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GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it
Project: cocalc-sagemath-dev-slelievre
Views: 418346############################################################################# ## #W col14.z GAP library of groups Hans Ulrich Besche ## Bettina Eick, Eamonn O'Brien ## SMALL_GROUP_LIB[ 612 ] := [ 3970169310802931729, 96698869524467743, 2587597558969522979313, 10565622701825, 59147178382174720031, 66375144645460644898800113, 4279493406419321329, 19314433772876032, 158003395297567, 6487204712943377, 4228100582495224305, 17184063985, 158003392155919, 10565754822401, 96698869589479455, 6466313984733201, 59179710693661212959, 17180922352, 96645723597050127, 59089266829926862879, 36162631299792693625119, 2421906181232065048593, 13565227649100238629442158879, 25197103014947391802442015, 178997728117023, 109924964416618783, 31560090783505, 328323466832904479, 67274078525128179999, 21079900888832, 257832255775, 17314087409, 158003458212127, 10565820878609, 96698869621981471 , 287 ]; PROPERTIES_SMALL_GROUPS[ 612 ] := rec( isNilpotent := [ 4, 12, 18, 36 ], isSupersolvable := [ 1, -7, 9, -21, 25, -29, 31, -36 ], isAbelian := [ 4, 12, 18, 36 ], lgLength := rec( lgLength := [ 3, 4, 5 ], pos := [ [ 26, -31, 34, -36 ], [ 7, -13, 16, -19, 21, -25, 32, -33 ], [ 1, -6, 14, -15, 20 ] ] ), frattFacs := rec( frattFacs := [ 5, 9, 13, 17, 22, 26, 30, 34, 38, 42, 46, 50 , 23, 27, 31, 35, 39, 43 ], pos := [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18 ] ) ); SMALL_GROUP_LIB[ 616 ] := [ 3115591283709005, 5606444250105009, 3480980242451500059, 1012532105900, 34202748582600059, 34202748582500059, 21068893213555500059, 34202748584000059 , 21068893213557000059, 21068893213556900059, 12978438219636801900059, 3453558566107500509, 9101325000509, 5606426229000509, 9101324900509, 9101326400509, 1919197169269100905, 5057753800905, 3115579816200905, 5057753700905, 5057755200905, 2144283751751701100059, 5650941561800059, 3480980116296200059, 5650941561700059, 5650941563200059, 1638500590, 1640000590, 622711605100590, 2489840457659000, 55523801600059, 14758400059, 8204800095, 9173420800059, 59 ]; PROPERTIES_SMALL_GROUPS[ 616 ] := rec( isNilpotent := [ 4, 27, -29, 35 ], isSupersolvable := [ 1, -29, 31, -35 ], isAbelian := [ 4, 27, 35 ], lgLength := rec( lgLength := [ 3, 4, 5 ], pos := [ [ 30, -35 ], [ 5, -29 ], [ 1, -4 ] ] ), frattFacs := rec( frattFacs := [ 4, 7, 10, 13, 17, 20, 23, 26, 29 ], pos := [ 1, 2, 3, 4, 11, 16, 21, 26, 29 ] ) ); SMALL_GROUP_LIB[ 620 ] := [ 2398745172332729, 3869856812729, 773479556103, 7469548652729, 4647109748490119, 415533570, 3869156160119, 6428160119, 478514538116103, 9196702237761930119, 23924859840119, 12052800119, 1270080873, 7495273440119, 119 ]; PROPERTIES_SMALL_GROUPS[ 620 ] := rec( isNilpotent := [ 6, 15 ], isAbelian := [ 6, 15 ], lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 7, -8, 11, -15 ], [ 1, -6, 9, -10 ] ] ), frattFacs := rec( frattFacs := [ 3, 5, 7, 9, 11, 13 ], pos := [ 1, 2, 3, 4, 5 , 6 ] ) ); SMALL_GROUP_LIB[ 621 ] := [ 74843173043, 120184923, 121824715, 74604222683, 11175 ]; PROPERTIES_SMALL_GROUPS[ 621 ] := rec( isAbelian := [ 1, -2, 5 ], lgLength := rec( lgLength := [ 2, 3, 4 ], pos := [ [ 5 ], [ 2, -4 ], [ 1 ] ] ), frattFacs := rec( frattFacs := [ 4, 8 ], pos := [ 1, 4 ] ) ); SMALL_GROUP_LIB[ 625 ] := [ 201612807, 322563, 1600521, 1001600523, 322565, 200322573, 322584, 201600537, 201600538, 201601050, 513, 520, 320521, 320524, 0 ]; PROPERTIES_SMALL_GROUPS[ 625 ] := rec( isAbelian := [ 1, -2, 5, 11, 15 ], lgLength := rec( lgLength := [ 1, 2, 3, 4 ], pos := [ [ 15 ], [ 2, -4, 11, -14 ], [ 5, -10 ], [ 1 ] ] ), frattFacs := rec( frattFacs := [ 5, 10, 23 ], pos := [ 1, 10, 14 ] ) ); SMALL_GROUP_LIB[ 630 ] := [ 152099759386127, 52255843243475, 32111003127285203, 81163042319, 402209074703, 241427770965, 254519226074579, 50967292657219, 32616817788915787, 32312941124719087, 20550626347831310371, 127417891, 80909218067, 82947152147, 50969848596755, 