"subgroup of index 2 in maximal subgroup of ru\n", 1167" structure:= 2^6:u[3,3]\n", 1168" 1st & 2nd orthogonality relations are satisfied\n", 1169" symmetric squares decompose properly\n", 1170" created september 1984\n", 1171"tests: 1.o.r., pow[2,3,7]" 1172], 1173[387072,6144,1536,512,128,108,36,12,384,128,384,128,64,64,32,12,7,7,16,16,16, 117416,12,12], 1175[,[1,1,1,1,2,6,7,7,3,4,3,4,3,4,4,6,17,18,9,10,11,12,16,16],[1,2,3,4,5,1,1,2, 117611,12,9,10,13,14,15,3,18,17,21,22,19,20,11,9],,,,[1,2,3,4,5,6,7,8,11,12,9,10, 117713,14,15,16,1,1,21,22,19,20,24,23]], 1178[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[6,6,-2,-2,-2,-3,0,0,-2,-2, 1179-2,-2,2,2,2,1,-1,-1,0,0,0,0,1,1],[7,7,-1,-1,-1,-2,1,1,3,3,3,3,-1,-1,-1,2,0,0, 1180-1,-1,-1,-1,0,0],[7,7,3,3,3,-2,1,1,-1-2*E(4),-1-2*E(4),-1+2*E(4),-1+2*E(4),1, 11811,1,0,0,0,E(4),E(4),-E(4),-E(4),-1+E(4),-1-E(4)], 1182[GALOIS,[4,3]],[14,14,-2,-2,-2,5,-1,-1,2,2,2,2,2,2,2,1,0,0,0,0,0,0,-1,-1],[21, 118321,5,5,5,3,0,0,1,1,1,1,1,1,1,-1,0,0,-1,-1,-1,-1,1,1],[21,21,1,1,1,3,0,0, 1184-3+2*E(4),-3+2*E(4),-3-2*E(4),-3-2*E(4),-1,-1,-1,1,0,0,E(4),E(4),-E(4),-E(4), 1185-E(4),E(4)], 1186[GALOIS,[8,3]],[27,27,3,3,3,0,0,0,3,3,3,3,-1,-1,-1,0,-1,-1,1,1,1,1,0,0],[28, 118728,-4,-4,-4,1,1,1,4*E(4),4*E(4),-4*E(4),-4*E(4),0,0,0,-1,0,0,0,0,0,0,E(4), 1188-E(4)], 1189[GALOIS,[11,3]],[32,32,0,0,0,-4,-1,-1,0,0,0,0,0,0,0,0,-E(7)-E(7)^2-E(7)^4, 1190-E(7)^3-E(7)^5-E(7)^6,0,0,0,0,0,0], 1191[GALOIS,[13,3]],[63,-1,15,-1,-1,0,3,-1,3,-1,3,-1,3,-1,-1,0,0,0,1,-1,1,-1,0, 11920],[63,-1,-9,7,-1,0,3,-1,3,-1,3,-1,-1,3,-1,0,0,0,-1,1,-1,1,0,0],[126,-2,6,6, 1193-2,0,-3,1,6,-2,6,-2,2,2,-2,0,0,0,0,0,0,0,0,0],[189,-3,-3,13,-3,0,0,0,-3,1,-3, 11941,-3,1,1,0,0,0,1,-1,1,-1,0,0],[189,-3,21,5,-3,0,0,0,-3,1,-3,1,1,-3,1,0,0,0,-1, 11951,-1,1,0,0],[189,-3,9,-7,1,0,0,0,-3-6*E(4),1+2*E(4),-3+6*E(4),1-2*E(4),-1,3, 1196-1,0,0,0,E(4),-E(4),-E(4),E(4),0,0], 1197[GALOIS,[20,3]],[189,-3,-15,1,1,0,0,0,-3+6*E(4),1-2*E(4),-3-6*E(4),1+2*E(4),3, 1198-1,-1,0,0,0,E(4),-E(4),-E(4),E(4),0,0], 1199[GALOIS,[22,3]],[378,-6,-6,-6,2,0,0,0,6,-2,6,-2,-2,-2,2,0,0,0,0,0,0,0,0,0]], 1200[(17,18),( 9,11)(10,12)(19,21)(20,22)(23,24)]); 1201ALF("2^6:u3(3)","Ru",[1,2,2,2,7,4,4,11,5,8,5,8,8,8,7,11,12,12,13,15,13,15, 120218,18],[ 1203"fusion map is unique, equal to that on the CAS table" 1204]); 1205ALF("2^6:u3(3)","U3(3)",[1,1,2,2,2,3,4,4,5,5,6,6,7,7,7,8,9,10,11,11,12,12, 120613,14]); 1207 1208MOT("2^{1+6}:3^{1+2}:2A4", 1209[ 1210"1st maximal subgroup of U5(2), origin: CAYLEY" 1211], 1212[82944,82944,1536,1152,1296,1296,1296,1296,216,216,36,2304,2304,384,96,144, 1213144,144,144,96,96,16,24,24,24,24,1728,1728,432,432,108,108,1728,1728,432,432, 1214144,144,144,144,144,144,144,144,108,108,96,96,36,36,36,36,18,18,144,144,72,72, 121524,24,24,24,18,18], 1216[,[1,1,1,2,6,5,6,5,9,9,10,1,1,2,3,5,6,5,6,12,12,14,16,17,17,16,28,27,30,29,32, 121731,27,28,30,29,29,30,27,28,28,27,29,30,32,31,28,27,31,32,32,31,54,53,34,33,36, 121835,35,36,47,48,53,54],[1,2,3,4,1,1,2,2,1,2,4,12,13,14,15,12,12,13,13,20,21,22, 121921,21,20,20,1,1,1,1,1,1,2,2,2,2,12,12,12,12,13,13,13,13,2,2,3,3,13,13,12,12,6, 12205,4,4,4,4,14,14,15,15,7,8]], 1221[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, 12221,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1, 12231,1,1,1,1,1,1,1,1,1,1,1,1,1,E(3),E(3)^2,E(3)^2,E(3),E(3),E(3)^2,E(3)^2,E(3), 1224E(3)^2,E(3),E(3),E(3)^2,E(3)^2,E(3),E(3),E(3)^2,E(3),E(3)^2,E(3),E(3)^2,E(3), 1225E(3)^2,E(3)^2,E(3),E(3),E(3)^2,E(3),E(3)^2,E(3)^2,E(3),E(3)^2,E(3),E(3), 1226E(3)^2,E(3)^2,E(3),E(3)^2,E(3)], 1227[TENSOR,[2,2]],[3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,-1,-1,-1,-1,-1,-1,-1,0, 12280,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[2, 12292,2,2,2,2,2,2,2,2,2,-2,-2,-2,-2,-2,-2,-2,-2,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1, 1230-1,-1,-1,-1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,-1,-1,1,1,1,1,-1, 1231-1], 1232[TENSOR,[5,2]], 1233[TENSOR,[5,3]],[8,8,8,8,8,8,8,8,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,2,2, 12342,2,2,2,2,2,2,0,0,0,0,0,0,0,0,2,2,2,2,0,0,0,0,-1,-1,2,2,2,2,0,0,0,0,-1,-1], 1235[TENSOR,[8,2]], 1236[TENSOR,[8,3]],[3,3,3,3,3*E(3),3*E(3)^2,3*E(3),3*E(3)^2,0,0,0,-1,-1,-1,-1, 1237-E(3)^2,-E(3),-E(3)^2,-E(3),1,1,1,E(3),E(3)^2,E(3)^2,E(3),E(3)+2*E(3)^2, 12382*E(3)+E(3)^2,-E(3)-2*E(3)^2,-2*E(3)-E(3)^2,E(3)-E(3)^2,-E(3)+E(3)^2, 12392*E(3)+E(3)^2,E(3)+2*E(3)^2,-E(3)-2*E(3)^2,-2*E(3)-E(3)^2,-E(3)^2,-E(3), 1240-E(3)^2,-E(3),-E(3),-E(3)^2,-E(3)^2,-E(3),E(3)-E(3)^2,-E(3)+E(3)^2, 1241E(3)+2*E(3)^2,2*E(3)+E(3)^2,-1,-1,-1,-1,0,0,2*E(3)+E(3)^2,E(3)+2*E(3)^2, 1242-E(3)-2*E(3)^2,-2*E(3)-E(3)^2,-E(3)^2,-E(3),-E(3)^2,-E(3),0,0], 1243[TENSOR,[11,3]], 1244[TENSOR,[11,2]], 1245[GALOIS,[12,2]], 1246[TENSOR,[14,3]], 1247[TENSOR,[14,2]],[6,6,6,6,6*E(3),6*E(3)^2,6*E(3),6*E(3)^2,0,0,0,2,2,2,2, 12482*E(3)^2,2*E(3),2*E(3)^2,2*E(3),0,0,0,0,0,0,0,-E(3)-2*E(3)^2,-2*E(3)-E(3)^2, 1249E(3)+2*E(3)^2,2*E(3)+E(3)^2,-E(3)+E(3)^2,E(3)-E(3)^2,-2*E(3)-E(3)^2, 1250-E(3)-2*E(3)^2,E(3)+2*E(3)^2,2*E(3)+E(3)^2,-E(3)^2,-E(3),-E(3)^2,-E(3),-E(3), 1251-E(3)^2,-E(3)^2,-E(3),-E(3)+E(3)^2,E(3)-E(3)^2,-E(3)-2*E(3)^2,-2*E(3)-E(3)^2, 1252-1,-1,-1,-1,0,0,-2*E(3)-E(3)^2,-E(3)-2*E(3)^2,E(3)+2*E(3)^2,2*E(3)+E(3)^2, 1253-E(3)^2,-E(3),-E(3)^2,-E(3),0,0], 1254[TENSOR,[17,3]], 1255[TENSOR,[17,2]], 1256[GALOIS,[18,2]], 