1#############################################################################
2##
3##  This file is part of GAP, a system for computational discrete algebra.
4##  This file's authors include Volkmar Felsch.
5##
6##  Copyright of GAP belongs to its developers, whose names are too numerous
7##  to list here. Please refer to the COPYRIGHT file for details.
8##
9##  SPDX-License-Identifier: GPL-2.0-or-later
10##
11##  This is the main secondary file of the GAP library of irreducible maximal
12##  finite (imf) integral matrix groups. It contains a list IMFList of length
13##  31 and a record IMFRec.
14##
15##  Each entry IMFList[dim] of IMFList is a record which contains information
16##  about the  Z-class  representative groups  (in case  dim < 12  or  dim in
17##  {13,17,19,23}, or about the Q-class representative groups (in case dim in
18##  {12,14,15,16,18,20,21,22,24,25,26,27,28,29,30,31}) of diminsion dim. More
19##  precisely, each of these records contains the following components:
20##
21##  IMFList[dim].size               the group size,
22##  IMFList[dim].isomorphismType    the isomorphism type,
23##  IMFList[dim].isSolvable         true, if the group is solvable, or false,
24##                                  else,
25##  IMFList[dim].elementaryDivisors the elementary divisors  of the quadratic
26##                                  form,
27##  IMFList[dim].minimalNorm        the norm of the "short vectors",
28##  IMFList[dim].orbitReps          representatives  of the  orbits  of short
29##                                  vectors,
30##  IMFList[dim].degrees            sizes  of the  orbits  of  short vectors,
31##                                  i. e.,   the   degrees   of   permutation
32##                                  representations  on  the  orbits  of  the
33##                                  short vectors.
34##
35##  Additional lists with the associated  Gram matrices and matrix generators
36##  are provided in the files  imf1to9.grp to  imf31.grp  of this library and
37##  will be loaded only if necessary.
38##
39##  The record IMFRec contains the following components:
40##
41##  IMFRec.maximalDimension the  maximal dimension  covered  by the  library,
42##                          i.e., 31,
43##  IMFRec.numberQQClasses  a list  containing  for each  dimension  dim  the
44##                          number   of   Q-classes   of   imf  subgroups  of
45##                          GL(dim,Q),
46##  IMFRec.numberQClasses   a list  containing  for each  dimension  dim  the
47##                          number of Q-classes of imf subgroups of dimension
48##                          dim available in the library,  i. e.,  the number
49##                          of Q-classes of  imf subgroups of  GL(dim,Z),  if
50##                          dim is at most 11  or a prime at most 23,  or the
51##                          number   of   Q-classes   of  imf  subgroups   of
52##                          GL(dim,Q), else,
53##  IMFRec.repsAreZReps     a list  containing  for each dimension dim a flag
54##                          which is true, if dim is at most 11 or a prime at
55##                          most 23, or false, else,
56##  IMFRec.bNumbers         a list  containing  for each dimension dim a list
57##                          of lists which, for each available Q-class,  give
58##                          the  list   of  the   position  numbers   of  its
59##                          representatives  with  respect  to the  lists  in
60##                          IMFList,
61##  IMFRec.maximalQClasses  a list  containing  for each dimension dim a list
62##                          of lists which, for each available Q-class,  give
63##                          the Q-class number  of the corresponding rational
64##                          imf class.
65##
66
67
68#############################################################################
69##
70##
71BindGlobal( "IMFRec", rec( ) );
72
73IMFRec.maximalDimension := 31;
74
75IMFRec.numberQQClasses :=
76 [1,2,1,3,2,6,2,9,2,8,2,19,4,12,6,31,3,17,2,31,8,12,4,65,5,16,5,37,2,33,4];
77
78IMFRec.numberQClasses :=
79 [1,2,1,5,2,9,3,16,8,21,2,19,4,12,6,31,6,17,2,31,8,12,7,65,5,16,5,37,2,33,4];
80
81IMFRec.repsAreZReps :=
82 [true,true,true,true,true,true,true,true,true,true,true,false,true,false,
83  false,false,true,false,true,false,false,false,true,false,false,false,
84  false,false,false,false,false];
85
86IMFRec.bNumbers := [
87 [[1]],
88 [[1],[2]],
89 [[1..3]],
90 [[2],[3],[5,6],[1],[4]],
91 [[1..3],[4..7]],
92 [[1..3],[7],[8,9],[12,13],[14],[15..17],[4,5],[6],[10,11]],
93 [[1..3],[6,7],[4,5]],
94 [[1..3],[4],[5],[6],[7],[14,15],[16],[18,19],[23..26],[11,12],[20,21],[22],
95  [8,9],[10],[13],[17]],
96 [[1..3],[15..18],[4..7],[8,9],[10,11],[12,13],[14],[19,20]],
97 [[1..3],[14..19],[25],[32,33],[38..41],[42,43],[44,45],[46],[4],[5],[6,7],
98  [8,9],[10,11],[12,13],[20..22],[23,24],[26,27],[28],[29,30],[31],[34..37]],
99 [[1..3],[4..9]],
100 [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12],[13],[14],[15],[16],
101  [17],[18],[19]],
102 [[1..3],[4..7],[8..13],[14..17]],
103 [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12]],
104 [[1],[2],[3],[4],[5],[6]],
105 [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12],[13],[14],[15],[16],
106  [17],[18],[19],[20],[21],[22],[23],[24],[25],[26],[27],[28],[29],[30],
107  [31]],
108 [[1..3],[4..9],[17..24],[10,11],[12,13],[14..16]],
109 [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12],[13],[14],[15],[16],
110  [17]],
111 [[1..3],[4..9]],
112 [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12],[13],[14],[15],[16],
113  [17],[18],[19],[20],[21],[22],[23],[24],[25],[26],[27],[28],[29],[30],
114  [31]],
115 [[1],[2],[3],[4],[5],[6],[7],[8]],
116 [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12]],
117 [[1..8],[9..11],[22..24],[25..28],[16..21],[12,13],[14,15]],
118 [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12],[13],[14],[15],[16],
119  [17],[18],[19],[20],[21],[22],[23],[24],[25],[26],[27],[28],[29],[30],[31],
120  [32],[33],[34],[35],[36],[37],[38],[39],[40],[41],[42],[43],[44],[45],[46],
121  [47],[48],[49],[50],[51],[52],[53],[54],[55],[56],[57],[58],[59],[60],[61],
122  [62],[63],[64],[65]],
123 [[1],[2],[3],[4],[5]],
124 [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12],[13],[14],[15],[16]],
125 [[1],[2],[3],[4],[5]],
126 [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12],[13],[14],[15],[16],
127  [17],[18],[19],[20],[21],[22],[23],[24],[25],[26],[27],[28],[29],[30],[31],
128  [32],[33],[34],[35],[36],[37]],
129 [[1],[2]],
130 [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12],[13],[14],[15],[16],
131  [17],[18],[19],[20],[21],[22],[23],[24],[25],[26],[27],[28],[29],[30],[31],
132  [32],[33]],
133 [[1],[2],[3],[4]]];
134
135IMFRec.maximalQClasses := [
136 [1],
137 [1,2],
138 [1],
139 [1,2,3,1,2],
140 [1,2],
141 [1,2,3,4,5,6,1,1,2],
142 [1,2,2],
143 [1,2,3,4,5,6,7,8,9,3,4,4,5,5,5,6],
144 [1,2,1,1,1,1,1,2],
145 [1,2,3,4,5,6,7,8,1,1,1,1,1,1,2,2,3,3,3,4,4],
146 [1,2],
147 [1..19],
148 [1..4],
149 [1..12],
150 [1..6],
151 [1..31],
152 [1,2,3,1,1,2],
153 [1..17],
154 [1,2],
155 [1..31],
156 [1..8],
157 [1..12],
158 [1,2,3,4,1,2,2],
159 [1..65],
160 [1..5],
161 [1..16],
162 [1..5],
163 [1..37],
164 [1,2],
165 [1..33],
166 [1..4]];
167
168MakeImmutable( IMFRec );
169
170
171BindGlobal( "IMFList", List([ 1 .. 31 ], i -> rec( ) ) );
172
173
174#############################################################################
175##
176##  Sizes  of the  class  representatives  of the  irreducible maximal finite
177##  integral matrix groups.
178##
179
180IMFList[1].size := [ # Z-classes of dimension 1
181 2];
182
183IMFList[2].size := [ # Z-classes of dimension 2
184 8,
185 12];
186
187IMFList[3].size := [ # Z-classes of dimension 3
188 48,
189 48,
190 48];
191
192IMFList[4].size := [ # Z-classes of dimension 4
193 384,
194 1152,
195 288,
196 144,
197 240,
198 240];
199
200IMFList[5].size := [ # Z-classes of dimension 5
201 3840,
202 3840,
203 3840,
204 1440,
205 1440,
206 1440,
207 1440];
208
209IMFList[6].size := [ # Z-classes of dimension 6
210 46080,
211 46080,
212 46080,
213 4608,
214 4608,
215 23040,
216 10368,
217 103680,
218 103680,
219 288,
220 288,
221 10080,
222 10080,
223 672,
224 240,
225 240,
226 240];
227
228IMFList[7].size := [ # Z-classes of dimension 7
229 645120,
230 645120,
231 645120,
232 80640,
233 80640,
234 2903040,
235 2903040];
236
237IMFList[8].size := [ # Z-classes of dimension 8
238 10321920,
239 10321920,
240 10321920,
241 2654208,
242 696729600,
243 6912,
244 497664,
245 62208,
246 62208,
247 41472,
248 725760,
249 725760,
250 2592,
251 115200,
252 115200,
253 28800,
254 57600,
255 1440,
256 1440,
257 1152,
258 1152,
259 3456,
260 672,
261 672,
262 672,
263 672];
264
265IMFList[9].size := [ # Z-classes of dimension 9
266 185794560,
267 185794560,
268 185794560,
269 663552,
270 663552,
271 663552,
272 663552,
273 36864,
274 36864,
275 2304,
276 2304,
277 165888,
278 165888,
279 1152,
280 7257600,
281 7257600,
282 7257600,
283 7257600,
284 1440,
285 1440];
286
287IMFList[10].size := [ # Z-classes of dimension 10
288 3715891200,
289 3715891200,
290 3715891200,
291 1857945600,
292 737280,
293 29491200,
294 29491200,
295 122880,
296 122880,
297 7680,
298 7680,
299 23040,
300 23040,
301 4147200,
302 4147200,
303 4147200,
304 4147200,
305 4147200,
306 4147200,
307 2073600,
308 2073600,
309 2073600,
310 480,
311 480,
312 29859840,
313 1866240,
314 1866240,
315 38880,
316 23040,
317 23040,
318 103680,
319 311040,
320 311040,
321 8640,
322 8640,
323 8640,
324 8640,
325 1440,
326 1440,
327 1440,
328 1440,
329 79833600,
330 79833600,
331 2640,
332 2640,
333 2640];
334
335IMFList[11].size := [ # Z-classes of dimension 11
336 81749606400,
337 81749606400,
338 81749606400,
339 958003200,
340 958003200,
341 958003200,
342 958003200,
343 958003200,
344 958003200];
345
346IMFList[12].size := [ # Q-classes of dimension 12
347 1961990553600,
348 9172942848,
349 21499084800,
350 2149908480,
351 78382080,
