1G:=function() 2local g1,g2,g3,g4,g5,g6,g7,g8,g9,g10,g11,g12,g13,g14,g15,g16,g17,g18,g19,g20,g\ 321,g22,g23,g24,g25,g26,g27,g28,g29,g30,g31,g32,g33,g34,g35,g36,g37,g38,g39,g40\ 4,g41,g42,g43,r,f,g,rws,x; 5f:=FreeGroup(43); 6g:=GeneratorsOfGroup(f); 7g1:=g[1]; 8g2:=g[2]; 9g3:=g[3]; 10g4:=g[4]; 11g5:=g[5]; 12g6:=g[6]; 13g7:=g[7]; 14g8:=g[8]; 15g9:=g[9]; 16g10:=g[10]; 17g11:=g[11]; 18g12:=g[12]; 19g13:=g[13]; 20g14:=g[14]; 21g15:=g[15]; 22g16:=g[16]; 23g17:=g[17]; 24g18:=g[18]; 25g19:=g[19]; 26g20:=g[20]; 27g21:=g[21]; 28g22:=g[22]; 29g23:=g[23]; 30g24:=g[24]; 31g25:=g[25]; 32g26:=g[26]; 33g27:=g[27]; 34g28:=g[28]; 35g29:=g[29]; 36g30:=g[30]; 37g31:=g[31]; 38g32:=g[32]; 39g33:=g[33]; 40g34:=g[34]; 41g35:=g[35]; 42g36:=g[36]; 43g37:=g[37]; 44g38:=g[38]; 45g39:=g[39]; 46g40:=g[40]; 47g41:=g[41]; 48g42:=g[42]; 49g43:=g[43]; 50rws:=SingleCollector(f,[ 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2,\ 51 2, 2, 2, 2, 2, 2, 2, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7 ]); 52r:=[ 53]; 54for x in r do SetPower(rws,x[1],x[2]);od; 55r:=[ 56[28,1,g28^5], 57[31,1,g31^5], 58[34,1,g34^5], 59[35,1,g35^5], 60[37,1,g37^5], 61[39,1,g39^5], 62[41,1,g41^5], 63[42,1,g42^5], 64[43,1,g43^5], 65[26,2,g26^5], 66[28,2,g28^5*g35^3*g41], 67[29,2,g29^5], 68[31,2,g31^5*g37^3*g42], 69[32,2,g32^5], 70[34,2,g34^5*g39^3*g43], 71[36,2,g36^5], 72[38,2,g38^5], 73[40,2,g40^5], 74[26,3,g26^5*g36^4], 75[27,3,g27^5], 76[28,3,g35^4*g41^6], 77[29,3,g29^5*g38^4], 78[30,3,g30^5], 79[31,3,g37^4*g42^6], 80[32,3,g32^5*g40^4], 81[33,3,g33^5], 82[34,3,g39^4*g43^6], 83[35,3,g35^5*g41^4], 84[37,3,g37^5*g42^4], 85[39,3,g39^5*g43^4], 86[26,4,g36^3], 87[27,4,g27^5], 88[29,4,g38^3], 89[30,4,g30^5], 90[32,4,g40^3], 91[33,4,g33^5], 92[35,4,g41^3], 93[36,4,g36^5], 94[37,4,g42^3], 95[38,4,g38^5], 96[39,4,g43^3], 97[40,4,g40^5], 98[41,4,g41^5], 99[42,4,g42^5], 100[43,4,g43^5], 101[6,5,g10^2*g14], 102[7,5,g11^2*g15], 103[8,5,g12^2*g16], 104[9,5,g13^2*g17], 105[10,5,g14^2], 106[11,5,g15^2], 107[12,5,g16^2], 108[13,5,g17^2], 109[18,5,g22], 110[19,5,g23], 111[20,5,g24], 112[21,5,g25], 113[22,5,g18*g22], 114[23,5,g19*g23], 115[24,5,g20*g24], 116[25,5,g21*g25], 117[26,5,g26^6*g29], 118[27,5,g27^6*g30], 119[28,5,g28^6*g31], 120[29,5,g29^6*g32], 121[30,5,g30^6*g33], 122[31,5,g31^6*g34], 123[32,5,g26*g32^6], 124[33,5,g27*g33^6], 125[34,5,g28*g34^6], 126[35,5,g35^6*g37], 127[36,5,g36^6*g38], 128[37,5,g37^6*g39], 129[38,5,g38^6*g40], 130[39,5,g35*g39^6], 131[40,5,g36*g40^6], 132[41,5,g41^6*g42], 133[42,5,g42^6*g43], 134[43,5,g41*g43^6], 135[34,6,g34], 136[39,6,g39], 137[43,6,g43], 138[32,7,g32], 139[34,7,g34^3*g39^6*g43^2], 140[40,7,g40], 141[32,8,g32^3*g40], 142[33,8,g33], 143[34,8,g39*g43^5], 144[39,8,g39^3*g43], 145[32,9,g40^6], 146[33,9,g33^3], 147[39,9,g43^6], 148[40,9,g40^3], 149[43,9,g43^3], 150[31,10,g31], 151[34,10,g34^3], 152[37,10,g37], 153[39,10,g39^3], 154[42,10,g42], 155[43,10,g43^3], 156[29,11,g29], 157[31,11,g31^3*g37^6*g42^2], 