1257[TENSOR,[20,2]], 1258[TENSOR,[20,3]],[9,9,9,9,9*E(3),9*E(3)^2,9*E(3),9*E(3)^2,0,0,0,-3,-3,-3,-3, 1259-3*E(3)^2,-3*E(3),-3*E(3)^2,-3*E(3),-1,-1,-1,-E(3),-E(3)^2,-E(3)^2,-E(3),0,0, 12600,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], 1261[GALOIS,[23,2]],[27,27,-5,3,0,0,0,0,0,0,0,3,3,3,-1,0,0,0,0,3,3,-1,0,0,0,0,9,9, 12620,0,0,0,9,9,0,0,0,0,3,3,3,3,0,0,0,0,1,1,0,0,0,0,0,0,-3,-3,0,0,0,0,-1,-1,0,0], 1263[TENSOR,[25,2]], 1264[TENSOR,[25,3]],[36,36,4,-4,0,0,0,0,3,3,-1,12,12,-4,0,0,0,0,0,0,0,0,0,0,0,0,6, 12656,3,3,0,0,6,6,3,3,3,3,0,0,0,0,3,3,0,0,-2,-2,0,0,0,0,0,0,2,2,-1,-1,-1,-1,0,0,0, 12660],[36,36,4,-4,0,0,0,0,3,3,-1,-12,-12,4,0,0,0,0,0,0,0,0,0,0,0,0,6,6,3,3,0,0,6, 12676,3,3,-3,-3,0,0,0,0,-3,-3,0,0,-2,-2,0,0,0,0,0,0,2,2,-1,-1,1,1,0,0,0,0], 1268[TENSOR,[28,2]], 1269[TENSOR,[29,2]], 1270[TENSOR,[28,3]], 1271[TENSOR,[29,3]],[54,54,-10,6,0,0,0,0,0,0,0,-6,-6,-6,2,0,0,0,0,0,0,0,0,0,0,0, 1272-9,-9,0,0,0,0,-9,-9,0,0,0,0,3,3,3,3,0,0,0,0,-1,-1,0,0,0,0,0,0,3,3,0,0,0,0,-1, 1273-1,0,0], 1274[TENSOR,[34,2]], 1275[TENSOR,[34,3]],[72,72,8,-8,0,0,0,0,-3,-3,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-6, 1276-6,6,6,0,0,-6,-6,6,6,0,0,0,0,0,0,0,0,0,0,2,2,0,0,0,0,0,0,-2,-2,-2,-2,0,0,0,0, 12770,0], 1278[TENSOR,[37,2]], 1279[TENSOR,[37,3]],[81,81,-15,9,0,0,0,0,0,0,0,9,9,9,-3,0,0,0,0,-3,-3,1,0,0,0,0,0, 12800,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[8, 1281-8,0,0,-1,-1,1,1,2,-2,0,-4,4,0,0,-1,-1,1,1,2,-2,0,1,1,-1,-1,-4,-4,2,2,-1,-1,4, 12824,-2,-2,2,2,2,2,-2,-2,-2,-2,1,1,0,0,1,1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,1,1], 1283[TENSOR,[41,2]], 1284[TENSOR,[41,3]],[16,-16,0,0,-2,-2,2,2,4,-4,0,8,-8,0,0,2,2,-2,-2,0,0,0,0,0,0,0, 12854,4,-2,-2,1,1,-4,-4,2,2,2,2,2,2,-2,-2,-2,-2,-1,-1,0,0,1,1,-1,-1,1,1,0,0,0,0,0, 12860,0,0,-1,-1], 1287[TENSOR,[44,2]], 1288[TENSOR,[44,3]],[24,-24,0,0,-3,-3,3,3,6,-6,0,-12,12,0,0,-3,-3,3,3,-2,2,0,-1, 1289-1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 12900,0,0],[24,-24,0,0,-3*E(3),-3*E(3)^2,3*E(3),3*E(3)^2,0,0,0,4,-4,0,0,E(3)^2, 1291E(3),-E(3)^2,-E(3),2,-2,0,E(3),E(3)^2,-E(3)^2,-E(3),-4*E(3)+4*E(3)^2, 12924*E(3)-4*E(3)^2,4*E(3)+2*E(3)^2,2*E(3)+4*E(3)^2,2*E(3)+E(3)^2,E(3)+2*E(3)^2, 1293-4*E(3)+4*E(3)^2,4*E(3)-4*E(3)^2,-4*E(3)-2*E(3)^2,-2*E(3)-4*E(3)^2,-2*E(3), 1294-2*E(3)^2,-2,-2,2,2,2*E(3),2*E(3)^2,-2*E(3)-E(3)^2,-E(3)-2*E(3)^2,0,0,-E(3), 1295-E(3)^2,E(3)^2,E(3),0,0,0,0,0,0,0,0,0,0,0,0], 1296[TENSOR,[48,3]], 1297[TENSOR,[48,2]], 1298[GALOIS,[50,2]], 1299[TENSOR,[51,2]], 1300[TENSOR,[51,3]],[48,-48,0,0,-6*E(3),-6*E(3)^2,6*E(3),6*E(3)^2,0,0,0,-8,8,0,0, 1301-2*E(3)^2,-2*E(3),2*E(3)^2,2*E(3),0,0,0,0,0,0,0,4*E(3)+8*E(3)^2, 13028*E(3)+4*E(3)^2,2*E(3)+4*E(3)^2,4*E(3)+2*E(3)^2,E(3)-E(3)^2,-E(3)+E(3)^2, 1303-8*E(3)-4*E(3)^2,-4*E(3)-8*E(3)^2,-2*E(3)-4*E(3)^2,-4*E(3)-2*E(3)^2,-2*E(3)^2, 1304-2*E(3),-2*E(3)^2,-2*E(3),2*E(3),2*E(3)^2,2*E(3)^2,2*E(3),-E(3)+E(3)^2, 1305E(3)-E(3)^2,0,0,-1,-1,1,1,0,0,0,0,0,0,0,0,0,0,0,0], 1306[TENSOR,[54,2]], 1307[TENSOR,[54,3]], 1308[GALOIS,[55,2]], 1309[TENSOR,[57,2]], 1310[TENSOR,[57,3]],[64,-64,0,0,-8,-8,8,8,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-8, 1311-8,4,4,-2,-2,8,8,-4,-4,0,0,0,0,0,0,0,0,2,2,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,-1, 1312-1], 1313[TENSOR,[60,2]], 1314[TENSOR,[60,3]],[72,-72,0,0,-9*E(3),-9*E(3)^2,9*E(3),9*E(3)^2,0,0,0,12,-12,0, 13150,3*E(3)^2,3*E(3),-3*E(3)^2,-3*E(3),-2,2,0,-E(3),-E(3)^2,E(3)^2,E(3),0,0,0,0, 13160,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], 1317[GALOIS,[63,2]]], 1318[( 5, 6)( 7, 8)(16,17)(18,19)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36) 1319(37,38)(39,40)(41,42)(43,44)(45,46)(47,48)(49,50)(51,52)(53,54)(55,56)(57,58) 1320(59,60)(61,62)(63,64)]); 1321ARC("2^{1+6}:3^{1+2}:2A4","tomfusion",rec(name:="2^(1+6)-:3^(1+2)+:2A4",map:=[ 13221,2,5,14,7,7,24,24,9,28,80,4,3,17,21,30,30,34,34,20,22,61,91,91,92,92,6,6,8,8, 132310,10,23,23,27,27,31,31,33,33,29,29,32,32,35,35,36,36,37,37,38,38,69,69,74,74, 132478,78,89,89,90,90,141,141],text:=[ 1325"fusion map is unique" 1326])); 1327ALF("2^{1+6}:3^{1+2}:2A4","U5(2)",[1,2,3,10,6,7,16,17,8,22,39,2,3,11,12, 132819,18,24,23,10,11,28,42,43,38,37,5,4,6,7,9,9,14,15,18,19,17,16,14,15,21, 132920,24,23,26,25,21,20,27,27,25,26,30,29,35,36,37,38,43,42,40,41,46,47],[ 1330"fusion is unique up to table automorphisms" 1331]); 1332ALN("2^{1+6}:3^{1+2}:2A4",["U5(2)C2A","U5(2)N2A"]); 1333 1334MOT("2^(4+4):(3xA5)", 1335[ 1336"origin: Dixon's Algorithm,\n", 1337"3rd maximal subgroup of U5(2)" 1338], 1339[46080,9216,4608,384,384,2880,576,288,2880,576,288,192,192,96,16,48,48,24,48, 134048,24,144,144,144,144,144,144,144,144,36,36,36,36,24,24,24,24,15,15,15,15,15, 134115], 1342[,[1,1,1,2,2,9,9,9,6,6,6,1,2,3,5,9,10,11,6,7,8,26,26,26,26,22,22,22,22,30,30, 134330,30,29,29,25,25,41,43,42,38,40,39],[1,2,3,4,5,1,2,3,1,2,3,12,13,14,15,12,13, 134414,12,13,14,1,3,2,2,1,3,2,2,1,3,2,2,4,5,4,5,41,41,41,38,38,38],,[1,2,3,4,5,9, 134510,11,6,7,8,12,13,14,15,19,20,21,16,17,18,26,27,28,29,22,23,24,25,30,31,33,32, 134636,37,34,35,1,9,6,1,9,6]], 1347[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, 13481,1,1,1,1],[3,3,3,3,3,3,3,3,3,3,3,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,0, 13490,0,0,0,0,0,0,0,0,-E(5)-E(5)^4,-E(5)-E(5)^4,-E(5)-E(5)^4,-E(5)^2-E(5)^3, 1350-E(5)^2-E(5)^3,-E(5)^2-E(5)^3], 