352 31104,
353 115200,
354 82944000,
355 2400,
356 2880,
357 1440,
358 8640,
359 203212800,
360 903168,
361 2688,
362 2688,
363 60480,
364 4032,
365 12454041600];
366
367IMFList[13].size := [ # Z-classes of dimension 13
368 51011754393600,
369 51011754393600,
370 51011754393600,
371 174356582400,
372 174356582400,
373 174356582400,
374 174356582400,
375 22464,
376 22464,
377 22464,
378 22464,
379 22464,
380 22464,
381 31200,
382 31200,
383 31200,
384 31200];
385
386IMFList[14].size := [ # Q-classes of dimension 14
387 1428329123020800,
388 16855282483200,
389 180592312320,
390 8491392,
391 48384,
392 17418240,
393 2615348736000,
394 10080,
395 80640,
396 4368,
397 2184,
398 4368];
399
400IMFList[15].size := [ # Q-classes of dimension 15
401 42849873690624000,
402 41845579776000,
403 103680,
404 2903040,
405 17915904000,
406 10080];
407
408IMFList[16].size := [ # Q-classes of dimension 16
409 1371195958099968000,
410 970864271032320000,
411 42268920643584,
412 89181388800,
413 17336861982720,
414 1036800,
415 4180377600,
416 95551488,
417 3732480,
418 79626240000,
419 288000,
420 57600,
421 1658880000,
422 3628800,
423 138240,
424 230400,
425 4147200,
426 172800,
427 86400,
428 2880,
429 17280,
430 960,
431 4032,
432 4032,
433 60480,
434 4032,
435 903168,
436 240,
437 240,
438 711374856192000,
439 9792];
440
441IMFList[17].size := [ # Z-classes of dimension 17
442 46620662575398912000,
443 46620662575398912000,
444 46620662575398912000,
445 12804747411456000,
446 12804747411456000,
447 12804747411456000,
448 12804747411456000,
449 12804747411456000,
450 12804747411456000,
451 17825792,
452 17825792,
453 69632,
454 69632,
455 4896,
456 4896,
457 4896,
458 32640,
459 32640,
460 32640,
461 32640,
462 32640,
463 32640,
464 32640,
465 32640];
466
467IMFList[18].size := [ # Q-classes of dimension 18
468 1678343852714360832000,
469 3916800,
470 6687075336192000,
471 50388480,
472 1872381094133760,
473 82944000,
474 105345515520000,
475 28800,
476 8640,
477 43545600,
478 6145155072000,
479 1820786688,
480 225792,
481 9792,
482 4896,
483 243290200817664000,
484 13680];
485
486IMFList[19].size := [ # Z-classes of dimension 19
487 63777066403145711616000,
488 63777066403145711616000,
489 63777066403145711616000,
490 4865804016353280000,
491 4865804016353280000,
492 4865804016353280000,
493 4865804016353280000,
494 4865804016353280000,
495 4865804016353280000];
496
497IMFList[20].size := [ # Q-classes of dimension 20
498 2551082656125828464640000,
499 243468982907043840,
500 656916480,
501 380160,
502 11520,
503 224685731296051200,
504 193491763200,
505 103195607040000,
506 829440,
507 103680,
508 4147200,
509 311040,
510 95551488000000,
511 120000,
512 172800,
513 161280,
514 1774080,
515 10080,
516 102181884343418880000,
517 483840,
518 80640,
519 12746807377920000,
520 15840,
521 13939200,
522 13939200,
523 15840,
524 31680,
525 479001600,
526 15840,
527 15840,
528 13680];
529
530IMFList[21].size := [ # Q-classes of dimension 21
531 107145471557284795514880000,
532 146794677780086784000,
533 2903040,
534 52254720,
535 2903040,
536 1512000,
537 10080,
538 2248001455555215360000];
539
540IMFList[22].size := [ # Q-classes of dimension 22
541 4714400748520531002654720000,
542 110361968640,
543 29658516531078758400,
544 1835540262420480000,
545 5748019200,
546 177408000,
547 3592512000,
548 51704033477769953280000,
549 12144,
550 12144,
551 24288,
552 24288];
553
554IMFList[23].size := [ # Z-classes of dimension 23
555 1240896803466478878720000,
556 1240896803466478878720000,
557 1240896803466478878720000,
558 1240896803466478878720000,
559 1240896803466478878720000,
560 1240896803466478878720000,
561 1240896803466478878720000,
562 1240896803466478878720000,
563 216862434431944426122117120000,
564 216862434431944426122117120000,
565 216862434431944426122117120000,
566 85571854663680,
567 85571854663680,
568 41783132160,
569 41783132160,
570 489646080,
571 489646080,
572 489646080,
573 489646080,
574 489646080,
575 489646080,
576 84610842624000,
577 84610842624000,
578 84610842624000,
579 991533312000,
580 991533312000,
581 991533312000,
582 991533312000];
583
584IMFList[24].size := [ # Q-classes of dimension 24
585 10409396852733332453861621760000,
586 2029289625631919702016000000,
587 8315553613086720000,
588 1728000,
589 1682857609853487022080,
590 940584960,
591 2773263883425546240000,
592 103680,
593 67184640,
594 4270826380475341209600,
595 12287500930252800,
596 59719680,
597 1934917632,
598 34560,
599 1981355655168,
600 1935360,
601 1161216,
602 31022420086661971968000000,
603 137594142720000000,
604 79626240000,
605 143327232000000,
606 145152000,
607 11520000,
608 16588800,
609 230400,
610 1728000,
611 138240,
612 311040,
613 4147200,
614 149299200,
615 17280,
616 247772652503040000,
617 387072,
618 4894274617344,
619 387072,
620 14450688,
621 5806080,
622 14450688,
623 387072,
624 52416,
625 112896,
626 30240,
627 103680,
628 5760,
629 34560,
630 7315660800,
631 32514048,
632 16128,
633 16128,
634 310206304349061120000,
635 134784,
636 74724249600,
637 1872,
638 12441600,
639 17915904000,
640 86400,
641 14400,
642 103680,
643 8064,
644 5376,
645 1820786688,
646 1209600,
647 80640,
648 31680,
649 2640];
650
651IMFList[25].size := [ # Q-classes of dimension 25
652 520469842636666622693081088000000,
653 743008370688000000,
654 2073600,
655 235200,
656 806582922253211271168000000];
657
658IMFList[26].size := [ # Q-classes of dimension 26
659 27064431817106664380040216576000000,
660 666248915354153228697600,
661 1009262592,
662 1946880000,
663 60800435652415979520000,
664 18720000,
665 1268047872,
666 24261120,
667 55024220160,
668 18720000,
669 62400,
670 31200,
671 31200,
672 187200,
673 1046139494400,
674 21777738900836704321536000000];
675
676IMFList[27].size := [ # Q-classes of dimension 27
677 1461479318123759876522171695104000000,
678 2293666840313856000000,
679 725760,
680 22464,
681 609776689223427721003008000000];
682
683IMFList[28].size := [ # Q-classes of dimension 28
684 81842841814930553085241614925824000000,
685 111929817779497742421196800,
686 13570563765858519346053120,
687 231158159769600000000,
688 1704603285530812549693440000,
689 606790169395200,
690 144207476195328,
691 203212800,
692 13005619200,
693 4682022912,
694 38158848,
695 9539712,
696 38158848,
697 13680098021793595392000000,
698 55024220160,
699 29030400,
700 2090188800,
701 349440,
702 1672151040,
703 2419200,
704 101896704,
705 1161216,
706 290304,
707 504000,
708 348364800,
709 80640,
710 2419200,
711 60480,
712 15692092416000,
713 483840,
714 52416,
715 26208,
716 26208,
717 26208,
718 26208,
719 48720,
720 17683523987479403909087232000000];
721
722IMFList[29].size := [ # Q-classes of dimension 29
723 4746884825265972078944013665697792000000,
724 530505719624382117272616960000000];
725
726IMFList[30].size := [ # Q-classes of dimension 30
727 284813089515958324736640819941867520000000,
728 20147367200309593635815424000,
729 6419592322744320000000,
730 1437659997167803170816000000,
731 12487741686153216000000,
732 16444762714275840,
733 95551488000000,
734 180551034077184000,
735 17915904000,
736 3052870564457742336000000,
737 110398464000,
738 110398464000,
739 16855282483200,
740 21499084800,
741 203212800,
742 3502105093579160420352000000,
743 103680,
744 78382080,
745 251073478656000,
746 67184640,
747 8640,
748 74649600,
749 483840,
750 17418240,
751 172800,
752 60480,
753 30240,
754 7257600,
755 483840,
756 48720,
757 29760,
758 59520,
759 16445677308355845635451125760000000];
760
761IMFList[31].size := [ # Q-classes of dimension 31
762 17658411549989416133671730836395786240000000,
763 327360,
764 1488000,
765 526261673867387060334436024320000000];
766
767
768#############################################################################
769##
770##  Elementary  divisors  of the  quadratic  forms  associated  to the  class
771##  representatives of the irreducible maximal finite integral matrix groups,
772##  given in form of lists [ d1, exp1, d2, exp2, ... ].
773##
774
775IMFList[1].elementaryDivisors := [ # Z-classes of dimension 1
776 [1,1]];
777
778IMFList[2].elementaryDivisors := [ # Z-classes of dimension 2
779 [1,2],
780 [1,1,3,1]];
781
782IMFList[3].elementaryDivisors := [ # Z-classes of dimension 3
783 [1,3],
784 [1,1,4,2],
785 [1,2,4,1]];
786
787IMFList[4].elementaryDivisors := [ # Z-classes of dimension 4
788 [1,4],
789 [1,2,2,2],
790 [1,2,3,2],
791 [1,1,3,2,9,1],
792 [1,3,5,1],
793 [1,1,5,3]];
794
795IMFList[5].elementaryDivisors := [ # Z-classes of dimension 5
796 [1,5],
797 [1,4,4,1],
798 [1,1,4,4],
799 [1,1,6,4],
800 [1,4,6,1],
801 [1,1,3,3,6,1],
802 [1,1,2,3,6,1]];
803
804IMFList[6].elementaryDivisors := [ # Z-classes of dimension 6
805 [1,6],
806 [1,4,2,2],
807 [1,2,2,4],
808 [1,4,4,2],
809 [1,2,4,4],
810 [1,1,2,4,4,1],
811 [1,3,3,3],
812 [1,5,3,1],
813 [1,1,3,5],
814 [1,3,3,1,12,2],
815 [1,2,4,1,12,3],
816 [1,1,7,5],
817 [1,5,7,1],
818 [1,3,7,3],
819 [1,3,5,3],
820 [1,3,5,1,10,2],
821 [1,2,2,1,10,3]];
822
823IMFList[7].elementaryDivisors := [ # Z-classes of dimension 7
824 [1,7],
825 [1,6,4,1],
826 [1,1,4,6],
827 [1,1,8,6],
828 [1,6,8,1],
829 [1,6,2,1],
830 [1,1,2,6]];
831
832IMFList[8].elementaryDivisors := [ # Z-classes of dimension 8
833 [1,8],
834 [1,6,2,2],
835 [1,2,2,6],
836 [1,4,2,4],
837 [1,8],
838 [1,4,6,4],
839 [1,4,3,4],
840 [1,3,3,4,9,1],
841 [1,1,3,4,9,3],
842 [1,2,3,4,9,2],
843 [1,7,9,1],
844 [1,1,9,7],
845 [1,1,3,3,9,3,27,1],
846 [1,6,5,2],
847 [1,2,5,6],
848 [1,4,5,4],
849 [1,1,5,6,25,1],
850 [1,2,5,2,15,4],
851 [1,4,3,2,15,2],
852 [1,2,2,2,6,4],
853 [1,4,3,2,6,2],
854 [1,2,2,2,6,2,12,2],
855 [1,1,3,4,21,3],
856 [1,3,7,4,21,1],
857 [1,5,7,2,21,1],
858 [1,1,3,2,21,5]];
859
860IMFList[9].elementaryDivisors := [ # Z-classes of dimension 9
861 [1,9],
862 [1,8,4,1],
863 [1,1,4,8],
864 [1,6,4,3],
865 [1,3,4,6],
866 [1,7,4,2],
867 [1,2,4,7],
868 [1,5,4,4],
869 [1,4,4,5],
870 [1,4,4,4,16,1],
871 [1,1,4,4,16,4],
872 [1,2,4,6,16,1],
873 [1,1,4,6,16,2],
874 [1,2,4,5,16,2],
875 [1,1,10,8],
876 [1,8,10,1],
877 [1,1,5,7,10,1],
878 [1,1,2,7,10,1],
879 [1,1,5,3,10,1,20,4],