158[32,11,g32^3], 159[34,11,g34*g39^2*g43^3], 160[38,11,g38], 161[40,11,g40^3], 162[29,12,g29^3*g38], 163[30,12,g30], 164[31,12,g37*g42^5], 165[32,12,g32*g40^5], 166[33,12,g33^3], 167[34,12,g39^5*g43^4], 168[37,12,g37^3*g42], 169[39,12,g39*g43^5], 170[29,13,g38^6], 171[30,13,g30^3], 172[32,13,g40^2], 173[33,13,g33], 174[37,13,g42^6], 175[38,13,g38^3], 176[39,13,g43^2], 177[40,13,g40], 178[42,13,g42^3], 179[43,13,g43], 180[28,14,g28], 181[31,14,g31], 182[34,14,g34], 183[35,14,g35], 184[37,14,g37], 185[39,14,g39], 186[41,14,g41], 187[42,14,g42], 188[43,14,g43], 189[26,15,g26], 190[28,15,g28^3*g35^6*g41^2], 191[29,15,g29], 192[31,15,g31^3*g37^6*g42^2], 193[32,15,g32], 194[34,15,g34^3*g39^6*g43^2], 195[36,15,g36], 196[38,15,g38], 197[40,15,g40], 198[26,16,g26^3*g36], 199[27,16,g27], 200[28,16,g35*g41^5], 201[29,16,g29^3*g38], 202[30,16,g30], 203[31,16,g37*g42^5], 204[32,16,g32^3*g40], 205[33,16,g33], 206[34,16,g39*g43^5], 207[35,16,g35^3*g41], 208[37,16,g37^3*g42], 209[39,16,g39^3*g43], 210[26,17,g36^6], 211[27,17,g27^3], 212[29,17,g38^6], 213[30,17,g30^3], 214[32,17,g40^6], 215[33,17,g33^3], 216[35,17,g41^6], 217[36,17,g36^3], 218[37,17,g42^6], 219[38,17,g38^3], 220[39,17,g43^6], 221[40,17,g40^3], 222[41,17,g41^3], 223[42,17,g42^3], 224[43,17,g43^3], 225[28,18,g28^5], 226[34,18,g34^5], 227[35,18,g35^5], 228[39,18,g39^5], 229[41,18,g41^5], 230[43,18,g43^5], 231[26,19,g26^5], 232[28,19,g28^5*g35^3*g41], 233[32,19,g32^5], 234[34,19,g34^5*g39^3*g43], 235[36,19,g36^5], 236[40,19,g40^5], 237[26,20,g26^5*g36^4], 238[27,20,g27^5], 239[28,20,g35^4*g41^6], 240[32,20,g32^5*g40^4], 241[33,20,g33^5], 242[34,20,g39^4*g43^6], 243[35,20,g35^5*g41^4], 244[39,20,g39^5*g43^4], 245[26,21,g36^3], 246[27,21,g27^5], 247[32,21,g40^3], 248[33,21,g33^5], 249[35,21,g41^3], 250[36,21,g36^5], 251[39,21,g43^3], 252[40,21,g40^5], 253[41,21,g41^5], 254[43,21,g43^5], 255[31,22,g31^5], 256[34,22,g34^5], 257[37,22,g37^5], 258[39,22,g39^5], 259[42,22,g42^5], 260[43,22,g43^5], 261[29,23,g29^5], 262[31,23,g31^5*g37^3*g42], 263[32,23,g32^5], 264[34,23,g34^5*g39^3*g43], 265[38,23,g38^5], 266[40,23,g40^5], 267[29,24,g29^5*g38^4], 268[30,24,g30^5], 269[31,24,g37^4*g42^6], 270[32,24,g32^5*g40^4], 271[33,24,g33^5], 272[34,24,g39^4*g43^6], 273[37,24,g37^5*g42^4], 274[39,24,g39^5*g43^4], 275[29,25,g38^3], 276[30,25,g30^5], 277[32,25,g40^3], 278[33,25,g33^5], 279[37,25,g42^3], 280[38,25,g38^5], 281[39,25,g43^3], 282[40,25,g40^5], 283[42,25,g42^5], 284[43,25,g43^5], 285[27,26,g36], 286[28,26,g35], 287[28,27,g41^2], 288[35,27,g41^6], 289[36,28,g41^6], 290[30,29,g38], 291[31,29,g37], 292[31,30,g42^2], 293[37,30,g42^6], 294[38,31,g42^6], 295[33,32,g40], 296[34,32,g39], 297[34,33,g43^2], 298[39,33,g43^6], 299[40,34,g43^6], 300]; 301for x in r do SetCommutator(rws,x[1],x[2],x[3]);od; 302return GroupByRwsNC(rws); 303end; 304G:=G(); 305Print("#I A group of order ",Size(G)," has been defined.\n"); 306Print("#I It is called G\n"); 307