1351[GALOIS,[2,2]],[4,4,4,4,4,4,4,4,4,4,4,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1 1352,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1],[5,5,5,5,5,5,5,5,5,5,5,1,1,1,1,1,1,1,1,1,1,-1, 1353-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0],[1,1,1,1,1,E(3),E(3) 1354,E(3),E(3)^2,E(3)^2,E(3)^2,1,1,1,1,E(3),E(3),E(3),E(3)^2,E(3)^2,E(3)^2,E(3), 1355E(3),E(3),E(3),E(3)^2,E(3)^2,E(3)^2,E(3)^2,1,1,1,1,E(3),E(3),E(3)^2,E(3)^2,1, 1356E(3),E(3)^2,1,E(3),E(3)^2], 1357[TENSOR,[6,6]], 1358[TENSOR,[3,6]], 1359[TENSOR,[3,7]], 1360[TENSOR,[2,6]], 1361[TENSOR,[2,7]], 1362[TENSOR,[4,6]], 1363[TENSOR,[4,7]], 1364[TENSOR,[5,6]], 1365[TENSOR,[5,7]],[15,15,15,-1,-1,0,0,0,0,0,0,3,3,3,-1,0,0,0,0,0,0,3,3,3,3,3,3,3 1366,3,0,0,0,0,-1,-1,-1,-1,0,0,0,0,0,0], 1367[TENSOR,[16,6]], 1368[TENSOR,[16,7]],[45,45,45,-3,-3,0,0,0,0,0,0,-3,-3,-3,1,0,0,0,0,0,0,0,0,0,0,0, 13690,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[10,-6,2,2,-2,-5,3,-1,-5,3,-1,2,2,-2,0,-1, 1370-1,1,-1,-1,1,1,-1,3,-3,1,-1,3,-3,-2,2,0,0,-1,1,-1,1,0,0,0,0,0,0], 1371[TENSOR,[20,6]], 1372[TENSOR,[20,7]],[10,-6,2,2,-2,-5*E(3),3*E(3),-E(3),-5*E(3)^2,3*E(3)^2,-E(3)^2 1373,2,2,-2,0,-E(3),-E(3),E(3),-E(3)^2,-E(3)^2,E(3)^2,-2*E(3)-3*E(3)^2, 13742*E(3)+3*E(3)^2,-2*E(3)-E(3)^2,2*E(3)+E(3)^2,-3*E(3)-2*E(3)^2,3*E(3)+2*E(3)^2, 1375-E(3)-2*E(3)^2,E(3)+2*E(3)^2,1,-1,E(3)-E(3)^2,-E(3)+E(3)^2,-E(3)^2,E(3)^2, 1376-E(3),E(3),0,0,0,0,0,0], 1377[GALOIS,[23,2]], 1378[TENSOR,[23,7]], 1379[TENSOR,[24,6]], 1380[TENSOR,[23,6]], 1381[TENSOR,[24,7]],[30,-18,6,6,-6,-15,9,-3,-15,9,-3,-2,-2,2,0,1,1,-1,1,1,-1,0,0, 13820,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], 1383[TENSOR,[29,6]], 1384[TENSOR,[29,7]],[40,8,-8,0,0,10,2,-2,10,2,-2,-4,4,0,0,2,-2,0,2,-2,0,-2,-2,2,2 1385,-2,-2,2,2,1,1,-1,-1,0,0,0,0,0,0,0,0,0,0],[40,8,-8,0,0,10,2,-2,10,2,-2,4,-4,0, 13860,-2,2,0,-2,2,0,-2,-2,2,2,-2,-2,2,2,1,1,-1,-1,0,0,0,0,0,0,0,0,0,0], 1387[TENSOR,[32,7]], 1388[TENSOR,[32,6]], 1389[TENSOR,[33,7]], 1390[TENSOR,[33,6]],[60,-36,12,-4,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3,-3,-3,3,3, 1391-3,-3,3,0,0,0,0,-1,1,-1,1,0,0,0,0,0,0], 1392[TENSOR,[38,7]], 1393[TENSOR,[38,6]],[80,16,-16,0,0,20,4,-4,20,4,-4,0,0,0,0,0,0,0,0,0,0,2,2,-2,-2, 13942,2,-2,-2,-1,-1,1,1,0,0,0,0,0,0,0,0,0,0], 1395[TENSOR,[41,6]], 1396[TENSOR,[41,7]]], 1397[(38,41)(39,42)(40,43), 1398( 6, 9)( 7,10)( 8,11)(16,19)(17,20)(18,21)(22,26)(23,27)(24,28)(25,29)(32,33) 1399(34,36)(35,37)(39,40)(42,43) 1400]); 1401ARC("2^(4+4):(3xA5)","tomfusion",rec(name:="2^(4+4):(3xA5)",map:=[1,2,3, 140211,12,5,20,21,5,20,21,4,13,16,56,26,67,76,26,67,76,6,23,24,22,6,23,24,22, 14037,25,28,28,74,77,74,77,19,79,79,19,79,79],text:=["fusion map is unique" 1404])); 1405ALF("2^(4+4):(3xA5)","U5(2)",[1,2,3,10,11,4,14,20,5,15,21,3,10,12,28,20, 140635,40,21,36,41,7,24,17,19,6,23,16,18,9,27,26,25,38,43,37,42,13,45,44,13, 140745,44],[ 1408"fusion map is unique up to table automorphisms" 1409]); 1410ALF("2^(4+4):(3xA5)","j3m4",[1,1,1,2,2,3,3,3,4,4,4,5,5,5,6,7,7,7,8,8,8,9, 14119,9,9,10,10,10,10,11,11,11,11,12,12,13,13,14,15,16,17,18,19]); 1412 1413MOT("3^4:S5", 1414[ 1415"origin: Dixon's Algorithm,\n", 1416"4th maximal subgroup of U5(2)" 1417], 1418[9720,1944,1944,972,972,486,324,72,72,72,36,36,36,54,27,54,54,27,27,5,324,324, 1419324,108,108,108,108,108,108,54,12,12,12,18,18,18], 1420[,[1,3,2,5,4,6,7,1,3,2,7,5,4,14,15,17,16,19,18,20,1,5,4,7,7,2,3,4,5,6,8,10,9, 142114,16,17],[1,1,1,1,1,1,1,8,8,8,8,8,8,1,1,5,4,5,4,20,21,21,21,21,21,21,21,21,21 1422,21,31,31,31,21,22,23],,[1,3,2,5,4,6,7,8,10,9,11,13,12,14,15,17,16,19,18,1,21, 142323,22,25,24,27,26,29,28,30,31,33,32,34,36,35]], 1424[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1, 14251,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1, 1426-1,-1,-1],[6,6,6,6,6,6,6,-2,-2,-2,-2,-2,-2,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0 1427,0,0,0,0,0],[4,4,4,4,4,4,4,0,0,0,0,0,0,1,1,1,1,1,1,-1,2,2,2,2,2,2,2,2,2,2,0,0, 14280,-1,-1,-1], 1429[TENSOR,[4,2]],[5,5,5,5,5,5,5,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,0,1,1,1,1,1,1,1,1 1430,1,1,-1,-1,-1,1,1,1], 1431[TENSOR,[6,2]],[5,E(3)+4*E(3)^2,4*E(3)+E(3)^2,-2*E(3)+E(3)^2,E(3)-2*E(3)^2,2, 1432-1,1,E(3),E(3)^2,1,E(3)^2,E(3),2,-1,2*E(3),2*E(3)^2,-E(3),-E(3)^2,0,-3, 1433-3*E(3)^2,-3*E(3),E(3)-E(3)^2,-E(3)+E(3)^2,-2*E(3)-E(3)^2,-E(3)-2*E(3)^2, 1434E(3)+2*E(3)^2,2*E(3)+E(3)^2,0,-1,-E(3),-E(3)^2,0,0,0], 1435[GALOIS,[8,2]], 1436[TENSOR,[8,2]], 1437[TENSOR,[9,2]],[10,2*E(3)+8*E(3)^2,8*E(3)+2*E(3)^2,-4*E(3)+2*E(3)^2, 14382*E(3)-4*E(3)^2,4,-2,2,2*E(3),2*E(3)^2,2,2*E(3)^2,2*E(3),-2,1,-2*E(3), 1439-2*E(3)^2,E(3),E(3)^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], 1440[GALOIS,[12,2]],[10,-4*E(3)+2*E(3)^2,2*E(3)-4*E(3)^2,5*E(3)+2*E(3)^2, 14412*E(3)+5*E(3)^2,1,1,-2,-2*E(3)^2,-2*E(3),1,E(3),E(3)^2,1,1,E(3),E(3)^2,E(3), 1442E(3)^2,0,-2,-E(3)-4*E(3)^2,-4*E(3)-E(3)^2,1,1,-2,-2,2*E(3)-E(3)^2, 1443-E(3)+2*E(3)^2,1,0,0,0,1,E(3)^2,E(3)], 1444[GALOIS,[14,2]], 1445[TENSOR,[14,2]], 1446[TENSOR,[15,2]],[10,-4*E(3)+2*E(3)^2,2*E(3)-4*E(3)^2,5*E(3)+2*E(3)^2, 14472*E(3)+5*E(3)^2,1,1,2,2*E(3)^2,2*E(3),-1,-E(3),-E(3)^2,1,1,E(3),E(3)^2,E(3), 1448E(3)^2,0,4,-E(3)+2*E(3)^2,2*E(3)-E(3)^2,3*E(3)+E(3)^2,E(3)+3*E(3)^2,-2*E(3)^2, 1449-2*E(3),E(3)^2,E(3),1,0,0,0,1,E(3)^2,E(3)], 1450[GALOIS,[18,2]], 1451[TENSOR,[18,2]], 