880 [1,4,2,1,4,3,20,1]];
881
882IMFList[10].elementaryDivisors := [ # Z-classes of dimension 10
883 [1,10],
884 [1,8,2,2],
885 [1,2,2,8],
886 [1,1,2,8,4,1],
887 [1,4,2,2,4,4],
888 [1,8,4,2],
889 [1,2,4,8],
890 [1,6,4,4],
891 [1,4,4,6],
892 [1,4,4,4,8,2],
893 [1,2,2,4,8,4],
894 [1,4,2,1,4,4,8,1],
895 [1,1,2,4,4,1,8,4],
896 [1,8,3,2],
897 [1,2,3,8],
898 [1,8,6,2],
899 [1,2,6,8],
900 [1,2,2,6,6,2],
901 [1,2,3,6,6,2],
902 [1,1,3,8,9,1],
903 [1,1,3,7,6,1,18,1],
904 [1,1,3,1,6,7,18,1],
905 [1,4,2,2,4,2,12,2],
906 [1,2,3,2,6,2,12,4],
907 [1,5,3,5],
908 [1,4,3,5,9,1],
909 [1,1,3,5,9,4],
910 [1,1,3,4,9,4,27,1],
911 [1,5,3,3,12,2],
912 [1,2,4,3,12,5],
913 [1,5,3,5],
914 [1,5,3,3,6,2],
915 [1,2,2,3,6,5],
916 [1,4,3,4,6,1,18,1],
917 [1,1,3,1,6,4,18,4],
918 [1,2,2,2,6,5,18,1],
919 [1,1,3,5,9,2,18,2],
920 [1,6,6,4],
921 [1,4,6,6],
922 [1,4,2,2,6,4],
923 [1,4,3,2,6,4],
924 [1,9,11,1],
925 [1,1,11,9],
926 [1,7,11,3],
927 [1,3,11,7],
928 [1,5,11,5]];
929
930IMFList[11].elementaryDivisors := [ # Z-classes of dimension 11
931 [1,11],
932 [1,10,4,1],
933 [1,1,4,10],
934 [1,1,12,10],
935 [1,1,3,10],
936 [1,1,4,9,12,1],
937 [1,1,3,9,12,1],
938 [1,10,3,1],
939 [1,10,12,1]];
940
941IMFList[12].elementaryDivisors := [ # Q-classes of dimension 12
942 [1,12],
943 [1,6,2,6],
944 [1,10,3,2],
945 [1,6,3,6],
946 [1,6,3,6],
947 [1,6,2,2,6,4],
948 [1,6,5,6],
949 [1,9,5,3],
950 [1,8,2,1,10,3],
951 [1,8,5,2,10,2],
952 [1,6,15,6],
953 [1,6,15,6],
954 [1,10,7,2],
955 [1,6,7,6],
956 [1,6,2,4,14,2],
957 [1,6,14,6],
958 [1,6,3,4,21,2],
959 [1,6,21,6],
960 [1,11,13,1]];
961
962IMFList[13].elementaryDivisors := [ # Z-classes of dimension 13
963 [1,13],
964 [1,12,4,1],
965 [1,1,4,12],
966 [1,1,14,12],
967 [1,12,14,1],
968 [1,1,7,11,14,1],
969 [1,1,2,11,14,1],
970 [1,6,3,7],
971 [1,7,3,6],
972 [1,7,3,5,12,1],
973 [1,6,3,6,12,1],
974 [1,1,4,5,12,7],
975 [1,1,4,6,12,6],
976 [1,1,2,8,10,4],
977 [1,9,5,3,10,1],
978 [1,1,2,3,10,9],
979 [1,4,5,8,10,1]];
980
981IMFList[14].elementaryDivisors := [ # Q-classes of dimension 14
982 [1,14],
983 [1,12,2,2],
984 [1,7,3,7],
985 [1,7,3,7],
986 [1,8,2,4,6,2],
987 [1,7,3,5,6,2],
988 [1,13,15,1],
989 [1,8,5,5,15,1],
990 [1,8,2,5,30,1],
991 [1,7,13,7],
992 [1,7,3,4,39,3],
993 [1,9,13,4,39,1]];
994
995IMFList[15].elementaryDivisors := [ # Q-classes of dimension 15
996 [1,15],
997 [1,14,16,1],
998 [1,10,3,5],
999 [1,9,2,5,6,1],
1000 [1,12,6,3],
1001 [1,10,7,5]];
1002
1003IMFList[16].elementaryDivisors := [ # Q-classes of dimension 16
1004 [1,16],
1005 [1,16],
1006 [1,8,2,8],
1007 [1,8,2,8],
1008 [1,8,3,8],
1009 [1,8,3,8],
1010 [1,8,3,8],
1011 [1,8,6,8],
1012 [1,8,6,8],
1013 [1,12,5,4],
1014 [1,4,5,12],
1015 [1,10,5,6],
1016 [1,8,5,8],
1017 [1,8,5,8],
1018 [1,8,2,4,10,4],
1019 [1,8,10,8],
1020 [1,8,3,4,15,4],
1021 [1,8,15,8],
1022 [1,8,15,8],
1023 [1,8,15,8],
1024 [1,8,30,8],
1025 [1,8,6,4,30,4],
1026 [1,8,3,4,21,4],
1027 [1,8,3,2,21,6],
1028 [1,8,21,8],
1029 [1,8,21,8],
1030 [1,10,7,4,21,2],
1031 [1,12,11,4],
1032 [1,12,55,4],
1033 [1,15,17,1],
1034 [1,11,17,5]];
1035
1036IMFList[17].elementaryDivisors := [ # Z-classes of dimension 17
1037 [1,17],
1038 [1,16,4,1],
1039 [1,1,4,16],
1040 [1,1,18,16],
1041 [1,16,18,1],
1042 [1,1,9,15,18,1],
1043 [1,1,2,15,18,1],
1044 [1,16,2,1],
1045 [1,1,2,16],
1046 [1,9,4,8],
1047 [1,8,4,9],
1048 [1,1,4,8,16,8],
1049 [1,8,4,8,16,1],
1050 [1,1,9,7,18,1,36,8],
1051 [1,8,2,1,4,8],
1052 [1,8,2,1,4,7,36,1],
1053 [1,1,3,8,6,8],
1054 [1,9,2,7,6,1],
1055 [1,8,2,8,12,1],
1056 [1,8,2,8,6,1],
1057 [1,1,2,8,4,7,12,1],
1058 [1,1,3,7,6,9],
1059 [1,1,6,8,12,8],
1060 [1,1,3,7,6,8,12,1]];
1061
1062IMFList[18].elementaryDivisors := [ # Q-classes of dimension 18
1063 [1,18],
1064 [1,10,2,8],
1065 [1,15,3,3],
1066 [1,13,3,5],
1067 [1,9,3,9],
1068 [1,9,5,9],
1069 [1,16,10,2],
1070 [1,9,5,1,10,8],
1071 [1,9,3,3,15,6],
1072 [1,9,3,7,30,2],
1073 [1,15,7,3],
1074 [1,9,7,9],
1075 [1,9,7,9],
1076 [1,9,17,9],
1077 [1,8,2,5,34,5],
1078 [1,17,19,1],
1079 [1,9,19,9]];
1080
1081IMFList[19].elementaryDivisors := [ # Z-classes of dimension 19
1082 [1,19],
1083 [1,1,4,18],
1084 [1,18,4,1],
1085 [1,1,20,18],
1086 [1,18,20,1],
1087 [1,18,5,1],
1088 [1,1,5,17,20,1],
1089 [1,1,4,17,20,1],
1090 [1,1,5,18]];
1091
1092IMFList[20].elementaryDivisors := [ # Q-classes of dimension 20
1093 [1,20],
1094 [1,10,2,10],
1095 [1,10,2,10],
1096 [1,10,2,10],
1097 [1,12,3,8],
1098 [1,10,3,10],
1099 [1,10,3,6,6,4],
1100 [1,16,6,4],
1101 [1,8,2,8,6,2,12,2],
1102 [1,14,6,5,54,1],
1103 [1,12,6,8],
1104 [1,10,3,2,6,8],
1105 [1,15,5,5],
1106 [1,17,5,3],
1107 [1,15,5,1,30,4],
1108 [1,10,7,10],
1109 [1,10,7,10],
1110 [1,10,7,10],
1111 [1,19,21,1],
1112 [1,18,2,1,42,1],
1113 [1,13,3,1,6,5,42,1],
1114 [1,18,11,2],
1115 [1,18,11,2],
1116 [1,14,11,6],
1117 [1,10,11,10],
1118 [1,10,11,10],
1119 [1,10,2,6,22,4],
1120 [1,10,3,8,33,2],
1121 [1,10,3,4,33,6],
1122 [1,10,33,10],
1123 [1,13,19,6,57,1]];
1124
1125IMFList[21].elementaryDivisors := [ # Q-classes of dimension 21
1126 [1,21],
1127 [1,18,2,3],
1128 [1,15,2,6],
1129 [1,19,3,2],
1130 [1,14,6,6,12,1],
1131 [1,1,2,1,10,19],
1132 [1,13,5,2,15,5,30,1],
1133 [1,20,22,1]];
1134
1135IMFList[22].elementaryDivisors := [ # Q-classes of dimension 22
1136 [1,22],
1137 [1,1,3,19,6,2],
1138 [1,11,3,11],
1139 [1,20,12,2],
1140 [1,10,3,10,12,1,36,1],
1141 [1,21,5,1],
1142 [1,1,5,20,15,1],
1143 [1,21,23,1],
1144 [1,19,23,3],
1145 [1,17,23,5],
1146 [1,15,23,7],
1147 [1,11,23,11]];
1148
1149IMFList[23].elementaryDivisors := [ # Z-classes of dimension 23
1150 [1,1,24,22],
1151 [1,22,24,1],
1152 [1,22,6,1],
1153 [1,1,3,21,24,1],
1154 [1,1,2,21,6,1],
1155 [1,1,3,21,6,1],
1156 [1,1,8,21,24,1],
1157 [1,1,6,22],
1158 [1,23],
1159 [1,22,4,1],
1160 [1,1,4,22],
1161 [1,1,2,22],
1162 [1,22,2,1],
1163 [1,1,8,22],
1164 [1,22,8,1],
1165 [1,1,12,22],
1166 [1,22,12,1],
1167 [1,1,3,21,12,1],
1168 [1,22,3,1],
1169 [1,1,3,22],
1170 [1,1,4,21,12,1],
1171 [1,23],
1172 [1,22,4,1],
1173 [1,1,4,22],
1174 [1,1,2,21,6,1],
1175 [1,22,6,1],
1176 [1,1,3,21,6,1],
1177 [1,1,6,22]];
1178
1179IMFList[24].elementaryDivisors := [ # Q-classes of dimension 24
1180 [1,24],
1181 [1,24],
1182 [1,24],
1183 [1,16,2,8],
1184 [1,12,2,12],
1185 [1,12,2,12],
1186 [1,20,3,4],
1187 [1,20,3,4],
1188 [1,16,3,8],
1189 [1,12,3,12],
1190 [1,12,3,12],
1191 [1,12,2,8,6,4],
1192 [1,12,2,4,6,8],
1193 [1,12,2,4,6,8],
1194 [1,12,6,12],
1195 [1,12,6,12],
1196 [1,12,6,12],
1197 [1,23,25,1],
1198 [1,18,5,6],
1199 [1,12,5,12],
1200 [1,12,5,12],
1201 [1,12,5,12],
1202 [1,16,2,2,10,6],
1203 [1,16,5,4,10,4],
1204 [1,16,10,8],
1205 [1,12,5,4,10,8],
1206 [1,12,10,12],
1207 [1,12,5,4,15,8],
1208 [1,12,15,12],
1209 [1,12,15,12],
1210 [1,12,3,4,15,4,30,4],
1211 [1,20,7,4],
1212 [1,20,7,4],
1213 [1,12,7,12],
1214 [1,12,7,12],
1215 [1,12,2,8,14,4],
1216 [1,12,2,8,14,4],
1217 [1,12,14,12],
1218 [1,12,14,12],
1219 [1,12,13,12],
1220 [1,18,2,6],
1221 [1,12,2,12],
1222 [1,12,10,12],
1223 [1,12,15,4,30,8],
1224 [1,12,30,12],
1225 [1,12,3,8,21,4],
1226 [1,12,21,12],
1227 [1,12,6,8,42,4],
1228 [1,12,42,12],
1229 [1,22,13,2],
1230 [1,22,13,2],
1231 [1,12,3,10,39,2],
1232 [1,12,3,10,39,2],
1233 [1,18,5,2,15,4],
1234 [1,12,3,6,15,6],
1235 [1,12,3,6,15,6],
1236 [1,12,3,4,6,2,30,6],
1237 [1,14,3,2,6,7,30,1],
1238 [1,20,7,4],
1239 [1,18,2,2,14,4],
1240 [1,15,7,6,21,3],
1241 [1,18,5,2,35,4],
1242 [1,12,7,6,35,6],
1243 [1,12,22,12],
1244 [1,16,11,7,55,1]];
1245
1246IMFList[25].elementaryDivisors := [ # Q-classes of dimension 25
1247 [1,25],
1248 [1,20,6,5],
1249 [1,16,6,8,36,1],
1250 [1,16,7,8,14,1],
1251 [1,24,26,1]];
1252
1253IMFList[26].elementaryDivisors := [ # Q-classes of dimension 26
1254 [1,26],
1255 [1,13,3,13],
1256 [1,12,3,14],
1257 [1,2,2,16,10,8],
1258 [1,24,14,2],
1259 [1,26],
1260 [1,1,3,25],
1261 [1,19,3,7],
1262 [1,13,3,13],
1263 [1,13,5,13],
1264 [1,16,5,9,15,1],
1265 [1,12,2,8,10,6],
1266 [1,13,3,3,15,10],
1267 [1,13,3,5,15,6,30,2],
1268 [1,13,3,11,42,2],
1269 [1,25,27,1]];
1270
1271IMFList[27].elementaryDivisors := [ # Q-classes of dimension 27
1272 [1,27],
1273 [1,24,10,3],
1274 [1,19,7,7,28,1],
1275 [1,16,13,10,52,1],
1276 [1,26,28,1]];
1277
1278IMFList[28].elementaryDivisors := [ # Q-classes of dimension 28
1279 [1,28],
1280 [1,14,3,14],
1281 [1,14,2,14],
1282 [1,21,5,7],
1283 [1,24,2,4],
1284 [1,14,3,10,6,4],
1285 [1,14,3,14],
1286 [1,16,5,10,15,2],
1287 [1,16,2,10,30,2],
1288 [1,16,2,8,6,4],
1289 [1,14,13,14],
1290 [1,14,3,8,39,6],
1291 [1,18,13,8,39,2],
1292 [1,26,15,2],
1293 [1,2,2,26],
1294 [1,2,2,26],
1295 [1,2,2,26],
1296 [1,2,2,26],
1297 [1,12,2,14,4,2],
1298 [1,2,3,26],
1299 [1,14,3,14],
1300 [1,4,3,22,6,2],
1301 [1,12,3,4,6,10,18,2],
1302 [1,19,5,9],
1303 [1,21,5,3,10,4],
1304 [1,21,5,1,10,6],
1305 [1,1,3,13,15,13,45,1],
1306 [1,13,3,3,15,11,45,1],
1307 [1,13,3,13,15,1,45,1],
1308 [1,2,5,10,10,1,30,14,90,1],
1309 [1,20,13,6,26,2],
1310 [1,14,3,8,39,6],
1311 [1,13,3,5,39,9,117,1],
1312 [1,14,39,14],
1313 [1,4,2,10,78,14],
1314 [1,9,29,19],
1315 [1,27,29,1]];
1316
1317IMFList[29].elementaryDivisors := [ # Q-classes of dimension 29
1318 [1,29],
1319 [1,28,30,1]];
1320
1321IMFList[30].elementaryDivisors := [ # Q-classes of dimension 30
1322 [1,30],
1323 [1,15,3,15],
1324 [1,6,6,24],
1325 [1,25,3,5],
1326 [1,5,7,25],
1327 [1,15,7,15],
1328 [1,15,5,15],
1329 [1,15,3,9,6,6],
1330 [1,18,6,12],
1331 [1,27,11,3],
1332 [1,21,11,9],
1333 [1,15,11,15],
1334 [1,18,2,10,6,2],
1335 [1,20,3,10],
1336 [1,20,7,10],
1337 [1,28,16,2],
1338 [1,24,4,1,12,5],
1339 [1,15,3,15],
1340 [1,15,3,13,48,2],
1341 [1,24,2,1,6,5],
1342 [1,12,2,11,6,7],
1343 [1,20,3,4,6,5,18,1],
1344 [1,12,2,3,6,15],
1345 [1,14,3,4,6,11,18,1],
1346 [1,15,5,9,30,6],
1347 [1,15,3,5,21,10],
1348 [1,15,3,3,21,12],
1349 [1,24,6,1,42,5],
1350 [1,15,7,9,42,6],
1351 [1,15,29,15],
1352 [1,23,31,7],
1353 [1,15,31,15],
1354 [1,29,31,1]];
1355
1356IMFList[31].elementaryDivisors := [ # Q-classes of dimension 31
1357 [1,31],
1358 [1,20,2,10,4,1],
1359 [1,19,5,12],
1360 [1,30,32,1]];
1361
1362
1363#############################################################################
1364##
1365##  Solvability  of  the  class  representatives  of the  irreducible maximal
1366##  finite integral matrix groups.
1367##
1368
1369IMFList[1].isSolvable := [ # Z-classes of dimension 1
1370 true];
1371
1372IMFList[2].isSolvable := [ # Z-classes of dimension 2
1373 true,
1374 true];
1375
1376IMFList[3].isSolvable := [ # Z-classes of dimension 3
1377 true,
1378 true,
1379 true];
1380
1381IMFList[4].isSolvable := [ # Z-classes of dimension 4
1382 true,
1383 true,
1384 true,
1385 true,
1386 false,
1387 false];
1388
1389IMFList[5].isSolvable := # Z-classes of dimension 5
1390 ListWithIdenticalEntries( 7, false );
1391
1392IMFList[6].isSolvable := [ # Z-classes of dimension 6
1393 false,
1394 false,
1395 false,
1396 true,
1397 true,
1398 false,
1399 true,
1400 false,
1401 false,
1402 true,
1403 true,
1404 false,
1405 false,
1406 false,
1407 false,
1408 false,
1409 false];
1410
1411IMFList[7].isSolvable := # Z-classes of dimension 7
1412 ListWithIdenticalEntries( 7, false );
1413
1414IMFList[8].isSolvable := [ # Z-classes of dimension 8
1415 false,
1416 false,
1417 false,
1418 true,
1419 false,
1420 true,
1421 true,
1422 true,
1423 true,
1424 true,
1425 false,
1426 false,
1427 true,
1428 false,
1429 false,
1430 false,
1431 false,
1432 false,
1433 false,
1434 true,
1435 true,
1436 true,
1437 false,
1438 false,
1439 false,
1440 false];
1441
1442IMFList[9].isSolvable := [ # Z-classes of dimension 9
1443 false,
1444 false,
1445 false,
1446 true,
1447 true,
1448 true,
1449 true,
1450 true,
1451 true,
1452 true,
1453 true,
1454 true,
1455 true,
1456 true,
1457 false,
1458 false,
1459 false,
1460 false,
1461 false,
1462 false];
1463
1464IMFList[10].isSolvable := # Z-classes of dimension 10
1465 ListWithIdenticalEntries( 46, false );
1466
1467IMFList[11].isSolvable := # Z-classes of dimension 11
1468 ListWithIdenticalEntries( 9, false );
1469
1470IMFList[12].isSolvable := [ # Q-classes of dimension 12
1471 false,
1472 true,
1473 false,
1474 false,
1475 false,
1476 true,
1477 false,
1478 false,
1479 false,
1480 false,
1481 false,
1482 false,
1483 false,
1484 false,
1485 false,
1486 false,
1487 false,
1488 false,
1489 false];
1490
1491IMFList[13].isSolvable := # Z-classes of dimension 13
1492 ListWithIdenticalEntries( 17, false );
1493
1494IMFList[14].isSolvable := # Q-classes of dimension 14
1495 ListWithIdenticalEntries( 12, false );
1496
1497IMFList[15].isSolvable := # Q-classes of dimension 15
1498 ListWithIdenticalEntries( 6, false );
1499
1500IMFList[16].isSolvable := [ # Q-classes of dimension 16
1501 false,
1502 false,
1503 true,
1504 false,
1505 false,
1506 false,
1507 false,
1508 true,
1509 false,
1510 false,
1511 false,
1512 false,
1513 false,
1514 false,
1515 false,
1516 false,
1517 false,
1518 false,
1519 false,
1520 false,
1521 false,
1522 true,
1523 false,
1524 false,
1525 false,
1526 false,
1527 false,
1528 true,
1529 true,
1530 false,
1531 false];
1532
1533IMFList[17].isSolvable := [ # Z-classes of dimension 17
1534 false,
1535 false,
1536 false,
1537 false,
1538 false,
1539 false,
1540 false,
1541 false,
1542 false,
1543 true,
1544 true,
1545 true,
1546 true,
1547 false,
1548 false,
1549 false,
1550 false,
1551 false,
1552 false,
1553 false,
1554 false,
1555 false,
1556 false,
1557 false];
1558
1559IMFList[18].isSolvable := # Q-classes of dimension 18
1560 ListWithIdenticalEntries( 17, false );
1561
1562IMFList[19].isSolvable := # Z-classes of dimension 19
1563 ListWithIdenticalEntries( 9, false );
1564
1565IMFList[20].isSolvable := # Q-classes of dimension 20
1566 ListWithIdenticalEntries( 31, false );
1567
1568IMFList[21].isSolvable := # Q-classes of dimension 21
1569 ListWithIdenticalEntries( 8, false );
1570
1571IMFList[22].isSolvable := # Q-classes of dimension 22
1572 ListWithIdenticalEntries( 12, false );
1573
1574IMFList[23].isSolvable := # Z-classes of dimension 23
1575 ListWithIdenticalEntries( 28, false );
1576
1577IMFList[24].isSolvable := [ # Q-classes of dimension 24
1578 false,
1579 false,
1580 false,
1581 false,
1582 false,
1583 false,
1584 false,
1585 false,
1586 false,
1587 false,
1588 false,
1589 false,
1590 true,
1591 false,
1592 true,
1593 false,
1594 false,
1595 false,
1596 false,
1597 false,
1598 false,
1599 false,
1600 false,
1601 false,
1602 false,
1603 false,
1604 false,
1605 false,
1606 false,
1607 false,
1608 false,
1609 false,
1610 false,
1611 false,
1612 false,
1613 false,
1614 false,
1615 false,
1616 false,
1617 false,
1618 false,
1619 false,
1620 false,
1621 false,
1622 false,
1623 false,
1624 false,
1625 false,
1626 false,
1627 false,
1628 false,
1629 false,
1630 true,
1631 false,
1632 false,
1633 false,
1634 false,
1635 false,
1636 false,
1637 false,
1638 false,
1639 false,
1640 false,
1641 false,
1642 false];
1643
1644IMFList[25].isSolvable := # Q-classes of dimension 25
1645 ListWithIdenticalEntries( 5, false );
1646
1647IMFList[26].isSolvable := # Q-classes of dimension 26
1648 ListWithIdenticalEntries( 16, false );
1649
1650IMFList[27].isSolvable := # Q-classes of dimension 27
1651 ListWithIdenticalEntries( 5, false );
1652
1653IMFList[28].isSolvable := # Q-classes of dimension 28
1654 ListWithIdenticalEntries( 37, false );
1655
1656IMFList[29].isSolvable := # Q-classes of dimension 29
1657 ListWithIdenticalEntries( 2, false );
1658
1659IMFList[30].isSolvable := # Q-classes of dimension 30
1660 ListWithIdenticalEntries( 33, false );
1661
1662IMFList[31].isSolvable := # Q-classes of dimension 31
1663 ListWithIdenticalEntries( 4, false );
1664
1665
1666#############################################################################
1667##
1668##  Descriptions of the isomorphism types of the class representatives of the
1669##  irreducible maximal finite integral matrix groups.
1670##
1671
1672IMFList[1].isomorphismType := [ # Z-classes of dimension 1
1673 "C2"];
1674
1675IMFList[2].isomorphismType := [ # Z-classes of dimension 2
1676 "C2 wr C2 = D8",
1677 "C2 x S3 = C2 x W(A2) = D12"];
1678
1679IMFList[3].isomorphismType := [ # Z-classes of dimension 3
1680 "C2 wr S3 = C2 x S4 = W(B3)",
1681 "C2 wr S3 = C2 x S4 = C2 x W(A3)",
1682 "C2 wr S3 = C2 x S4 = C2 x W(A3)"];
1683
1684IMFList[4].isomorphismType := [ # Z-classes of dimension 4
1685 "C2 wr S4 = W(B4)",
1686 "W(F4)",
1687 "D12 wr C2 = (C2 x W(A2)) wr C2",
1688 "(D12 Y D12):C2",
1689 "C2 x S5 = C2 x W(A4)",
1690 "C2 x S5 = C2 x W(A4)"];
1691
1692IMFList[5].isomorphismType := [ # Z-classes of dimension 5
1693 "C2 wr S5 = W(B5)",
1694 "C2 wr S5 = C2 x W(D5)",
1695 "C2 wr S5 = C2 x W(D5)",
1696 "C2 x S6",
1697 "C2 x S6",
1698 "C2 x S6",
1699 "C2 x S6"];
1700
1701IMFList[6].isomorphismType := [ # Z-classes of dimension 6
1702 "C2 wr S6 = W(B6)",
1703 "C2 wr S6 = C2 x W(D6)",
1704 "C2 wr S6 = C2 x W(D6)",
1705 "(C2 x S4) wr C2 = (C2 x W(A3)) wr C2",
1706 "(C2 x S4) wr C2 = (C2 x W(A3)) wr C2",
1707 "subgroup of index 2 of C2 wr S6",
1708 "(C2 x S3) wr S3 = (C2 x W(A2)) wr S3 = D12 wr S3",
1709 "C2 x W(E6)",
1710 "C2 x W(E6)",
1711 "C2 x S3 x S4 = D12 x S4 = C2 x W(A2) x W(A3)",
1712 "C2 x S3 x S4 = D12 x S4 = C2 x W(A2) x W(A3)",
1713 "C2 x S7 = C2 x W(A6)",
1714 "C2 x S7 = C2 x W(A6)",
1715 "C2 x PGL(2,7)",
1716 "C2 x S5",
1717 "C2 x S5",
1718 "C2 x S5"];
1719
1720IMFList[7].isomorphismType := [ # Z-classes of dimension 7
1721 "C2 wr S7 = W(B7)",
1722 "C2 wr S7 = C2 x W(D7)",
1723 "C2 wr S7 = C2 x W(D7)",
1724 "C2 x S8 = C2 x W(A7)",
1725 "C2 x S8 = C2 x W(A7)",
1726 "W(E7)",
1727 "W(E7)"];
1728
1729IMFList[8].isomorphismType := [ # Z-classes of dimension 8
1730 "C2 wr S8 = W(B8)",
1731 "C2 wr S8 = C2 x W(D8)",
1732 "C2 wr S8 = C2 x W(D8)",
1733 "W(F4) wr C2",
1734 "W(E8)",
1735 "S3 x W(F4) = W(A2) x W(F4)",
1736 "D12 wr S4 = (W(A2) x C2) wr S4",
1737 "C2 x (S3 wr S4)",
1738 "C2 x (S3 wr S4)",
1739 "(C2 x (S3 wr C2)) wr C2",
1740 "C2 x S9 = C2 x W(A8)",
1741 "C2 x S9 = C2 x W(A8)",
1742 "C2 x (S3 wr S3)",
1743 "(C2 x S5) wr C2",
1744 "(C2 x S5) wr C2",
1745 "(SL(2,5) Y SL(2,5)):(C2 x C2)",
1746 "C2 x (S5 wr C2)",
1747 "C2 x S5 x S3",
1748 "C2 x S5 x S3",
1749 "W(F4)",
1750 "W(F4)",
1751 "S3 subd W(F4) = (C3 x (SL(2,3) Y SL(2,3)):C2).C2",
1752 "C2 x PGL(2,7)",
1753 "C2 x PGL(2,7)",
1754 "C2 x PGL(2,7)",
1755 "C2 x PGL(2,7)"];
1756
1757IMFList[9].isomorphismType := [ # Z-classes of dimension 9
1758 "C2 wr S9",
1759 "C2 wr S9",
1760 "C2 wr S9",
1761 "(C2 wr S3) wr S3",
1762 "(C2 wr S3) wr S3",
1763 "(C2 wr S3) wr S3",
1764 "(C2 wr S3) wr S3",
1765 "C2^9:(S3 wr C2)",
1766 "C2^9:(S3 wr C2)",
1767 "C2 x (S4 wr C2)",
1768 "C2 x (S4 wr C2)",
1769 "C2 x (S4 wr S3)",
1770 "C2 x (S4 wr S3)",
1771 "C2 x S4 x S4",
1772 "C2 x S10",
1773 "C2 x S10",
1774 "C2 x S10",
1775 "C2 x S10",
1776 "C2 x S6",
1777 "C2 x S6"];
1778
1779IMFList[10].isomorphismType := [ # Z-classes of dimension 10
1780 "C2 wr S10",
1781 "C2 wr S10",
1782 "C2 wr S10",
1783 "C2^9:S10",