1452[TENSOR,[19,2]],[15,3*E(3)+12*E(3)^2,12*E(3)+3*E(3)^2,-6*E(3)+3*E(3)^2, 14533*E(3)-6*E(3)^2,6,-3,-1,-E(3),-E(3)^2,-1,-E(3)^2,-E(3),0,0,0,0,0,0,0,-3, 1454-3*E(3)^2,-3*E(3),E(3)-E(3)^2,-E(3)+E(3)^2,-2*E(3)-E(3)^2,-E(3)-2*E(3)^2, 1455E(3)+2*E(3)^2,2*E(3)+E(3)^2,0,1,E(3),E(3)^2,0,0,0], 1456[GALOIS,[22,2]], 1457[TENSOR,[22,2]], 1458[TENSOR,[23,2]],[20,8,8,2,2,-1,-4,0,0,0,0,0,0,2,-1,2,2,-1,-1,0,-6,-6,-6,0,0,0 1459,0,0,0,3,0,0,0,0,0,0], 1460[TENSOR,[26,2]],[20,-8*E(3)+4*E(3)^2,4*E(3)-8*E(3)^2,10*E(3)+4*E(3)^2, 14614*E(3)+10*E(3)^2,2,2,0,0,0,0,0,0,-1,-1,-E(3),-E(3)^2,-E(3),-E(3)^2,0,2,2,2, 14622*E(3),2*E(3)^2,2*E(3),2*E(3)^2,2*E(3),2*E(3)^2,2,0,0,0,-1,-E(3)^2,-E(3)], 1463[GALOIS,[28,2]], 1464[TENSOR,[28,2]], 1465[TENSOR,[29,2]],[30,-6,-6,3,3,-6,3,2,2,2,-1,-1,-1,0,0,0,0,0,0,0,-6,3,3,-3,-3, 14660,0,3,3,0,0,0,0,0,0,0], 1467[TENSOR,[32,2]],[30,-6,-6,3,3,-6,3,-2,-2,-2,1,1,1,0,0,0,0,0,0,0,0, 1468-3*E(3)+3*E(3)^2,3*E(3)-3*E(3)^2,E(3)-E(3)^2,-E(3)+E(3)^2,-2*E(3)+2*E(3)^2, 14692*E(3)-2*E(3)^2,E(3)-E(3)^2,-E(3)+E(3)^2,0,0,0,0,0,0,0], 1470[TENSOR,[34,2]],[40,16,16,4,4,-2,-8,0,0,0,0,0,0,-2,1,-2,-2,1,1,0,0,0,0,0,0,0, 14710,0,0,0,0,0,0,0,0,0]], 1472[( 2, 3)( 4, 5)( 9,10)(12,13)(16,17)(18,19)(22,23)(24,25)(26,27)(28,29)(32,33) 1473(35,36)]); 1474ARC("3^4:S5","tomfusion",rec(name:="3^4:S5",map:=[1,4,4,5,5,6,7,3,23,23, 147524,26,26,8,9,38,38,41,41,13,2,15,15,20,20,19,19,16,16,17,12,54,54,25,80, 147680],text:=[ 1477"fusion map is unique" 1478])); 1479ALF("3^4:S5","U5(2)",[1,4,5,6,7,8,9,3,20,21,27,23,24,8,9,30,29,32,31,13,2, 148016,17,26,25,15,14,19,18,22,12,40,41,22,46,47],[ 1481"fusion map is unique up to table automorphisms" 1482]); 1483ALF("3^4:S5","A5.2",[1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,4,5,5,5,5,5,5, 14845,5,5,5,6,6,6,7,7,7]); 1485 1486MOT("3.s7x2", 1487[ 1488"origin: CAS library,\n", 1489"tests: 1.o.r., pow[2,3,5,7]" 1490], 14910, 14920, 14930, 1494[(14,15)(36,37),(16,38)(17,39)(18,40)(19,41)(20,42)(21,43)(22,44)], 1495["ConstructDirectProduct",[["Cyclic",2],["3.A7.2"]],(),(5,11,10,9,8,7,6)(17, 149618)(21,22)(27,33,32,31,30,29,28)(39,40)(43,44)]); 1497ALF("3.s7x2","He.2",[1,4,2,10,4,5,6,17,9,21,10,10,13,23,24,2,3,6,10,11,16, 149817,27,29,27,30,30,31,28,36,35,43,29,30,37,44,45,27,27,28,30,31,35,36],[ 1499"fusion map is unique up to table autom.,\n", 1500"compatible with Brauer tables,\n", 1501"the representative is equal to the fusion map on the CAS table" 1502]); 1503ALF("3.s7x2","S7x2",[1,1,3,3,5,7,9,9,11,11,13,13,15,15,15,17,19,21,23,25, 150427,29,2,2,4,4,6,8,10,10,12,12,14,14,16,16,16,18,20,22,24,26,28,30]); 1505 1506MOT("4.s4", 1507[ 1508"origin: CAS library,\n", 1509" test:= 1. o.r., sym 2 decompose correctly \n", 1510"tests: 1.o.r., pow[2,3]" 1511], 1512[96,96,96,96,16,16,12,12,12,12,16,16,16,16,8,8], 1513[,[1,1,2,2,1,2,7,7,8,8,5,5,5,5,3,4],[1,2,4,3,5,6,1,2,4,3,12,11,14,13,16,15]], 1514[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1],[2, 15152,2,2,2,2,-1,-1,-1,-1,0,0,0,0,0,0],[3,3,3,3,-1,-1,0,0,0,0,1,1,1,1,-1,-1], 1516[TENSOR,[4,2]],[1,1,-1,-1,-1,1,1,1,-1,-1,-E(4),E(4),-E(4),E(4),-E(4),E(4)], 1517[TENSOR,[2,6]], 1518[TENSOR,[3,6]], 1519[TENSOR,[4,7]], 1520[TENSOR,[4,6]],[2,-2,2*E(4),-2*E(4),0,0,-1,1,-E(4),E(4),-1+E(4),-1-E(4), 15211-E(4),1+E(4),0,0], 1522[TENSOR,[11,2]], 1523[TENSOR,[11,6]], 1524[TENSOR,[11,7]],[4,-4,4*E(4),-4*E(4),0,0,1,-1,E(4),-E(4),0,0,0,0,0,0], 1525[TENSOR,[15,6]]], 1526[( 3, 4)( 9,10)(11,12)(13,14)(15,16),(11,13)(12,14)]); 1527ALF("4.s4","U3(3)",[1,2,5,6,2,7,3,8,13,14,5,6,7,7,11,12],[ 1528"fusion is unique up to table automorphisms,\n", 1529"the representative is equal to the fusion map on the CAS table" 1530]); 1531 1532MOT("4^2:s3", 1533[ 1534"origin: CAS library,\n", 1535"maximal subgroup of U3(3),\n", 1536" test:= 1. o.r., sym 2 decompose correctly \n", 1537"tests: 1.o.r., pow[2,3]" 1538], 1539[96,32,32,32,16,8,3,8,8,8], 1540[,[1,1,2,2,2,2,7,1,4,3],[1,2,4,3,5,6,1,8,10,9]], 1541[[1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,-1,1,-1,-1,-1],[2,2,2,2,2,0,-1,0,0,0],[3,-1, 1542-1-2*E(4),-1+2*E(4),1,-1,0,1,-E(4),E(4)], 1543[GALOIS,[4,3]],[3,3,-1,-1,-1,-1,0,-1,1,1], 1544[TENSOR,[6,2]], 1545[TENSOR,[4,2]], 1546[TENSOR,[5,2]],[6,-2,2,2,-2,0,0,0,0,0]], 1547[( 3, 4)( 9,10)]); 1548ARC("4^2:s3","tomfusion",rec(name:="4^2:S3",map:=[1,2,6,6,7,8,4,3,16,16], 1549text:=[ 1550"fusion map is unique" 1551])); 1552ALF("4^2:s3","L3(5)",[1,2,4,5,6,6,3,2,11,10],[ 1553"fusion map is unique up to table autom." 1554]); 1555ALF("4^2:s3","U3(3)",[1,2,5,6,7,7,4,2,12,11],[ 1556"fusion is unique up to table automorphisms,\n", 1557"the representative is equal to the fusion map on the CAS table" 1558]); 1559 1560MOT("A11Syl2", 1561[ 1562"origin: cayley, tests: 1.o.r.\n", 1563"table of sylow 2 subgroup of the alternating group A11," 1564], 1565[128,128,64,32,32,32,32,32,32,16,16,32,32,32,16,16,16,8,8,8], 1566[,[1,1,1,1,1,1,1,1,1,1,1,2,3,3,2,3,3,4,5,12]], 1567[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,-1,1,1,1,1,-1,1, 15681,-1,-1,-1],[1,1,1,1,1,1,1,-1,-1,-1,-1,1,-1,-1,-1,1,-1,-1,1,1], 1569[TENSOR,[2,3]],[1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,1,1,-1,-1,-1,-1,1], 1570[TENSOR,[3,5]], 1571[TENSOR,[2,6]], 1572[TENSOR,[2,5]],[2,2,2,2,-2,-2,-2,0,0,0,0,-2,0,0,0,2,0,0,0,0], 1573[TENSOR,[9,5]],[2,2,2,-2,2,0,0,-2,-2,0,0,-2,0,0,0,0,2,0,0,0], 1574[TENSOR,[11,3]],[2,2,2,-2,-2,0,0,0,0,0,2,2,-2,-2,0,0,0,0,0,0], 1575[TENSOR,[13,3]],[4,4,-4,0,0,0,0,0,0,2,0,0,0,0,-2,0,0,0,0,0], 1576[TENSOR,[15,2]],[4,-4,0,0,0,-2,2,2,-2,0,0,0,-2,2,0,0,0,0,0,0], 1577[TENSOR,[17,3]], 1578[TENSOR,[17,6]], 1579[TENSOR,[17,5]]], 1580[( 8, 9)(13,14),( 6, 7)(13,14),( 4, 5)( 6, 8)( 7, 9)(16,17)(18,19)]); 1581ALF("A11Syl2","A11",[1,3,2,3,2,3,2,3,2,3,3,8,7,9,8,7,9,8,9,18],[ 1582"fusion map is unique up to table autom.,\n", 1583"unique map that is compatible with LyN2 -> 2.A11" 1584]); 1585 1586MOT("a4", 1587[ 1588"origin: CAS library,\n", 1589" names:= a4; psl[2,3]\n", 1590" a1(3) (lie-not.)