1784 "C2^10:S6",
1785 "C2^10:(S5 wr C2)",
1786 "C2^10:(S5 wr C2)",
1787 "C2^10:S5",
1788 "C2^10:S5",
1789 "C2^6:S5",
1790 "C2^6:S5",
1791 "C2^5:S6",
1792 "C2^5:S6",
1793 "(C2 x S6) wr C2",
1794 "(C2 x S6) wr C2",
1795 "(C2 x S6) wr C2",
1796 "(C2 x S6) wr C2",
1797 "(C2 x S6) wr C2",
1798 "(C2 x S6) wr C2",
1799 "C2 x (S6 wr C2)",
1800 "C2 x (S6 wr C2)",
1801 "C2 x (S6 wr C2)",
1802 "(C2^2 x A5):C2",
1803 "(C2^2 x A5):C2",
1804 "(C2 x S3) wr S5",
1805 "C2 x (S3 wr S5)",
1806 "C2 x (S3 wr S5)",
1807 "C2 x (C3^4:C2):S5",
1808 "S3 x (C2 wr S5)",
1809 "S3 x (C2 wr S5)",
1810 "C2 x SU(4,2):C2",
1811 "(C6 x SU(4,2)):C2",
1812 "(C6 x SU(4,2)):C2",
1813 "D12 x S6",
1814 "D12 x S6",
1815 "D12 x S6",
1816 "D12 x S6",
1817 "C2 x S6",
1818 "C2 x S6",
1819 "C2 x S6",
1820 "C2 x S6",
1821 "C2 x S11",
1822 "C2 x S11",
1823 "C2 x PGL(2,11)",
1824 "C2 x PGL(2,11)",
1825 "C2 x PGL(2,11)"];
1826
1827IMFList[11].isomorphismType := [ # Z-classes of dimension 11
1828 "C2 wr S11 = W(B11)",
1829 "C2 wr S11 = C2 x W(D11)",
1830 "C2 wr S11 = C2 x W(D11)",
1831 "C2 x S12 = C2 x W(A11)",
1832 "C2 x S12 = C2 x W(A11)",
1833 "C2 x S12 = C2 x W(A11)",
1834 "C2 x S12 = C2 x W(A11)",
1835 "C2 x S12 = C2 x W(A11)",
1836 "C2 x S12 = C2 x W(A11)"];
1837
1838IMFList[12].isomorphismType := [ # Q-classes of dimension 12
1839 "C2 wr S12 = W(B12)",
1840 "W(F4) wr S3",
1841 "(C2 x W(E6)) wr C2",
1842 "D12 wr S6 = (C2 x S3) wr S6 = (C2 x W(A2)) wr S6",
1843 "C6.PSU(4,3).(C2 x C2)",
1844 "((3+^(1+2):SL(2,3)) x SL(2,3)).C2",
1845 "(C2 x S5) wr C2",
1846 "(C2 x S5) wr S3 = (C2 x W(A4)) wr S3",
1847 "(C2 x D10 x A5):C2",
1848 "(SL(2,5) Y SL(2,3)).C2",
1849 "C2 x S3 x S5",
1850 "(C2 x C3.A6).(C2 x C2)",
1851 "(C2 x S7) wr C2 = (C2 x W(A6)) wr C2",
1852 "(C2 x PGL(2,7)) wr C2",
1853 "(PSL(2,7) x D8):C2",
1854 "(PSL(2,7) x D8):C2",
1855 "C2 x S3 x S7 = C2 x W(A2) x W(A6)",
1856 "C2 x S3 x PGL(2,7)",
1857 "C2 x S13 = C2 x W(A12)"];
1858
1859IMFList[13].isomorphismType := [ # Z-classes of dimension 13
1860 "C2 wr S13 = W(B13)",
1861 "C2 wr S13 = C2 x W(D13)",
1862 "C2 wr S13 = C2 x W(D13)",
1863 "C2 x S14 = C2 x W(A13)",
1864 "C2 x S14 = C2 x W(A13)",
1865 "C2 x S14 = C2 x W(A13)",
1866 "C2 x S14 = C2 x W(A13)",
1867 "C2 x SL(3,3):C2",
1868 "C2 x SL(3,3):C2",
1869 "C2 x SL(3,3):C2",
1870 "C2 x SL(3,3):C2",
1871 "C2 x SL(3,3):C2",
1872 "C2 x SL(3,3):C2",
1873 "C2 x PSL(2,25):C2",
1874 "C2 x PSL(2,25):C2",
1875 "C2 x PSL(2,25):C2",
1876 "C2 x PSL(2,25):C2"];
1877
1878IMFList[14].isomorphismType := [ # Q-classes of dimension 14
1879 "C2 wr S14 = W(B14)",
1880 "W(E7) wr C2",
1881 "(C2 x S3) wr S7 = D12 wr S7 = (C2 x W(A2)) wr S7",
1882 "C2 x G2(3)",
1883 "(SU(3,3) x C4).C2",
1884 "S3 x W(E7) = W(A2) x W(E7)",
1885 "C2 x S15 = C2 x W(A14)",
1886 "C2 x S7",
1887 "C2 x S8",
1888 "C2 x PGL(2,13)",
1889 "C2 x PSL(2,13)",
1890 "C2 x PGL(2,13)"];
1891
1892IMFList[15].isomorphismType := [ # Q-classes of dimension 15
1893 "C2 wr S15 = W(B15)",
1894 "C2 x S16 = C2 x W(A15)",
1895 "C2 x W(E6)",
1896 "C2 x Sp(6,2)",
1897 "(C2 x S6) wr S3 = (C2 x W(A5)) wr S3",
1898 "C2 x S7"];
1899
1900IMFList[16].isomorphismType := [ # Q-classes of dimension 16
1901 "C2 wr S16 = W(B16)",
1902 "W(E8) wr C2",
1903 "W(F4) wr S4",
1904 "2+^(1+8).O+(8,2)",
1905 "(C2 x S3) wr S8 = (C2 x W(A2)) wr S8",
1906 "(SL(2,9) Y SL(2,9)).(C2 x C2)",
1907 "W(E8) x W(A2)",
1908 "(S3 x W(F4)) wr C2 = (W(A2) x W(F4)) wr C2",
1909 "((Sp(4,3) x C3) Y SL(2,3)).C2",
1910 "(C2 x S5) wr S4 = (C2 x W(A4)) wr S4",
1911 "(((SL(2,5) Y SL(2,5)):C2) x D10):C2",
1912 "C2 x (S5 x S5):C2",
1913 "((SL(2,5) Y SL(2,5)):(C2 x C2)) wr C2",
1914 "C2.A10",
1915 "S5 x W(F4)",
1916 "(SL(2,5) Y (D8 Y Q8).A5).C2",
1917 "(C2 x S3 x S5) wr C2",
1918 "S3 x (SL(2,5) Y SL(2,5)):(C2 x C2)",
1919 "(SL(2,5) Y SL(2,9)):C2",
1920 "(C2 x A6).(C2 x C2)",
1921 "(SL(2,5) Y ((SL(2,3) x C3).C2)).C2",
1922 "D120.(C4 x C2)",
1923 "(SL(2,7) Y C2.S3).C2",
1924 "C2 x S3 x PGL(2,7)",
1925 "(C2.A7 Y C2.S3).C2",
1926 "(SL(2,7) Y C2.S3).C2",
1927 "(C2 x PGL(2,7)) wr C2",
1928 "D120.C2",
1929 "D120.C2",
1930 "C2 x S17 = C2 x W(A16)",
1931 "C2 x PGL(2,17)"];
1932
1933IMFList[17].isomorphismType := [ # Z-classes of dimension 17
1934 "C2 wr S17",
1935 "C2 wr S17",
1936 "C2 wr S17",
1937 "C2 x S18",
1938 "C2 x S18",
1939 "C2 x S18",
1940 "C2 x S18",
1941 "C2 x S18",
1942 "C2 x S18",
1943 "C2^17:(C17:C8)",
1944 "C2^17:(C17:C8)",
1945 "C2^9:(C17:C8)",
1946 "C2^9:(C17:C8)",
1947 "C2 x PSL(2,17)",
1948 "C2 x PSL(2,17)",
1949 "C2 x PSL(2,17)",
1950 "C2 x SL(2,16):C4",
1951 "C2 x SL(2,16):C4",
1952 "C2 x SL(2,16):C4",
1953 "C2 x SL(2,16):C4",
1954 "C2 x SL(2,16):C4",
1955 "C2 x SL(2,16):C4",
1956 "C2 x SL(2,16):C4",
1957 "C2 x SL(2,16):C4"];
1958
1959IMFList[18].isomorphismType := [ # Q-classes of dimension 18
1960 "C2 wr S18 = W(B18)",
1961 "(C2 x Sp(4,4)).C2",
1962 "(C2 x W(E6)) wr S3",
1963 "(C2 x 3+^(1+4):Sp(4,3)).C2",
1964 "(C2 x S3) wr S9 = (C2 x W(A2)) wr S9",
1965 "(C2 x S5) wr S3",
1966 "(C2 x S10) wr C2 = (C2 x W(A9)) wr C2",
1967 "(C2 x A5 x A5).(C2 x C2)",
1968 "(C2 x C3.A6).(C2 x C2)",
1969 "C2 x S3 x S10 = C2 x W(A2) x W(A9)",
1970 "(C2 x S7) wr S3 = (C2 x W(A6)) wr S3",
1971 "(C2 x PGL(2,7)) wr S3",
1972 "(C2 x PSL(2,7) x PSL(2,7)).(C2 x C2)",
1973 "C2 x PGL(2,17)",
1974 "C2 x PSL(2,17)",
1975 "C2 x S19 = C2 x W(A18)",
1976 "C2 x PGL(2,19)"];
1977
1978IMFList[19].isomorphismType := [ # Z-classes of dimension 19
1979 "C2 wr S19",
1980 "C2 wr S19",
1981 "C2 wr S19",
1982 "C2 x S20",
1983 "C2 x S20",
1984 "C2 x S20",
1985 "C2 x S20",
1986 "C2 x S20",
1987 "C2 x S20"];
1988
1989IMFList[20].isomorphismType := [ # Q-classes of dimension 20
1990 "C2 wr S20",
1991 "W(F4) wr S5",
1992 "(SU(5,2) x SL(2,3)).C2",
1993 "C2.M12.C2",
1994 "(D8 x S6).C2",
1995 "(C2 x S3) wr S10 = (C2 x W(A2)) wr S10",
1996 "((SU(4,2) x C6):C2) wr C2",
1997 "(C2 x S6) wr S4 = (C2 x W(A5)) wr S4",
1998 "W(F4) x S6 = W(F4) x W(A5)",
1999 "(C2 x SU(4,2)).C2",
2000 "(C2 x S6) wr C2",
2001 "(SU(4,2) x C6).C2",
2002 "(C2 x S5) wr S5 = (C2 x W(A4)) wr S5",
2003 "C2 x 5+^(1+2):GL(2,5)",
2004 "C2 x S5 x S6 = C2 x W(A4) x W(A5)",
2005 "(C2.PSL(3,4)).(C2 x C2)",
2006 "C2.M22.C2",
2007 "C2 x S7",
2008 "C2 x S21 = C2 x W(A20)",
2009 "(C2 x PSL(3,4)).(C2 x S3)",
2010 "C2 x S8",
2011 "(C2 x S11) wr C2 = (C2 x W(A10)) wr C2",
2012 "(PSL(2,11) x D12).C2",
2013 "(C2 x PGL(2,11)) wr C2",
2014 "(C2 x PGL(2,11)) wr C2",
2015 "(PSL(2,11) x D12).C2",
2016 "(SL(2,11) Y SL(2,3)).C2",
2017 "C2 x S3 x S11 = C2 x W(A2) x W(A10)",
2018 "C2 x S3 x PGL(2,11)",
2019 "C2 x S3 x PGL(2,11)",
2020 "C2 x PGL(2,19)"];
2021
2022IMFList[21].isomorphismType := [ # Q-classes of dimension 21
2023 "C2 wr S21",
2024 "W(E7) wr S3",
2025 "W(E7)",
2026 "(C2 x PSU(4,3)).D8",
2027 "C2 x Sp(6,2)",
2028 "(C2 x PSU(3,5)).S3",
2029 "C2 x S7",
2030 "C2 x S22 = C2 x W(A21)"];
2031
2032IMFList[22].isomorphismType := [ # Q-classes of dimension 22
2033 "C2 wr S22 = W(B22)",
2034 "(C2 x PSU(6,2)).S3",
2035 "(C2 x S3) wr S11 = (C2 x W(A2)) wr S11",
2036 "(C2 x S12) wr C2 = (C2 x W(A11)) wr C2",
2037 "C2 x S3 x S12 = C2 x W(A2) x W(A11)",
2038 "(C2 x HS).C2",
2039 "(C2 x Mc).C2",
2040 "C2 x S23 = C2 x W(A22)",
2041 "C2 x PSL(2,23)",
2042 "C2 x PSL(2,23)",
2043 "C2 x PGL(2,23)",
2044 "C2 x PGL(2,23)"];
2045
2046IMFList[23].isomorphismType := [ # Z-classes of dimension 23
2047 "C2 x S24",
2048 "C2 x S24",
2049 "C2 x S24",
2050 "C2 x S24",
2051 "C2 x S24",
2052 "C2 x S24",
2053 "C2 x S24",
2054 "C2 x S24",
2055 "C2 wr S23",
2056 "C2 wr S23",
2057 "C2 wr S23",
2058 "C2 wr M23",
2059 "C2 wr M23",
2060 "C2^12:M23",
2061 "C2^12:M23",
2062 "C2 x M24",
2063 "C2 x M24",
2064 "C2 x M24",
2065 "C2 x M24",
2066 "C2 x M24",
2067 "C2 x M24",
2068 "C2 x Co2",
2069 "C2 x Co2",
2070 "C2 x Co2",
2071 "C2 x Co3",
2072 "C2 x Co3",
2073 "C2 x Co3",
2074 "C2 x Co3"];
2075
2076IMFList[24].isomorphismType := [ # Q-classes of dimension 24
2077 "C2 wr S24 = W(B24)",
2078 "W(E8) wr S3",
2079 "C2.Co1",
2080 "(((SL(2,5) Y SL(2,5)):C2) x A5).C2",
2081 "W(F4) wr S6",
2082 "(C6 x PSU(4,3).C2 Y SL(2,3)).C2",
2083 "(C2 x W(E6)) wr S4",
2084 "((C2 x C3.A6).C2 Y SL(2,3)).C2",
2085 "(Sp(4,3) x 3+^(1+2):SL(2,3)).C2",
2086 "(C2 x S3) wr S12 = (C2 x W(A2)) wr S12",
2087 "(C6.PSU(4,3).(C2 x C2)) wr C2",
2088 "W(F4) x W(E6)",
2089 "((3+^(1+2):SL(2,3) x SL(2,3)).C2) wr C2",
2090 "(C3.S6 x D8).C2",
2091 "(S3 x W(F4)) wr S3",
2092 "(C6.PSL(3,4).C2 Y D8).C2",
2093 "((SL(2,3) Y C4).C2 x PSU(3,3)).C2",
2094 "C2 x S25 = C2 x W(A24)",
2095 "(C2 x S5) wr S6 = (C2 x W(A4)) wr S6",
2096 "(C2 x S5) wr S4",
2097 "((SL(2,5) Y SL(2,5)):(C2 x C2)) wr S3",
2098 "(C2.J2 Y SL(2,5)):C2",
2099 "((C2 x D10 x A5).C2) wr C2",
2100 "((SL(2,5) Y SL(2,3)).C2) wr C2",
2101 "(SL(2,5) Y (D8 Y Q8).A5).C2",