\n", 1591" order: 2^2.3 = 12\n", 1592" number of classes: 4\n", 1593" source: generated by dixon-algorithm aachen (1982)\n", 1594" comments: alternating group, catalogue nr.12.5\n", 1595" test: orth, min, sym(3)\n", 1596"tests: 1.o.r., pow[2,3]" 1597], 1598[12,4,3,3], 1599[,[1,1,4,3],[1,2,1,1]], 1600[[1,1,1,1],[1,1,E(3),E(3)^2], 1601[TENSOR,[2,2]],[3,-1,0,0]], 1602[(3,4)]); 1603ARC("a4","ClassParameters",[[1,[1,1,1,1]],[1,[2,2]],[1,[[3,1],'+']],[1,[[3,1], 1604'-']]]); 1605ARC("a4","projectives",["2.L2(3)",[[2,0,-1,-1]],]); 1606ALF("a4","A5",[1,2,3,3],[ 1607"fusion map is unique" 1608]); 1609ALF("a4","Symm(4)",[1,2,3,3],[ 1610"fusion map is unique" 1611]); 1612ALF("a4","L2(13)",[1,2,3,3]); 1613ALF("a4","L2(27)",[1,2,3,4]); 1614ALN("a4",["L2(3)"]); 1615 1616MOT("2.L2(3)", 1617[ 1618"origin: Dixon's Algorithm" 1619], 1620[24,24,4,6,6,6,6], 1621[,[1,1,2,6,6,4,4],[1,2,3,1,2,1,2],,[1,2,3,6,7,4,5]], 16220, 1623[(4,6)(5,7)], 1624["ConstructProj",[["a4",[]],["2.L2(3)",[]]]]); 1625ALF("2.L2(3)","a4",[1,1,2,3,3,4,4]); 1626ALF("2.L2(3)","2.A5",[1,2,3,4,5,4,5]); 1627ALF("2.L2(3)","2A4xA5",[1,6,11,16,21,26,31],[ 1628"fusion map determined by the direct product construction" 1629]); 1630ALF("2.L2(3)","2.L2(13)",[1,2,3,4,5,4,5]); 1631ALF("2.L2(3)","2.L2(27)",[1,2,3,4,5,6,7],[ 1632"fusion map is unique up to table autom.,\n", 1633"representative compatible with factors" 1634]); 1635ALN("2.L2(3)",["sl(2,3)"]); 1636 1637MOT("a5wc2", 1638[ 1639"origin: CAS library,\n", 1640"tests: 1.o.r., pow[2,3,5]" 1641], 1642[7200,240,120,32,180,18,8,300,300,50,50,25,12,6,20,20,10,10,15,15], 1643[,[1,1,1,1,5,6,4,9,8,11,10,12,5,6,8,9,10,11,20,19],[1,2,3,4,1,1,7,9,8,11,10, 164412,2,3,16,15,18,17,9,8],,[1,2,3,4,5,6,7,1,1,1,1,1,13,14,2,2,3,3,5,5]], 1645[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,-1,1,1,1,-1,1,1,1,1,1,1,-1,1, 16461,-1,-1,1,1],[6,2,0,-2,3,0,0,-3*E(5)-4*E(5)^2-4*E(5)^3-3*E(5)^4, 1647-4*E(5)-3*E(5)^2-3*E(5)^3-4*E(5)^4,-2*E(5)^2-2*E(5)^3,-2*E(5)-2*E(5)^4,1,-1,0, 1648E(5)^2+E(5)^3,E(5)+E(5)^4,0,0,-E(5)^2-E(5)^3,-E(5)-E(5)^4], 1649[GALOIS,[3,2]],[8,4,0,0,5,2,0,3,3,-2,-2,-2,1,0,-1,-1,0,0,0,0],[9,-3,-3,1,0,0, 16501,-3*E(5)^2-3*E(5)^3,-3*E(5)-3*E(5)^4,-E(5)-2*E(5)^2-2*E(5)^3-E(5)^4, 1651-2*E(5)-E(5)^2-E(5)^3-2*E(5)^4,-1,0,0,E(5)+E(5)^4,E(5)^2+E(5)^3,E(5)^2+E(5)^3, 1652E(5)+E(5)^4,0,0], 1653[TENSOR,[6,2]], 1654[GALOIS,[6,2]], 1655[TENSOR,[8,2]],[10,6,0,2,4,-2,0,5,5,0,0,0,0,0,1,1,0,0,-1,-1],[16,0,4,0,4,1,0, 1656-4,-4,1,1,1,0,1,0,0,-1,-1,-1,-1], 1657[TENSOR,[11,2]],[18,-6,0,2,0,0,0,3,3,-2,-2,3,0,0,-1,-1,0,0,0,0],[24,-4,0,0,3, 16580,0,3*E(5)-E(5)^2-E(5)^3+3*E(5)^4,-E(5)+3*E(5)^2+3*E(5)^3-E(5)^4, 16592*E(5)^2+2*E(5)^3,2*E(5)+2*E(5)^4,-1,-1,0,1,1,0,0,-E(5)^2-E(5)^3, 1660-E(5)-E(5)^4], 1661[GALOIS,[14,2]],[25,5,-5,1,-5,1,-1,0,0,0,0,0,-1,1,0,0,0,0,0,0], 1662[TENSOR,[16,2]],[30,-2,0,-2,-3,0,0,-5*E(5)^2-5*E(5)^3,-5*E(5)-5*E(5)^4,0,0,0, 16631,0,-E(5)-E(5)^4,-E(5)^2-E(5)^3,0,0,E(5)^2+E(5)^3,E(5)+E(5)^4], 1664[GALOIS,[18,2]],[40,4,0,0,1,-2,0,-5,-5,0,0,0,1,0,-1,-1,0,0,1,1]], 1665[( 8, 9)(10,11)(15,16)(17,18)(19,20)]); 1666ARC("a5wc2","tomfusion",rec(name:="(A5xA5):2",map:=[1,2,3,4,5,6,11,14,14, 166716,16,15,19,21,32,32,34,34,45,45],text:=[ 1668"fusion map is unique" 1669])); 1670ALF("a5wc2","S4(4)",[1,3,2,4,6,5,8,11,12,10,9,13,15,14,19,18,16,17,22,23],[ 1671"fusion map is unique up to table autom." 1672]); 1673 1674MOT("S4(4)M6", 1675[ 1676"6th maximal subgroup of S4(4),\n", 1677"differs from S4(4)M5 only by fusion map" 1678], 16790, 16800, 16810, 16820, 1683["ConstructPermuted",["a5wc2"]]); 1684ALF("S4(4)M6","S4(4)",[1,2,3,4,5,6,8,9,10,11,12,13,14,15,17,16,19,18,20, 168521],[ 1686"fusion map is unique up to table autom.,\n", 1687"equals the map from S4(4)M5, mapped under the outer autom." 1688],"tom:490"); 1689 1690MOT("affine", 1691[ 1692"origin: CAS library,\n", 1693"tests: 1.o.r., pow[2,3,5]" 1694], 1695[311040,3888,3840,3456,432,192,32,576,72,64,16,432,54,48,24,36,18,10,10,96, 1696288,36,192,192,32,8,48,24,48,24,12,24,24], 1697[,[1,2,1,1,2,3,3,4,5,4,6,12,13,12,14,12,13,18,18,3,1,2,6,6,6,7,8,9,8,9,14,15, 169815],[1,1,3,4,4,6,7,8,8,10,11,1,1,3,6,4,4,18,19,20,21,21,23,24,25,26,27,27,29, 169929,20,24,23],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,1,3,20,21,22,24,23, 170025,26,29,30,27,28,31,33,32]], 1701[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1, 17021,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[4,4, 17034,4,4,4,0,0,0,0,0,1,1,1,1,1,1,-1,-1,2,2,2,2,2,2,0,0,0,0,0,-1,-1,-1], 1704[TENSOR,[3,2]],[5,5,5,5,5,5,1,1,1,1,1,-1,-1,-1,-1,-1,-1,0,0,-1,-1,-1,-1,-1,-1, 17051,1,1,1,1,-1,-1,-1], 1706[TENSOR,[5,2]],[6,6,6,6,6,6,-2,-2,-2,-2,-2,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0, 