2102 "(((SL(2,5) Y SL(2,5)):C2) x A5):C2",
2103 "W(F4) x S5",
2104 "(SL(2,5) Y (C2 x 3+^(1+2)).GL(2,3)).C2",
2105 "(C2 x S3 x S5) wr C2",
2106 "((C2 x C3.A6).(C2 x C2)) wr C2",
2107 "S3 x (SL(2,5) Y SL(2,3)).C2",
2108 "(C2 x S7) wr S4 = (C2 x W(A6)) wr S4",
2109 "(PSL(2,7) x W(F4)).C2",
2110 "(C2 x PGL(2,7)) wr S4",
2111 "(PSL(2,7) x W(F4)).C2",
2112 "((PSL(2,7) x D8).C2) wr C2",
2113 "W(F4) x S7 = W(F4) x W(A6)",
2114 "((PSL(2,7) x D8).C2) wr C2",
2115 "W(F4) x PGL(2,7)",
2116 "(SL(2,13) Y SL(2,3)).C2",
2117 "(SL(2,7) x PSL(2,7)).C2",
2118 "C6.A7:C2",
2119 "(C3.M10 x SL(2,3)).C2",
2120 "(A5 x ((C3 x D8).C2)).C2",
2121 "(C3.M10 x D8).C2",
2122 "(C2 x S3 x S7) wr C2 = (C2 x W(A2) x W(A6)) wr C2",
2123 "(C2 x S3 x PGL(2,7)) wr C2",
2124 "S3 x ((PSL(2,7) x D8).C2)",
2125 "S3 x ((PSL(2,7) x D8).C2)",
2126 "(C2 x S13) wr C2 = (C2 x W(A12)) wr C2",
2127 "((C2 x PSL(3,3)).C2 x C3).C2",
2128 "C2 x S3 x S13 = C2 x W(A2) x W(A12)",
2129 "(C2 x D78).C12",
2130 "C2 x S5 x W(E6) = C2 x W(A4) x W(E6)",
2131 "(C2 x S3 x S5) wr S3 = ((C2 x W(A2)) x W(A4)) wr S3",
2132 "(C2 x C3.PGL(2,9) x D10).C2",
2133 "S3 x (C2 x D10 x A5).C2",
2134 "(C2 x PSU(4,2)).C2",
2135 "SL(2,7) Y (C2.S4)",
2136 "(SL(2,7) Y Q16).C2",
2137 "(C2 x PGL(2,7)) wr S3",
2138 "C2 x S5 x S7 = C2 x W(A4) x W(A6)",
2139 "C2 x S5 x PGL(2,7)",
2140 "(SL(2,11) Y SL(2,3)).C2",
2141 "C2 x PSL(2,11):C2"];
2142
2143IMFList[25].isomorphismType := [ # Q-classes of dimension 25
2144 "C2 wr S25 = W(B25)",
2145 "(C2 x W(A5)) wr S5 = (C2 x S6) wr S5",
2146 "C2 x (S6 x S6):C2",
2147 "C2 x PGL(2,49)",
2148 "C2 x S26 = C2 x W(A25)"];
2149
2150IMFList[26].isomorphismType := [ # Q-classes of dimension 26
2151 "C2 wr S26 = W(B26)",
2152 "(C2 x S3) wr S13 = (C2 x W(A2)) wr S13",
2153 "(C2 x PGL(3,3):C2) wr C2",
2154 "(C2 x PSL(2,25):C2) wr C2",
2155 "(C2 x S14) wr C2 = (C2 x W(A13)) wr C2",
2156 "(C2 x PSp(4,5)).C2",
2157 "C2 x 3D4(2):C3",
2158 "C2 x PGL(4,3)",
2159 "(C2 x PSp(6,3) x C3).C2",
2160 "C2 x PSp(4,5):C2",
2161 "C2 x PGL(2,25):C2",
2162 "C2 x PSL(2,25):C2",
2163 "C2 x PSL(2,25):C2",
2164 "C2 x S3 x PSL(2,25):C2",
2165 "C2 x S3 x S14 = C2 x W(A2) x W(A13)",
2166 "C2 x S27 = C2 x W(A26)"];
2167
2168IMFList[27].isomorphismType := [ # Q-classes of dimension 27
2169 "C2 wr S27 = W(B27)",
2170 "(C2 x S10) wr S3 = (C2 x W(A9)) wr S3",
2171 "C2 x S9",
2172 "C2 x PGL(3,3):C2",
2173 "C2 x S28 = C2 x W(A27)"];
2174
2175IMFList[28].isomorphismType := [ # Q-classes of dimension 28
2176 "C2 wr S28 = W(B28)",
2177 "(C2 x S3) wr S14 = (C2 x W(A2)) wr S14",
2178 "W(F4) wr S7",
2179 "(C2 x S5) wr S7 = (C2 x W(A4)) wr S7",
2180 "W(E7) wr S4",
2181 "(W(A2) x W(E7)) wr C2",
2182 "(C2 x G2(3)) wr C2",
2183 "(C2 x S7) wr C2",
2184 "(C2 x S8) wr C2",
2185 "((SU(3,3) x C4).C2) wr C2",
2186 "(C2 x PGL(2,13)) wr C2",
2187 "(C2 x PSL(2,13)) wr C2",
2188 "(C2 x PGL(2,13)) wr C2",
2189 "(C2 x S15) wr C2 = (C2 x W(A14)) wr C2",
2190 "(Sp(6,3) x C3).C2",
2191 "(C2.J2 Y SL(2,3)).C2",
2192 "(C2 x PO+(8,2)):S3",
2193 "Sz(8):C3 x C4",
2194 "W(F4) Y W(E7)",
2195 "(C2 x J2).C2",
2196 "(C2 x S3 x G2(3)).C2",
2197 "(PSU(3,3) x (Q8 Y C4).S3).C2",
2198 "S3 x (PSU(3,3) x C4).C2",
2199 "C2 x PSU(3,5):C2",
2200 "W(A4) x W(E7)",
2201 "C2 x S8",
2202 "C2 x J2:C2",
2203 "C2 x W(A2) x S7",
2204 "C2 x W(A2) x W(A14)",
2205 "C2 x W(A2) x S8",
2206 "(SL(2,13) Y SL(2,3)).C2",
2207 "(C2 x W(A2) x PSL(2,13)).C2",
2208 "C2 x W(A2) x PGL(2,13)",
2209 "C2 x W(A2) x PGL(2,13)",
2210 "(C2 x PSL(2,13) x S3).C2",
2211 "C2 x PGL(2,29)",
2212 "C2 x S29 = C2 x W(A28)"];
2213
2214IMFList[29].isomorphismType := [ # Q-classes of dimension 29
2215 "C2 wr S29 = W(B29)",
2216 "C2 x S30 = C2 x W(A29)"];
2217
2218IMFList[30].isomorphismType := [ # Q-classes of dimension 30
2219 "C2 wr S30 = W(B30)",
2220 "(C2 x W(A2)) wr S15",
2221 "(C2 x W(A5)) wr S6",
2222 "(C2 x W(E6)) wr S5",
2223 "(C2 x W(A6)) wr S5",
2224 "(C2 x PGL(2,7)) wr S5",
2225 "(C2 x S5) wr S5",
2226 "((C6 x PSU(4,2)).C2) wr S3",
2227 "(C2 x S6) wr S3",
2228 "(C2 x W(A10)) wr S3",
2229 "(C2 x PGL(2,11)) wr S3",
2230 "(C2 x PGL(2,11)) wr S3",
2231 "(C2 x Sp(6,2)) wr C2",
2232 "(C2 x W(E6)) wr C2",
2233 "(C2 x W(A6)) wr C2",
2234 "(C2 x W(A15)) wr C2",
2235 "(C2 x PSU(4,2)):C2",
2236 "(C2 x C3.PSU(4,3)).(C2 x C2)",
2237 "C2 x W(A2) x W(A15)",
2238 "(C2 x PSU(4,2) x 3+^(1+2):SL(2,3)).C2",
2239 "(C2 x C3.S6).C2",
2240 "C2 x W(A5) x W(E6)",
2241 "(C2 x C3.PSL(3,4)).(C2 x C2)",
2242 "C2 x W(A2) x Sp(6,2)",
2243 "C2 x W(A5) x S5",
2244 "C2 x W(A2) x W(A6)",
2245 "C2 x C3.S7",
2246 "C2 x W(A5) x W(A6)",
2247 "C2 x W(A5) x PGL(2,7)",
2248 "C2 x PGL(2,29)",
2249 "C2 x PSL(2,31)",
2250 "C2 x PGL(2,31)",
2251 "C2 x S31 = C2 x W(A30)"];
2252
2253IMFList[31].isomorphismType := [ # Q-classes of dimension 31
2254 "C2 wr S31 = W(B31)",
2255 "C2 x PSL(2,32):C5",
2256 "C2 x PSL(3,5):C2",
2257 "C2 x S32 = C2 x W(A31)"];
2258
2259
2260#############################################################################
2261##
2262##  Norms  of  the  short  vectors  for  the  class  representatives  of  the
2263##  irreducible maximal finite integral matrix groups.
2264##
2265
2266IMFList[1].minimalNorm := [ # Z-classes of dimension 1
2267 1];
2268
2269IMFList[2].minimalNorm := [ # Z-classes of dimension 2
2270 1,2];
2271
2272IMFList[3].minimalNorm := [ # Z-classes of dimension 3
2273 1,3,2];
2274
2275IMFList[4].minimalNorm := [ # Z-classes of dimension 4
2276 1,2,2,4,2,4];
2277
2278IMFList[5].minimalNorm := [ # Z-classes of dimension 5
2279 1,2,4,5,2,4,3];
2280
2281IMFList[6].minimalNorm := [ # Z-classes of dimension 6
2282 1,2,2,2,3,3,2,2,4,4,6,6,2,4,3,4,5];
2283
2284IMFList[7].minimalNorm := [ # Z-classes of dimension 7
2285 1,2,4,7,2,2,3];
2286
2287IMFList[8].minimalNorm := [ # Z-classes of dimension 8
2288 1,2,2,2,2,4,2,4,6,4,2,8,8,2,4,4,8,8,4,4,3,6,8,6,4,14];
2289
2290IMFList[9].minimalNorm := [ # Z-classes of dimension 9
2291 1,2,4,2,3,2,4,3,4,4,9,6,8,6,9,2,8,4,12,4];
2292
2293IMFList[10].minimalNorm := [ # Z-classes of dimension 10
2294 1,2,2,4,4,2,4,3,4,4,5,4,5,2,4,2,5,3,4,5,6,9,4,8,2,4,6,10,4,8,3,4,6,4,10,6,8,
2295 3,4,4,4,2,10,4,10,6];
2296
2297IMFList[11].minimalNorm := [ # Z-classes of dimension 11
2298 1,2,4,11,5,8,6,2,2];
2299
2300IMFList[12].minimalNorm := [ # Q-classes of dimension 12
2301 1,2,2,2,4,4,3,2,4,4,6,8,2,4,4,8,4,8,2];
2302
2303IMFList[13].minimalNorm := [ # Z-classes of dimension 13
2304 1,2,4,13,2,12,4,3,3,4,4,12,12,5,4,12,6];
2305
2306IMFList[14].minimalNorm := [ # Q-classes of dimension 14
2307 1,2,2,4,3,4,2,4,4,7,6,6];
2308
2309IMFList[15].minimalNorm := [ # Q-classes of dimension 15
2310 1,2,3,3,2,3];
2311
2312IMFList[16].minimalNorm := [ # Q-classes of dimension 16
2313 1,2,2,4,2,4,4,4,6,2,8,4,4,6,4,8,4,8,10,8,12,8,6,8,12,10,4,4,6,2,6];
2314
2315IMFList[17].minimalNorm := [ # Z-classes of dimension 17
2316 1,2,4,17,2,16,4,2,4,4,4,16,6,34,4,6,8,3,4,4,7,10,17,8];
2317
2318IMFList[18].minimalNorm := [ # Q-classes of dimension 18
2319 1,3,2,4,2,3,2,5,6,4,2,4,6,9,6,2,10];
2320
2321IMFList[19].minimalNorm := [ # Z-classes of dimension 19
2322 1,4,2,19,2,2,10,8,9];
2323
2324IMFList[20].minimalNorm := [ # Q-classes of dimension 20
2325 1,2,4,4,3,2,4,2,4,4,3,6,2,4,4,5,8,4,2,4,4,2,4,4,6,8,6,4,8,12,8];
2326
2327IMFList[21].minimalNorm := [ # Q-classes of dimension 21
2328 1,2,3,3,4,21,6,2];
2329
2330IMFList[22].minimalNorm := [ # Q-classes of dimension 22
2331 1,8,2,2,4,3,12,2,4,6,8,12];
2332
2333IMFList[23].minimalNorm := [ # Z-classes of dimension 23
2334 23,2,2,6,4,6,16,11,1,2,4,4,2,16,4,23,4,8,3,8,12,3,4,12,5,4,10,15];
2335
2336IMFList[24].minimalNorm := [ # Q-classes of dimension 24
2337 1,2,4,4,2,4,2,4,4,2,4,4,4,4,4,8,8,2,2,3,4,8,4,4,6,8,6,8,6,8,8,2,4,4,8,4,4,8,
2338 8,12,4,4,8,10,16,4,8,8,16,2,4,4,6,4,4,8,8,6,4,4,4,4,8,12,6];
2339
2340IMFList[25].minimalNorm := [ # Q-classes of dimension 25
2341 1,2,4,6,2];
2342
2343IMFList[26].minimalNorm := [ # Q-classes of dimension 26
2344 1,2,3,5,2,3,8,4,6,5,6,4,6,8,4,2];
2345
2346IMFList[27].minimalNorm := [ # Q-classes of dimension 27
2347 1,2,4,6,2];
2348
2349IMFList[28].minimalNorm := [ # Q-classes of dimension 28
2350 1,2,2,2,2,4,4,4,4,3,7,6,6,2,6,6,6,6,4,8,6,8,6,4,4,4,16,8,4,24,6,8,12,14,26,
2351 28,2];
2352
2353IMFList[29].minimalNorm := [ # Q-classes of dimension 29
2354 1,2];
2355
2356IMFList[30].minimalNorm := [ # Q-classes of dimension 30
2357 1,2,5,2,6,4,3,4,3,2,4,6,3,3,3,2,3,6,4,4,4,4,8,6,6,6,10,4,8,15,8,16,2];
2358
2359IMFList[31].minimalNorm := [ # Q-classes of dimension 31
2360 1,4,5,2];
2361
2362
2363#############################################################################
2364##
2365##  Degrees, i.e. orbit sizes of short vectors, for the class representatives
2366##  of the irreducible maximal finite integral matrix groups.
2367##
2368
2369IMFList[1].degrees := [ # Z-classes of dimension 1
2370 2];
2371
2372IMFList[2].degrees := [ # Z-classes of dimension 2
2373 4,
2374 6];
2375
2376IMFList[3].degrees := [ # Z-classes of dimension 3
2377 6,
2378 8,
2379 12];
2380
2381IMFList[4].degrees := [ # Z-classes of dimension 4
2382 8,
2383 24,
2384 12,
2385 18,
2386 20,
2387 10];
2388
2389IMFList[5].degrees := [ # Z-classes of dimension 5
2390 10,
2391 40,
2392 10,
2393 12,
2394 30,
2395 30,
2396 20];
2397
2398IMFList[6].degrees := [ # Z-classes of dimension 6
2399 12,
2400 60,
2401 12,
2402 24,
2403 16,
2404 32,
2405 18,
2406 72,
2407 54,
2408 36,
2409 24,
2410 14,
2411 42,
2412 42,
2413 20,
2414 30,
2415 24];
2416
2417IMFList[7].degrees := [ # Z-classes of dimension 7
2418 14,
2419 84,
2420 14,
2421 16,
2422 56,
2423 126,
2424 56];
2425
2426IMFList[8].degrees := [ # Z-classes of dimension 8
2427 16,
2428 112,
2429 16,
2430 48,
2431 240,
2432 72,
2433 24,
2434 108,
2435 24,
2436 36,
2437 72,
2438 18,
2439 54,
2440 40,
2441 20,
2442 120,
2443 50,
2444 30,
2445 60,
2446 24,
2447 32,
2448 96,
2449 42,
2450 56,
2451 84,
2452 48];
2453
2454IMFList[9].degrees := [ # Z-classes of dimension 9
2455 18,
2456 144,
2457 18,
2458 36,
2459 24,
2460 36,
2461 18,
2462 48,
2463 [18,144],
2464 72,
2465 32,
2466 96,
2467 36,
2468 48,
2469 20,
2470 90,
2471 90,
2472 90,
2473 30,
2474 90];
2475
2476IMFList[10].degrees := [ # Z-classes of dimension 10
2477 20,
2478 180,
2479 20,
2480 180,
2481 [20,240],
2482 80,
2483 20,
2484 80,
2485 [20,80],
2486 40,
2487 64,
2488 120,
2489 32,
2490 60,
2491 60,
2492 60,
2493 24,
2494 40,
2495 60,
2496 72,
2497 60,
2498 40,
2499 60,
2500 60,
2501 30,
2502 180,
2503 30,
2504 162,
2505 120,
2506 30,
2507 80,
2508 270,
2509 240,
2510 90,
2511 36,
2512 60,
2513 90,
2514 40,
2515 30,
2516 90,
2517 30,
2518 110,
2519 22,
2520 [110,110],
2521 132,
2522 110];
2523
2524IMFList[11].degrees := [ # Z-classes of dimension 11
2525 22,
2526 220,
2527 22,
2528 24,
2529 132,
2530 132,
2531 132,
2532 132,
2533 132];
2534
2535IMFList[12].degrees := [ # Q-classes of dimension 12
2536 24,
2537 72,
2538 144,
2539 36,
2540 756,
2541 216,
2542 40,
2543 60,
2544 [120,300],
2545 360,
2546 60,
2547 270,
2548 84,
2549 84,
2550 [168,168],
2551 [168,168],
2552 126,
2553 126,
2554 156];
2555
2556IMFList[13].degrees := [ # Z-classes of dimension 13
2557 26,
2558 312,
2559 26,
2560 28,
2561 182,
2562 182,
2563 182,
2564 52,
2565 104,
2566 468,
2567 234,
2568 52,
2569 104,
2570 52,
2571 [130,650],
2572 130,
2573 130];
2574
2575IMFList[14].degrees := [ # Q-classes of dimension 14
2576 28,
2577 252,
2578 42,
2579 756,
2580 112,
2581 378,
2582 210,
2583 210,
2584 [420,840],
2585 156,
2586 182,
2587 [182,364]];
2588
2589IMFList[15].degrees := [ # Q-classes of dimension 15
2590 30,
2591 240,
2592 240,
2593 240,
2594 90,
2595 70];
2596
2597IMFList[16].degrees := [ # Q-classes of dimension 16
2598 32,
2599 480,
2600 96,
2601 4320,
2602 48,
2603 720,
2604 720,
2605 144,
2606 960,
2607 80,
2608 600,
2609 [200,240],
2610 240,
2611 2400,
2612 240,
2613 1200,
2614 120,
2615 360,
2616 1440,
2617 180,
2618 480,
2619 [120,240],
2620 336,
2621 [168,252],
2622 1680,
2623 336,
2624 168,
2625 [120,120,120,120],
2626 [120,120,120],
2627 272,
2628 [272,816]];
2629
2630IMFList[17].degrees := [ # Z-classes of dimension 17
2631 34,
2632 544,
2633 34,
2634 36,
2635 306,
2636 306,
2637 306,
2638 306,
2639 306,
2640 34,
2641 34,
2642 34,
2643 2176,
2644 36,
2645 204,
2646 [816,1224],
2647 102,
2648 136,
2649 [510,816],
2650 2040,
2651 816,
2652 1020,
2653 240,
2654 102];
2655
2656IMFList[18].degrees := [ # Q-classes of dimension 18
2657 36,
2658 240,
2659 216,
2660 6480,
2661 54,
2662 60,
2663 180,
2664 72,
2665 180,
2666 270,
2667 126,
2668 126,
2669 336,
2670 272,
2671 204,
2672 342,
2673 342];
2674
2675IMFList[19].degrees := [ # Z-classes of dimension 19
2676 38,
2677 38,
2678 684,
2679 40,
2680 380,
2681 380,
2682 380,
2683 380,
2684 380];
2685
2686IMFList[20].degrees := [ # Q-classes of dimension 20
2687 40,
2688 120,
2689 3960,
2690 3960,
2691 80,
2692 60,
2693 540,
2694 120,
2695 360,
2696 540,
2697 80,
2698 1440,
2699 100,
2700 [300,6000,6000],
2701 300,
2702 112,
2703 [1540,4620],
2704 70,
2705 420,
2706 [840,6720,7560],
2707 420,
2708 220,
2709 [660,660,660,1980,1980,2640,3960],
2710 [220,220],
2711 220,
2712 660,
2713 1320,
2714 330,
2715 [330,330],
2716 330,
2717 [570,1710]];
2718
2719IMFList[21].degrees := [ # Q-classes of dimension 21
2720 42,
2721 378,
2722 672,
2723 1680,
2724 630,
2725 300,
2726 [210,210],
2727 462];
2728
2729IMFList[22].degrees := [ # Q-classes of dimension 22
2730 44,
2731 1782,
2732 66,
2733 264,
2734 396,
2735 2200,
2736 550,
2737 506,
2738 [506,506,506],
2739 [506,506,1012,2024],
2740 [506,1518,2024],
2741 506];
2742
2743IMFList[23].degrees := [ # Z-classes of dimension 23
2744 48,
2745 552,
2746 552,
2747 552,
2748 552,
2749 552,
2750 552,
2751 552,
2752 46,
2753 1012,
2754 46,
2755 46,
2756 46,
2757 46,
2758 [1012,64768],
2759 48,
2760 [552,53130],
2761 1518,
2762 2576,
2763 1518,
2764 2576,
2765 4600,
2766 93150,
2767 4600,
2768 552,
2769 75900,
2770 22356,
2771 552];
2772
2773IMFList[24].degrees := [ # Q-classes of dimension 24
2774 48,
2775 720,
2776 196560,
2777 [3600,8640],
2778 144,
2779 3024,
2780 288,
2781 [2160,6480,12960],
2782 2160,
2783 72,
2784 1512,
2785 864,
2786 432,
2787 144,
2788 216,
2789 [3024,7560],
2790 [4536,6048],
2791 600,
2792 120,
2793 80,
2794 360,
2795 37800,
2796 [240,600],
2797 720,
2798 2400,
2799 1800,
2800 240,
2801 1080,
2802 120,
2803 540,
2804 1080,
2805 168,
2806 [1008,3024],
2807 168,
2808 [1008,3024],
2809 [336,336],
2810 504,
2811 [336,336],
2812 504,
2813 [2184,2184,8736],
2814 [2352,8064,14112],
2815 3024,
2816 1080,
2817 144,
2818 [1080,1080],
2819 252,
2820 252,
2821 [504,504],
2822 [504,504],
2823 312,
2824 [936,5616,8424],
2825 468,
2826 [624,936],
2827 720,
2828 180,
2829 [1080,2160,2700],
2830 [360,900],
2831 [240,1440],
2832 [1008,1008,2016],
2833 336,
2834 252,
2835 420,
2836 420,
2837 1320,
2838 [220,220,660]];
2839
2840IMFList[25].degrees := [ # Q-classes of dimension 25
2841 50,
2842 150,
2843 450,
2844 [350,2450],
2845 650];
2846
2847IMFList[26].degrees := [ # Q-classes of dimension 26
2848 52,
2849 78,
2850 104,
2851 104,
2852 364,
2853 3120,
2854 1638,
2855 4212,
2856 21840,
2857 312,
2858 [2600,3900],
2859 130,
2860 130,
2861 [390,1950],
2862 546,
2863 702];
2864
2865IMFList[27].degrees := [ # Q-classes of dimension 27
2866 54,
2867 270,
2868 756,
2869 468,
2870 756];
2871
2872IMFList[28].degrees := [ # Q-classes of dimension 28
2873 56,
2874 84,
2875 168,
2876 140,
2877 504,
2878 756,
2879 1512,
2880 420,
2881 [840,1680],
2882 224,
2883 312,
2884 364,
2885 [364,728],
2886 420,
2887 6720,
2888 6720,
2889 6720,
2890 6720,
2891 1512,
2892 1260,
2893 17472,
2894 1512,
2895 336,
2896 350,
2897 1260,
2898 1260,
2899 630,
2900 630,
2901 630,
2902 210,
2903 2184,
2904 1092,
2905 [546,1092],
2906 468,
2907 168,
2908 870,
2909 812];
2910
2911IMFList[29].degrees := [ # Q-classes of dimension 29
2912 58,
2913 870];
2914
2915IMFList[30].degrees := [ # Q-classes of dimension 30
2916 60,
2917 90,
2918 72,
2919 360,
2920 70,
2921 210,
2922 100,
2923 810,
2924 120,
2925 330,
2926 [330,330],
2927 330,
2928 480,
2929 480,
2930 140,
2931 480,
2932 240,
2933 [3240,10080],
2934 720,
2935 3240,
2936 180,
2937 1080,
2938 3780,
2939 720,
2940 300,
2941 210,
2942 630,
2943 630,
2944 630,
2945 812,
2946 [930,1860,3720,3720,7440],
2947 930,
2948 930];
2949
2950IMFList[31].degrees := [ # Q-classes of dimension 31
2951 62,
2952 2046,
2953 372,
2954 992];
2955
2956
2957#############################################################################
2958##
2959##  Orbit representatives of short vectors  for the  class representatives of
2960##  the irreducible maximal finite integral matrix groups.