17070,0,0,0,0],[5,5,5,-3,-3,1,1,1,1,1,-1,2,2,2,-2,0,0,0,0,3,-1,-1,-3,-3,1,1,-1,-1, 1708-1,-1,0,0,0], 1709[TENSOR,[8,2]],[10,10,10,-6,-6,2,2,2,2,2,-2,-2,-2,-2,2,0,0,0,0,0,0,0,0,0,0,0, 17100,0,0,0,0,0,0],[15,15,15,-9,-9,3,-1,-1,-1,-1,1,0,0,0,0,0,0,0,0,3,-1,-1,-3,-3, 17111,-1,1,1,1,1,0,0,0], 1712[TENSOR,[11,2]],[10,10,10,2,2,-2,2,-2,-2,-2,0,1,1,1,1,-1,-1,0,0,4,0,0,2,2,-2, 17130,0,0,0,0,1,-1,-1], 1714[TENSOR,[13,2]],[10,10,10,2,2,-2,-2,2,2,2,0,1,1,1,1,-1,-1,0,0,2,-2,-2,4,4,0,0, 17150,0,0,0,-1,1,1], 1716[TENSOR,[15,2]],[20,20,20,4,4,-4,0,0,0,0,0,-1,-1,-1,-1,1,1,0,0,-2,-2,-2,2,2,2, 17170,0,0,0,0,1,-1,-1], 1718[TENSOR,[17,2]],[4,4,-4,0,0,0,0,2,2,-2,0,-2,-2,2,0,0,0,-1,1,0,0,0, 17192*E(8)+2*E(8)^3,-2*E(8)-2*E(8)^3,0,0,E(8)+E(8)^3,E(8)+E(8)^3,-E(8)-E(8)^3, 1720-E(8)-E(8)^3,0,E(8)+E(8)^3,-E(8)-E(8)^3], 1721[TENSOR,[19,2]],[16,16,-16,0,0,0,0,0,0,0,0,-2,-2,2,0,0,0,1,-1,0,0,0, 17224*E(8)+4*E(8)^3,-4*E(8)-4*E(8)^3,0,0,0,0,0,0,0,-E(8)-E(8)^3,E(8)+E(8)^3], 1723[TENSOR,[21,2]],[20,20,-20,0,0,0,0,2,2,-2,0,2,2,-2,0,0,0,0,0,0,0,0, 1724-2*E(8)-2*E(8)^3,2*E(8)+2*E(8)^3,0,0,E(8)+E(8)^3,E(8)+E(8)^3,-E(8)-E(8)^3, 1725-E(8)-E(8)^3,0,-E(8)-E(8)^3,E(8)+E(8)^3], 1726[TENSOR,[23,2]],[24,24,-24,0,0,0,0,-4,-4,4,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,0, 17270,0,0,0,0,0],[80,-1,0,8,-1,0,0,8,-1,0,0,8,-1,0,0,2,-1,0,0,0,8,-1,0,0,0,0,2,-1, 17282,-1,0,0,0], 1729[TENSOR,[26,2]],[160,-2,0,16,-2,0,0,16,-2,0,0,-8,1,0,0,-2,1,0,0,0,0,0,0,0,0,0, 17300,0,0,0,0,0,0],[240,-3,0,24,-3,0,0,-8,1,0,0,0,0,0,0,0,0,0,0,0,8,-1,0,0,0,0,-2, 17311,-2,1,0,0,0], 1732[TENSOR,[29,2]],[160,-2,0,-16,2,0,0,0,0,0,0,-8,1,0,0,2,-1,0,0,0,0,0,0,0,0,0, 17332*E(8)+2*E(8)^3,-E(8)-E(8)^3,-2*E(8)-2*E(8)^3,E(8)+E(8)^3,0,0,0], 1734[TENSOR,[31,2]],[320,-4,0,-32,4,0,0,0,0,0,0,8,-1,0,0,-2,1,0,0,0,0,0,0,0,0,0,0, 17350,0,0,0,0,0]], 1736[(23,24)(27,29)(28,30)(32,33)]); 1737ALF("affine","twd5a",[1,1,2,3,3,4,5,6,6,7,8,9,9,10,11,12,12,13,14,15,16, 173816,17,18,19,20,21,21,22,22,23,24,25]); 1739 1740MOT("b33141", 1741[ 1742"origin: CAS library,\n", 1743"names:b33141\n", 1744"order: 2^6.3^2 = 576\n", 1745"number of classes: 23\n", 1746"source:generated by dixon-algorithm\n", 1747"aachen [1981],\n", 1748"brown, h. / buelow, r. / neubueser, j.\n", 1749"wondratschek, h. / zassenhaus, h.\n", 1750"crystallographic groups of\n", 1751"four dimensional space\n", 1752"comments:isomorphism type 576.1\n", 1753"q-classes: 33/14\n", 1754"generators:\n", 1755"a: 1 0 0 0 b: -1 -1 -1 2 c: 1 0 0 0\n", 1756"0 -1 0 0 0 0 1 0 0 -1 0 0\n", 1757"0 0 -1 0 0 -1 0 0 0 0 1 0\n", 1758"0 -1 -1 1 -1 -1 0 1 1 0 1 -1\n", 1759"\n", 1760"d: 0 0 -1 0 e: 0 -1 0 1 f: 0 1 0 -1\n", 1761"1 1 1 -2 -1 0 0 1 0 0 -1 -1\n", 1762"-1 0 0 0 1 1 1 -1 1 0 0 -1\n", 1763"0 0 0 -1 0 0 1 0 1 1 0 -1 \n", 1764"\n", 1765"test: 1. o.r., sym 2, 3 decompose correctly\n", 1766"tests: 1.o.r., pow[2,3]" 1767], 1768[576,32,48,576,18,18,12,12,12,12,36,36,36,36,12,12,72,72,72,72,48,8,48], 1769[,[1,1,4,1,5,5,11,12,11,12,12,11,12,11,20,19,18,17,18,17,1,2,1],[1,2,3,4,1,4, 177021,21,23,23,1,1,4,4,3,3,1,1,4,4,21,22,23],,[1,2,3,4,5,6,8,7,10,9,12,11,14,13, 177116,15,18,17,20,19,21,22,23],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19, 177220,21,22,23]], 1773[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,-E(3),-E(3)^2, 1774-E(3),-E(3)^2,E(3)^2,E(3),E(3)^2,E(3),E(3)^2,E(3),E(3)^2,E(3),E(3)^2,E(3),-1, 1775-1,-1],[1,1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1], 1776[TENSOR,[2,2]], 1777[TENSOR,[3,4]], 1778[TENSOR,[2,3]],[2,2,2,2,-1,-1,0,0,0,0,2,2,2,2,-1,-1,-1,-1,-1,-1,0,0,0], 1779[TENSOR,[7,4]], 1780[TENSOR,[7,2]],[4,0,0,-4,1,-1,E(3),E(3)^2,-E(3),-E(3)^2,E(3)^2,E(3),-E(3)^2, 1781-E(3),0,0,-2*E(3)^2,-2*E(3),2*E(3)^2,2*E(3),-2,0,2], 1782[TENSOR,[10,2]], 1783[TENSOR,[10,6]], 1784[TENSOR,[10,3]], 1785[TENSOR,[10,4]], 1786[TENSOR,[10,5]],[6,-2,2,6,0,0,0,0,0,0,0,0,0,0,-E(3)^2,-E(3),3*E(3)^2,3*E(3), 17873*E(3)^2,3*E(3),0,0,0], 1788[TENSOR,[16,2]], 1789[TENSOR,[16,4]],[8,0,0,-8,-1,1,0,0,0,0,2*E(3),2*E(3)^2,-2*E(3),-2*E(3)^2,0,0, 17902*E(3),2*E(3)^2,-2*E(3),-2*E(3)^2,0,0,0], 1791[TENSOR,[19,4]], 1792[TENSOR,[19,2]],[9,1,-3,9,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-3,1,-3], 1793[TENSOR,[22,2]]], 1794[( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20),( 7, 9)( 8,10)(21,23)]); 1795ARC("b33141","tomfusion",rec(name:="2.(A4xA4).2",map:=[1,4,16,2,6,19,21, 179621,23,23,7,7,22,22,37,37,8,8,20,20,3,13,5],text:=[ 1797"fusion map is unique up to table autom." 1798])); 1799ALF("b33141","U4(2)",[1,3,8,2,7,15,13,14,16,16,6,6,13,14,19,20,4,5,11,12, 18002,9,3],[ 1801"fusion map is unique up to table autom." 1802]); 1803ALF("b33141","w(f4)",[1,3,4,2,9,10,24,24,25,25,7,7,8,8,11,11,5,5,6,6,18, 180421,19],[ 1805"fusion map is unique up to table autom." 