2961##
2962
2963CallFuncList(function()
2964local i;
2965
2966i := IdentityMat( 1 );
2967IMFList[1].orbitReps := [ # Z-classes of dimension 1
2968 i[1]];
2969
2970i := IdentityMat( 2 );
2971IMFList[2].orbitReps := [ # Z-classes of dimension 2
2972 i[1],
2973 i[1]];
2974
2975i := IdentityMat( 3 );
2976IMFList[3].orbitReps := [ # Z-classes of dimension 3
2977 i[1],
2978 i[1],
2979 i[1]];
2980
2981i := IdentityMat( 4 );
2982IMFList[4].orbitReps := [ # Z-classes of dimension 4
2983 i[1],
2984 i[1],
2985 i[1],
2986 i[1],
2987 i[1],
2988 i[1]];
2989
2990i := IdentityMat( 5 );
2991IMFList[5].orbitReps := [ # Z-classes of dimension 5
2992 i[1],
2993 i[1],
2994 i[1],
2995 i[1],
2996 i[1],
2997 i[1],
2998 i[1]];
2999
3000i := IdentityMat( 6 );
3001IMFList[6].orbitReps := [ # Z-classes of dimension 6
3002 i[1],
3003 i[1],
3004 i[1],
3005 i[1],
3006 i[1],
3007 i[1],
3008 i[1],
3009 i[1],
3010 i[1],
3011 i[1],
3012 i[1],
3013 i[1],
3014 i[1],
3015 i[1],
3016 i[1],
3017 i[1],
3018 i[1]];
3019
3020i := IdentityMat( 7 );
3021IMFList[7].orbitReps := [ # Z-classes of dimension 7
3022 i[1],
3023 i[1],
3024 i[1],
3025 i[1],
3026 i[1],
3027 i[1],
3028 i[1]];
3029
3030i := IdentityMat( 8 );
3031IMFList[8].orbitReps := [ # Z-classes of dimension 8
3032 i[1],
3033 i[1],
3034 i[1],
3035 i[1],
3036 i[1],
3037 i[1],
3038 i[1],
3039 i[1],
3040 i[1],
3041 i[1],
3042 i[1],
3043 i[1],
3044 i[1],
3045 i[1],
3046 i[1],
3047 i[1],
3048 i[1],
3049 i[1],
3050 i[1],
3051 i[1],
3052 i[1],
3053 i[1],
3054 i[1],
3055 i[1],
3056 i[1],
3057 i[1]];
3058
3059i := IdentityMat( 9 );
3060IMFList[9].orbitReps := [ # Z-classes of dimension 9
3061 i[1],
3062 i[1],
3063 i[1],
3064 i[1],
3065 i[1],
3066 i[1],
3067 i[1],
3068 i[1],
3069 [i[7]-i[8]+i[9],i[1]],
3070 i[1],
3071 i[1],
3072 i[1],
3073 i[1],
3074 i[1],
3075 i[1],
3076 i[1],
3077 i[1],
3078 i[1],
3079 i[1],
3080 i[1]];
3081
3082i := IdentityMat( 10 );
3083IMFList[10].orbitReps := [ # Z-classes of dimension 10
3084 i[1],
3085 i[1],
3086 i[1],
3087 i[1],
3088 [i[1],i[2]],
3089 i[1],
3090 i[1],
3091 i[1],
3092 [i[1],i[2]],
3093 i[1],
3094 i[1],
3095 i[1],
3096 i[1],
3097 i[1],
3098 i[1],
3099 i[1],
3100 i[1],
3101 i[1],
3102 i[1],
3103 i[1],
3104 i[1],
3105 i[1],
3106 i[1],
3107 i[1],
3108 i[1],
3109 i[1],
3110 i[1],
3111 i[1],
3112 i[1],
3113 i[1],
3114 i[1],
3115 i[1],
3116 i[1],
3117 i[1],
3118 i[1],
3119 i[1],
3120 i[1],
3121 i[1],
3122 i[1],
3123 i[1],
3124 i[1],
3125 i[1],
3126 i[1],
3127 [i[1],i[2]],
3128 i[1],
3129 i[1]];
3130
3131i := IdentityMat( 11 );
3132IMFList[11].orbitReps := [ # Z-classes of dimension 11
3133 i[1],
3134 i[1],
3135 i[1]+i[2],
3136 i[1],
3137 i[1],
3138 i[1]-i[2],
3139 i[1]-i[2],
3140 i[1]-i[2],
3141 i[1]];
3142
3143i := IdentityMat( 12 );
3144IMFList[12].orbitReps := [ # Q-classes of dimension 12
3145 i[1],
3146 i[1],
3147 i[1],
3148 i[1],
3149 i[1],
3150 i[1],
3151 i[1],
3152 i[1],
3153 [i[4],i[1]],
3154 i[1],
3155 i[1],
3156 i[1],
3157 i[1],
3158 i[1],
3159 [i[1],i[7]],
3160 [i[1],i[6]],
3161 i[1],
3162 i[1],
3163 i[1]];
3164
3165i := IdentityMat( 13 );
3166IMFList[13].orbitReps := [ # Z-classes of dimension 13
3167 i[1],
3168 i[1],
3169 i[1]+i[2],
3170 i[1],
3171 i[1],
3172 i[1],
3173 i[1]-i[2],
3174 i[1]-i[3]+i[6],
3175 i[1],
3176 i[1],
3177 i[1],
3178 i[1]+i[2]+i[3]-i[6],
3179 i[1]+i[3],
3180 i[1],
3181 [i[1]+i[2],i[1]],
3182 i[1]+i[2],
3183 i[1]];
3184
3185i := IdentityMat( 14 );
3186IMFList[14].orbitReps := [ # Q-classes of dimension 14
3187 i[1],
3188 i[1],
3189 i[1],
3190 i[1],
3191 i[1],
3192 i[1],
3193 i[1],
3194 i[1],
3195 [i[1],i[6]],
3196 i[1],
3197 i[1],
3198 [i[2],i[1]]];
3199
3200i := IdentityMat( 15 );
3201IMFList[15].orbitReps := [ # Q-classes of dimension 15
3202 i[1],
3203 i[1],
3204 i[1],
3205 i[1],
3206 i[1],
3207 i[1]];
3208
3209i := IdentityMat( 16 );
3210IMFList[16].orbitReps := [ # Q-classes of dimension 16
3211 i[1],
3212 i[1],
3213 i[1],
3214 i[1],
3215 i[1],
3216 i[1],
3217 i[1],
3218 i[1],
3219 i[1],
3220 i[1],
3221 i[1],
3222 [i[1],i[7]],
3223 i[1],
3224 i[1],
3225 i[1],
3226 i[1],
3227 i[1],
3228 i[1],
3229 i[1],
3230 i[1],
3231 i[1],
3232 [i[4],i[1]],
3233 i[1],
3234 [i[9],i[1]],
3235 i[1],
3236 i[1],
3237 i[1],
3238 [i[1],i[2],i[4],i[5]],
3239 [i[1],i[3],i[7]],
3240 i[1],
3241 [i[3],i[1]]];
3242
3243i := IdentityMat( 17 );
3244IMFList[17].orbitReps := [ # Z-classes of dimension 17
3245 i[1],
3246 i[1],
3247 i[1]+i[2],
3248 i[1],
3249 i[1],
3250 i[1],
3251 i[1]-i[2],
3252 i[1]-i[2],
3253 i[1]-i[2],
3254 i[1]-i[2]-i[3]+i[4]+i[7]+i[15],
3255 i[1]-i[2]-i[5]+i[6]-i[12],
3256 i[1]+i[3]-i[4]+i[5]+i[7]-i[8]+i[9]+i[11],
3257 i[1]-i[3],
3258 i[1]-i[3]+i[6]-i[9]+i[11],
3259 i[1],
3260 [i[1]-i[9],i[1]],
3261 i[1]+i[6],
3262 i[1],
3263 [i[1],i[1]-i[5]],
3264 i[1],
3265 i[1],
3266 i[1],
3267 i[1],
3268 i[1]];
3269
3270i := IdentityMat( 18 );
3271IMFList[18].orbitReps := [ # Q-classes of dimension 18
3272 i[1],
3273 i[1],
3274 i[1],
3275 i[1],
3276 i[1],
3277 i[1],
3278 i[1],
3279 i[1],
3280 i[1],
3281 i[1],
3282 i[1],
3283 i[1],
3284 i[1],
3285 i[1],
3286 i[1],
3287 i[1],
3288 i[1]];
3289
3290i := IdentityMat( 19 );
3291IMFList[19].orbitReps := [ # Z-classes of dimension 19
3292 i[1],
3293 i[1],
3294 i[1],
3295 i[1],
3296 i[1],
3297 i[1],
3298 i[1],
3299 i[1],
3300 i[1]];
3301
3302i := IdentityMat( 20 );
3303IMFList[20].orbitReps := [ # Q-classes of dimension 20
3304 i[1],
3305 i[1],
3306 i[1],
3307 i[1],
3308 i[1],
3309 i[1],
3310 i[1],
3311 i[1],
3312 i[1],
3313 i[1],
3314 i[1],
3315 i[1],
3316 i[1],
3317 [i[6]-i[7],i[1],i[2]],
3318 i[1],
3319 i[1],
3320 [i[1],i[2]],
3321 i[1],
3322 i[1],
3323 [i[20],i[5],i[1]],
3324 i[1],
3325 i[1],
3326 [i[1],i[8],i[10],i[12],i[13],i[3],i[2]],
3327 [i[1],i[2]],
3328 i[1],
3329 i[1],
3330 i[1],
3331 i[1],
3332 [i[1],i[3]],
3333 i[1],
3334 [i[5],i[1]]];
3335
3336i := IdentityMat( 21 );
3337IMFList[21].orbitReps := [ # Q-classes of dimension 21
3338 i[1],
3339 i[1],
3340 i[1],
3341 i[1],
3342 i[1],
3343 i[1],
3344 [i[1],i[1]+i[15]+i[20]],
3345 i[1]];
3346
3347i := IdentityMat( 22 );
3348IMFList[22].orbitReps := [ # Q-classes of dimension 22
3349 i[1],
3350 i[1],
3351 i[1],
3352 i[1],
3353 i[1],
3354 i[1],
3355 i[1],
3356 i[1],
3357 [i[1],i[2],i[3]],
3358 [i[1],i[16],i[3],i[4]],
3359 [i[4],i[1],i[2]],
3360 i[1]];
3361
3362i := IdentityMat( 23 );
3363IMFList[23].orbitReps := [ # Z-classes of dimension 23
3364 i[1],
3365 i[1],
3366 i[1],
3367 i[1],
3368 i[1],
3369 i[1],
3370 i[2],
3371 i[1],
3372 i[1],
3373 i[1],
3374 i[1],
3375 i[1],
3376 i[1],
3377 i[12],
3378 [i[12],i[1]],
3379 i[1],
3380 [i[10],i[1]],
3381 i[14],
3382 i[11],
3383 i[6],
3384 i[12],
3385 i[1],
3386 i[2],
3387 i[2],
3388 i[7],
3389 i[1],
3390 i[6],
3391 i[18]];
3392
3393i := IdentityMat( 24 );
3394IMFList[24].orbitReps := [ # Q-classes of dimension 24
3395 i[1],
3396 i[1],
3397 i[1],
3398 [i[2],i[1]],
3399 i[1],
3400 i[1],
3401 i[1],
3402 [i[1],i[18],i[13]],
3403 i[1],
3404 i[1],
3405 i[1],
3406 i[1],
3407 i[1],
3408 i[1],
3409 i[1],
3410 [i[1],i[2]],
3411 [i[2],i[1]],
3412 i[1],
3413 i[1],
3414 i[1],
3415 i[1],
3416 i[1],
3417 [i[4],i[1]],
3418 i[1],
3419 i[1],
3420 i[1],
3421 i[1],
3422 i[1],
3423 i[1],
3424 i[1],
3425 i[1],
3426 i[1],
3427 [i[10],i[1]],
3428 i[1],
3429 [i[7],i[1]],
3430 [i[1],i[7]],
3431 i[1],
3432 [i[1],i[6]],
3433 i[1],
3434 [i[5],i[9],i[1]],
3435 [i[1],i[11],i[6]],
3436 i[1],
3437 i[1],
3438 i[1],
3439 [i[1],i[4]],
3440 i[1],
3441 i[1],
3442 [i[1],i[7]],
3443 [i[1],i[6]],
3444 i[1],
3445 [i[3],i[10],i[1]],
3446 i[1],
3447 [i[11],i[1]],
3448 i[1],
3449 i[1],
3450 [i[4]-i[23]-i[24],i[1],i[2]],
3451 [i[4],i[1]],
3452 [i[10],i[1]],
3453 [i[1],i[14],i[2]],
3454 i[1],
3455 i[1],
3456 i[1],
3457 i[1],
3458 i[1],
3459 [i[2],i[3],i[1]]];
3460
3461i := IdentityMat( 25 );
3462IMFList[25].orbitReps := [ # Q-classes of dimension 25
3463 i[1],
3464 i[1],
3465 i[1],
3466 [i[23],i[1]],
3467 i[1]];
3468
3469i := IdentityMat( 26 );
3470IMFList[26].orbitReps := [ # Q-classes of dimension 26
3471 i[1],
3472 i[1],
3473 i[1]-i[3]+i[6],
3474 i[1],
3475 i[1],
3476 i[1],
3477 i[1],
3478 i[1],
3479 i[1],
3480 i[1],
3481 [i[1],i[2]],
3482 i[1],
3483 i[1],
3484 [i[22]+i[23]+i[26],i[1]],
3485 i[1],
3486 i[1]];
3487
3488i := IdentityMat( 27 );
3489IMFList[27].orbitReps := [ # Q-classes of dimension 27
3490 i[1],
3491 i[1],
3492 i[1],
3493 i[1],
3494 i[1]];
3495
3496i := IdentityMat( 28 );
3497IMFList[28].orbitReps := [ # Q-classes of dimension 28
3498 i[1],
3499 i[1],
3500 i[1],
3501 i[1],
3502 i[1],
3503 i[1],
3504 i[1],
3505 i[1],
3506 [i[1],i[28]],
3507 i[1],
3508 i[1],
3509 i[1],
3510 [i[2],i[1]],
3511 i[1],
3512 i[1],
3513 i[1],
3514 i[1],
3515 i[1],
3516 i[1],
3517 i[1],
3518 i[1],
3519 i[1],
3520 i[1],
3521 i[1],
3522 i[1],
3523 i[1],
3524 i[1],
3525 i[1],
3526 i[1],
3527 i[1],
3528 i[1],
3529 i[1],
3530 [i[1],i[28]],
3531 i[1],
3532 i[1],
3533 i[1],
3534 i[1]];
3535
3536i := IdentityMat( 29 );
3537IMFList[29].orbitReps := [ # Q-classes of dimension 29
3538 i[1],
3539 i[1]];
3540
3541i := IdentityMat( 30 );
3542IMFList[30].orbitReps := [ # Q-classes of dimension 30
3543 i[1],
3544 i[1],
3545 i[1],
3546 i[1],
3547 i[1],
3548 i[1],
3549 i[1],
3550 i[1],
3551 i[1],
3552 i[1],
3553 [i[1],i[2]],
3554 i[1],
3555 i[1],
3556 i[1],
3557 i[1],
3558 i[1],
3559 i[1],
3560 [i[28],i[1]],
3561 i[1],
3562 i[1],
3563 i[1],
3564 i[1],
3565 i[1],
3566 i[1],
3567 i[1],
3568 i[1],
3569 i[1],
3570 i[1],
3571 i[1],
3572 i[1],
3573 [i[5],i[1],i[2],i[7],i[3]],
3574 i[1],
3575 i[1]];
3576
3577i := IdentityMat( 31 );
3578IMFList[31].orbitReps := [ # Q-classes of dimension 31
3579 i[1],
3580 i[1],
3581 i[1],
3582 i[1]];
3583
3584for i in [ 1 .. 31 ] do
3585  MakeImmutable( IMFList[i].size );
3586  MakeImmutable( IMFList[i].elementaryDivisors );
3587  MakeImmutable( IMFList[i].isSolvable );
3588  MakeImmutable( IMFList[i].isomorphismType );
3589  MakeImmutable( IMFList[i].minimalNorm);
3590  MakeImmutable( IMFList[i].degrees );
3591  MakeImmutable( IMFList[i].orbitReps );
3592od;
3593
3594end,[]);
3595
3596if IsHPCGAP then
3597  MakeReadOnlyObj( IMFList );
3598fi;
3599