1806]); 1807 1808MOT("bd10", 1809[ 1810"origin: CAS library,\n", 1811"names:=bd10\n", 1812" order: 2^2.5 = 20\n", 1813" number of classes: 8\n", 1814" source: generated by dixon-algorithm\n", 1815" aachen [1984]\n", 1816" comments:generators: a,b,c\n", 1817" relations: a^2=b^2=c^5=a*b*c \n", 1818" test: 1. o.r., sym 2 decompose correctly \n", 1819"tests: 1.o.r., pow[2,5]" 1820], 1821[20,4,4,20,10,10,10,10], 1822[,[1,4,4,1,6,5,5,6],,,[1,2,3,4,1,1,4,4]], 1823[[1,1,1,1,1,1,1,1],[1,-1,-1,1,1,1,1,1],[1,E(4),-E(4),-1,1,1,-1,-1], 1824[TENSOR,[2,3]],[2,0,0,-2,E(5)+E(5)^4,E(5)^2+E(5)^3,-E(5)^2-E(5)^3, 1825-E(5)-E(5)^4], 1826[TENSOR,[5,3]], 1827[GALOIS,[6,2]], 1828[TENSOR,[7,3]]], 1829[(5,6)(7,8),(2,3)]); 1830ALF("bd10","D10",[1,4,4,1,2,3,3,2]); 1831ALF("bd10","C4",[1,2,4,3,1,1,3,3]); 1832ALF("bd10","2.A5",[1,3,3,2,6,8,9,7],[ 1833"fusion map is unique up to table autom.,\n", 1834"representative compatible with factors" 1835]); 1836 1837MOT("bd6", 1838[ 1839"origin: CAS library,\n", 1840"names:=bd6\n", 1841" order: 2^2.3 = 12\n", 1842" number of classes: 6\n", 1843" source:generated by dixon-algorithm\n", 1844" aachen [1984]\n", 1845" test: 1. o.r., sym 2, 3 decompose correctly\n", 1846" comments:generators: a,b,c\n", 1847" relations: a^2=b^2=c^3=a*b*c \n", 1848"tests: 1.o.r., pow[2,3]" 1849], 18500, 18510, 18520, 18530, 1854["ConstructPermuted",["2.S3"],(2,4,6,3,5),(3,5,4)]); 1855ALF("bd6","C4",[1,2,4,3,1,3]); 1856ALF("bd6","S3",[1,3,3,1,2,2]); 1857 1858MOT("bd8", 1859[ 1860"origin: CAS library,\n", 1861"names:=bd8\n", 1862" order: 2^4 = 16\n", 1863" number of classes: 7\n", 1864" source: generated by dixon-algorithm\n", 1865" aachen [1984]\n", 1866" test: 1. o.r., sym 2 decompose correctly\n", 1867" comments:generators: a,b,c\n", 1868" relations: a^2=b^2=c^4=a*b*c \n", 1869"tests: 1.o.r., pow[2]" 1870], 18710, 18720, 18730, 18740, 1875["ConstructPermuted",["2.D8"],(2,3,7,4,5,6),(3,4)(5,7)]); 1876 1877MOT("M22C2A", 1878[ 1879"origin: CAS library,\n", 1880"centralizer of an involution in the sporadic simple Mathieu group M22,\n", 1881"computed using CAYLEY,\n", 1882"tests: 1.o.r., pow[2,3],\n", 1883"2nd power map determined only up to matrix automorphisms," 1884], 1885[384,384,16,8,32,48,16,64,8,32,12,12,12,12,16,16,16], 1886[,[1,1,1,5,1,1,8,1,10,2,11,11,11,11,8,2,8],[1,2,3,4,5,6,7,8,9,10,1,2,6,6,15, 188716,17]], 1888[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,-1,-1,1,1,-1,1,-1,1,1,1,1,1,-1,-1, 18891],[1,1,1,1,1,-1,-1,1,-1,1,1,1,-1,-1,1,-1,-1], 1890[TENSOR,[2,3]],[2,2,0,0,2,2,0,2,0,2,-1,-1,-1,-1,0,0,2], 1891[TENSOR,[5,3]],[3,3,-1,1,-1,3,-1,3,1,-1,0,0,0,0,-1,-1,-1], 1892[TENSOR,[7,2]], 1893[TENSOR,[7,3]], 1894[TENSOR,[7,4]],[6,6,0,0,-2,0,2,-2,0,2,0,0,0,0,0,-2,0],[6,6,2,0,2,0,0,-2,0,-2, 18950,0,0,0,-2,0,0], 1896[TENSOR,[11,2]], 1897[TENSOR,[12,2]],[8,-8,0,0,0,0,0,0,0,0,2,-2,0,0,0,0,0],[8,-8,0,0,0,0,0,0,0,0, 1898-1,1,E(3)-E(3)^2,-E(3)+E(3)^2,0,0,0], 1899[TENSOR,[16,3]]], 1900[(13,14)]); 1901ALF("M22C2A","M22",[1,2,2,4,2,2,4,2,10,4,3,7,7,7,5,5,5],[ 1902"determined using the fusion M22N2 -> M22" 1903]); 1904ALF("M22C2A","M23C2A",[1,2,4,8,4,3,7,3,14,6,5,9,10,11,7,6,7],[ 1905"fusion map is unique up to table automorphisms" 1906]); 1907ALN("M22C2A",["M22N2A"]); 1908 1909MOT("M24C2B", 1910[ 1911"origin: CAS library,\n", 1912"tests: 1.o.r., pow[2,3,5],\n", 1913"2nd power map determined only up to matrix automorphisms," 1914], 1915[7680,7680,3840,512,512,256,96,96,32,32,128,128,64,64,64,32,32,24,24,12,16,16, 191616,16,12,12,20,20,20,20], 1917[,[1,1,1,1,1,1,1,2,4,5,1,1,1,5,5,6,6,18,18,18,11,12,15,15,18,19,27,27,27,27],[ 19181,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,1,2,3,21,22,24,23,7,8,27,28,30, 191929],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,1, 19202,3,3]], 1921[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1, 1922-1,-1,-1,-1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,1,1,1,1],[4,4,4,4,4,4,2,2,2, 19232,0,0,0,0,0,0,0,1,1,1,0,0,0,0,-1,-1,-1,-1,-1,-1], 1924[TENSOR,[3,2]],[5,5,5,5,5,5,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,1,1,0, 19250,0,0], 1926[TENSOR,[5,2]],[6,6,6,6,6,6,0,0,0,0,-2,-2,-2,-2,-2,-2,-2,0,0,0,0,0,0,0,0,0,1, 19271,1,1],[6,6,-6,-2,-2,2,0,0,0,0,2,2,-2,-2,2,0,0,0,0,0,-2,2,0,0,0,0,1,1,-1,-1], 1928[TENSOR,[8,2]],[12,-12,0,-4,4,0,0,0,0,0,-4,4,0,0,0,-2,2,0,0,0,0,0,0,0,0,0,2, 1929-2,0,0],[15,15,15,-1,-1,-1,3,3,-1,-1,3,3,3,-1,-1,-1,-1,0,0,0,1,1,-1,-1,0,0,0, 19300,0,0], 1931[TENSOR,[11,2]],[15,15,15,-1,-1,-1,-3,-3,1,1,-1,-1,-1,3,3,-1,-1,0,0,0,1,1,-1, 1932-1,0,0,0,0,0,0], 1933[TENSOR,[13,2]],[24,24,-24,-8,-8,8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1, 1934-1,1,1],[30,30,30,-2,-2,-2,0,0,0,0,-2,-2,-2,-2,-2,2,2,0,0,0,0,0,0,0,0,0,0,0,0, 19350],[10,10,-10,2,2,-2,4,-4,0,0,2,2,-2,2,-2,0,0,1,1,-1,0,0,0,0,1,-1,0,0,0,0],[ 193620,-20,0,4,-4,0,0,0,0,0,-4,4,0,0,0,2,-2,2,-2,0,0,0,0,0,0,0,0,0,0,0], 1937[TENSOR,[17,2]],[40,-40,0,8,-8,0,0,0,0,0,0,0,0,0,0,0,0,-2,2,0,0,0,0,0,0,0,0,0, 19380,0],[20,20,-20,4,4,-4,2,-2,-2,2,0,0,0,0,0,0,0,-1,-1,1,0,0,0,0,-1,1,0,0,0,0], 1939[TENSOR,[21,2]],[10,10,-10,2,2,-2,2,-2,2,-2,-2,-2,2,-2,2,0,0,1,1,-1,0,0,0,0, 1940-1,1,0,0,0,0], 1941[TENSOR,[23,2]],[20,-20,0,4,-4,0,0,0,0,0,4,-4,0,0,0,-2,2,2,-2,0,0,0,0,0,0,0,0, 19420,0,0],[12,-12,0,-4,4,0,0,0,0,0,4,-4,0,0,0,2,-2,0,0,0,0,0,0,0,0,0,2,-2,0,0],[ 194324,-24,0,-8,8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1, 1944E(5)-E(5)^2-E(5)^3+E(5)^4,-E(5)+E(5)^2+E(5)^3-E(5)^4], 1945[GALOIS,[27,2]],[6,6,-6,-2,-2,2,0,0,0,0,-2,-2,2,2,-2,0,0,0,0,0,0,0,-2*E(4), 19462*E(4),0,0,1,1,-1,-1], 1947[TENSOR,[29,2]]], 1948[(29,30),(23,24),(11,12)(16,17)(21,22)]); 1949ARC("M24C2B","tomfusion",rec(name:="2^2.(2^4S5)",map:=[1,2,3,4,5,6,9,30, 195076,57,7,8,10,48,36,71,60,11,85,89,79,81,292,292,86,310,82,300,301,301], 1951text:=[ 1952"fusion map is unique up to table autom." 1953])); 1954ALF("M24C2B","M24",[1,3,3,3,2,2,3,8,8,6,2,3,3,6,7,7,6,5,11,11,7,8,14,14,11, 195518,9,15,15,15],[ 1956"fusion map is unique up to table automorphisms" 1957]); 1958ALF("M24C2B","2^2.L3(4).2_2",[1,2,3,4,5,6,24,25,27,26,4,5,6,10,11,13,12,7, 19598,9,27,26,30,31,28,29,14,15,16,17],[ 1960"fusion map is unique up to table autom." 1961]); 1962ALF("M24C2B","A5.2",[1,1,1,1,1,1,5,5,5,5,2,2,2,2,2,2,2,3,3,3,6,6,6,6,7,7, 19634,4,4,4]); 1964ALN("M24C2B",["M24N2B"]); 1965 1966MOT("c3d2", 1967[ 1968"origin: CAS library,\n", 1969"tests: 1.o.r., pow[2,3,7]" 1970], 1971[1008,336,144,48,504,36,36,18,18,72,36,36,18,18,12,12,12,12,42,42,14,14,21, 197221], 1973[,[1,1,1,1,5,7,6,9,8,5,6,7,8,9,6,7,6,7,19,20,19,20,23,24],[1,2,3,4,1,1,1,1,1, 19743,3,3,3,3,2,2,4,4,20,19,22,21,20,19],,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15, 197516,17,18,1,1,2,2,5,5]], 1976[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,-1,1,-1,1,1,1,1,1,1,1,1, 19771,1,-1,-1,-1,-1,1,1,-1,-1,1,1],[1,1,1,1,1,E(3)^2,E(3),E(3)^2,E(3),1,E(3), 1978E(3)^2,E(3),E(3)^2,E(3),E(3)^2,E(3),E(3)^2,1,1,1,1,1,1], 1979[TENSOR,[2,3]], 1980[TENSOR,[3,3]], 1981[TENSOR,[2,5]],[2,0,2,0,-1,2*E(3),2*E(3)^2,-E(3),-E(3)^2,-1,2*E(3)^2,2*E(3), 1982-E(3)^2,-E(3),0,0,0,0,2,2,0,0,-1,-1], 1983[TENSOR,[7,3]], 1984[TENSOR,[7,5]],[3,3,3,3,3,0,0,0,0,3,0,0,0,0,0,0,0,0,E(7)^3+E(7)^5+E(7)^6, 1985E(7)+E(7)^2+E(7)^4,E(7)^3+E(7)^5+E(7)^6,E(7)+E(7)^2+E(7)^4, 1986E(7)^3+E(7)^5+E(7)^6,E(7)+E(7)^2+E(7)^4], 1987[TENSOR,[10,2]], 1988[GALOIS,[11,3]], 1989[TENSOR,[12,2]],[6,0,6,0,-3,0,0,0,0,-3,0,0,0,0,0,0,0,0,2*E(7)^3+2*E(7)^5 1990 +2*E(7)^6,2*E(7)+2*E(7)^2+2*E(7)^4,0,0,-E(7)^3-E(7)^5-E(7)^6, 1991-E(7)-E(7)^2-E(7)^4], 1992[GALOIS,[14,3]],[7,-7,-1,1,7,E(3),E(3)^2,E(3),E(3)^2,-1,-E(3)^2,-E(3),-E(3)^2, 1993-E(3),-E(3)^2,-E(3),E(3)^2,E(3),0,0,0,0,0,0], 1994[TENSOR,[16,2]], 1995[TENSOR,[16,5]], 1996[TENSOR,[16,6]], 1997[TENSOR,[16,3]], 1998[TENSOR,[16,4]],[14,0,-2,0,-7,2*E(3)^2,2*E(3),-E(3)^2,-E(3),1,-2*E(3), 1999-2*E(3)^2,E(3),E(3)^2,0,0,0,0,0,0,0,0,0,0], 2000[TENSOR,[22,3]], 2001[TENSOR,[22,5]]], 2002[(19,20)(21,22)(23,24),( 6, 7)( 8, 9)(11,12)(13,14)(15,16)(17,18)]); 2003ALF("c3d2","Co3",[1,2,3,3,6,5,5,6,6,15,14,14,15,15,13,13,14,14,16,16,29, 200429,35,35],[ 2005"fusion map is unique" 2006]); 2007ALN("c3d2",["co3d2"]); 2008 2009MOT("D120", 2010[ 2011"origin: CAS library,\n", 2012"names:d60\n", 2013"order: 2^3.3.5 = 120\n", 2014"number of classes: 33\n", 2015"source:generated by dixon-algorithm\n", 2016"aachen [1980]\n", 2017"test: 1. o.r., sym 2 decompose correctly\n", 2018"comments:generators: a,b\n", 2019"relations: a^60 = b^2 = (ab)^2 = 1 \n", 2020"tests: 1.o.r., pow[2,3,5]" 2021], 20220, 20230, 20240, 2025[(12,13)(18,19)(20,21)(26,29)(27,32)(28,33)(30,31),(12,13)(14,17)(15,16) 2026(22,24)(23,25)(26,30)(27,33)(28,32)(29,31),( 7, 8)(10,11)(14,16,17,15) 2027(18,20,19,21)(22,25,24,23)(26,27,31,28)(29,32,30,33),(2,4),(14,17)(15,16) 2028(18,19)(20,21)(22,24)(23,25)(26,31)(27,28)(29,30)(32,33)], 2029["ConstructPermuted",["Dihedral",120],(2,26,13,7,10,21,5,14,28,18,33,4,19,11, 20309,15,22,20,30,29,16,6,12,31,3,23,25,8,32)(24,27),(2,3,4)(5,30,15,26,16,9,10, 203113,18,14,7,21,31,20,25,19,6,17,29,11,32,23,27,33,28,8,24)(12,22)]); 2032ARC("D120","tomfusion",rec(name:="30.2^2",map:=[1,2,3,4,5,7,9,9,11,15,15, 203318,18,20,20,20,20,22,22,22,22,26,26,26,26,30,30,30,30,30,30,30,30],text:=[ 2034"fusion map is unique up to table autom." 2035])); 2036ALF("D120","D10",[1,4,1,4,1,1,2,3,1,3,2,1,1,3,2,2,3,2,2,3,3,3,2,3,2,3,2,2, 20373,3,3,2,2]); 2038ALF("D120","D24",[1,8,7,9,5,4,1,1,3,7,7,2,6,5,5,5,5,4,4,4,4,3,3,3,3,6,6,6, 20392,2,6,2,2]); 2040ALF("D120","D8",[1,4,2,5,1,3,1,1,2,2,2,3,3,1,1,1,1,3,3,3,3,2,2,2,2,3,3,3,3, 20413,3,3,3]); 2042ALF("D120","S3",[1,3,1,3,2,1,1,1,2,1,1,2,2,2,2,2,2,1,1,1,1,2,2,2,2,2,2,2,2, 20432,2,2,2]); 2044ALF("D120","L2(121)",[1,33,33,33,23,18,15,27,13,9,21,8,28,7,11,31,19,30,6, 204524,12,17,5,29,25,4,26,16,32,22,14,10,20],[ 2046"fusion map is unique up to table autom." 2047]); 2048 2049MOT("esp43t", 2050[ 2051"origin: CAS library,\n", 2052"tests: 1.o.r., pow[2,3,5]" 2053], 20540, 20550, 20560, 20570, 2058["ConstructPermuted",["3^(1+4).2U4(2).2"],(11,20,28,35,16,50,38,63,72,59,68, 205957,53,41,30)(12,19,27,26,25,24,23,49,37,62,69,58,54,43,32,13,18,52,40,65,70, 206061,67,55,42,31)(14,21,29,36,17,51,39,64,71,60,66,56,44,33)(15,22,34)(45,46,47) 2061(73,75)(76,77,78)(79,85,82,83,80,86,81,84)(87,89)(88,90),(3,6,13,16,19,37,32, 206225,36,30,20,23,28,15,18,34,38,33,26,5,4)(14,17,22,27)(21,24,35,29)(39,40)(42, 206343)(44,45)(47,48)(53,54)(58,59)(63,64)(67,68,70,69,71,72)(74,76)(79,80)(81,82) 2064(83,85,86)]); 2065ALF("esp43t","2.U4(2).2",[1,1,1,2,2,3,3,3,4,4,11,11,11,12,12,13,13,5,5,5, 20665,5,9,9,9,9,7,7,7,16,16,16,16,8,10,10,18,18,18,18,19,19,19,19,17,17,17,17, 20678,6,6,6,20,20,23,23,23,23,24,24,24,14,14,15,15,21,21,21,21,22,22,22,26,26, 206825,29,27,28,33,33,34,34,32,32,30,31,37,38,35,36]); 2069 2070MOT("j2nd2", 2071[ 2072"origin: CAS library,\n", 2073"tests: 1.o.r., pow[2,3,5]" 2074], 20750, 20760, 20770, 20780, 2079["ConstructPermuted",["a4xa5"],(12,14,13)(15,16)(17,19,20),(4,8,10,7,6,9)(17, 208018)]); 2081ALN("j2nd2",["j2d2"]); 2082 2083LIBTABLE.LOADSTATUS.ctomisc1:="userloaded"; 2084 2085############################################################################# 2086## 2087#E 2088 2089