81163524431, 50968064969039, 52255843476755, 32111003127518483, 135364883, 638005523, 383201565, 403993184531, 128397667, 402209556815, 241428253077, 254519226307859, 80646949699, 253393757181623, 152100771371109, 160347124855503635, 275 ]; PROPERTIES_SMALL_GROUPS[ 630 ] := rec( isNilpotent := [ 12, 32 ], isAbelian := [ 12, 32 ], lgLength := rec( lgLength := [ 4, 5 ], pos := [ [ 13, -15, 20, -23, 28, -32 ] , [ 1, -12, 16, -19, 24, -27 ] ] ), frattFacs := rec( frattFacs := [ 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25 ] , pos := [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 ] ) ); SMALL_GROUP_LIB[ 632 ] := [ 583821297490652285, 12015568841796, 368974114473185213693, 923764394311277, 583819800564772589, 923764357296221, 923764616401613, 18988729734, 19247835126, 7581764123365926, 1460466049613, 77 ]; PROPERTIES_SMALL_GROUPS[ 632 ] := rec( isNilpotent := [ 2, 8, -10, 12 ], isAbelian := [ 2, 8, 12 ], lgLength := rec( lgLength := [ 2, 3, 4 ], pos := [ [ 11, -12 ], [ 3, -10 ], [ 1, -2 ] ] ), frattFacs := rec( frattFacs := [ 4, 7, 11, 14 ], pos := [ 1, 2, 7, 10 ] ) ); SMALL_GROUP_LIB[ 636 ] := [ 2392368204721, 121624352504771, 77353530317390183, 3750864364, 77295993748765635, 49149651527205994855, 126379118321767, 4773374160880, 191154888807, 3977521757, 121624462176359, 103 ]; PROPERTIES_SMALL_GROUPS[ 636 ] := rec( isNilpotent := [ 4, 12 ], isSupersolvable := [ 1, -7, 9, -12 ], isAbelian := [ 4, 12 ], lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 7, -12 ], [ 1, -6 ] ] ), frattFacs := rec( frattFacs := [ 3, 5, 7, 9 ], pos := [ 1, 2, 3, 4 ] ) ); SMALL_GROUP_LIB[ 644 ] := [ 387051125961, 1624822341273, 1053506079606419, 120176210, 8885228881539, 2526216835, 607192019, 1635860247427, 131 ]; PROPERTIES_SMALL_GROUPS[ 644 ] := rec( isNilpotent := [ 4, 9 ], isAbelian := [ 4, 9 ], lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 5, -9 ], [ 1, -4 ] ] ), frattFacs := rec( frattFacs := [ 3, 5, 7, 9 ], pos := [ 1, 2, 3, 4 ] ) ); SMALL_GROUP_LIB[ 650 ] := [ 13587964131927, 76049073119, 8995024396639287, 10658871, 117449183, 32514615, 76325401055, 20863071831, 49612934855135, 479 ]; PROPERTIES_SMALL_GROUPS[ 650 ] := rec( isNilpotent := [ 4, 10 ], isAbelian := [ 4, 10 ], lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 5, 8, -10 ], [ 1, -4, 6, -7 ] ] ), frattFacs := rec( frattFacs := [ 3, 5, 7, 9 ], pos := [ 1, 2, 3, 4 ] ) ); SMALL_GROUP_LIB[ 656 ] := [ 18500930586136473600039, 724191885416896000, 12131844558123500236800039, 28202637682892800039, 18500885324564684800039, 12136610329262049484800039, 12136610329330836070400039, 7961616376041085041766400039, 28202637682790400039, 18500885324564582400039, 28202637682585600039, 18500930379777945600039, 18500885324564377600039, 28202637684121600039, 12757024945325151436800039, 8368608364133338885836800039, 8368608364133338885939200039, 5489807086871470348585267200039, 28202637684019200039, 1103941120062400, 2202850201662400, 1446170855321662400 , 1103941734462400, 723087945830462400, 474345692524544062400, 311170774257535488062400, 204128027912904647782462400, 7958482896115037700812800039, 12131844512862241484800039, 7958490000392360207052800039, 18493665484957593600039, 12131844512862242713600039, 18493665484957798400039, 12131844512862242918400039, 18493665484959027200039, 18500885255779635200039, 42991629516800039, 28202568899379200039, 28202568899174400039, 45189470617600039, 19446684299024998400039, 19446684299022131200039, 12757024900201149849600039, 42991629209600039, 42991632384000039, 1677824001560, 1679360001560, 723086267494401560, 1102265139201560, 12131824297311011328000039, 28191563880960000039, 65444249600039, 39 ]; PROPERTIES_SMALL_GROUPS[ 656 ] := rec( isNilpotent := [ 2, 20, -27, 46, -49, 53 ], isAbelian := [ 2, 20, 23, 46, 53 ], lgLength := rec( lgLength := [ 2, 3, 4, 5 ], pos := [ [ 52, -53 ], [ 11, -14, 19, -22, 31, -32, 35, -49, 51 ], [ 4, -10, 15, -18, 23, -27, 29, -30, 33, -34 , 50 ], [ 1, -3, 28 ] ] ), frattFacs := rec( frattFacs := [ 5, 9, 14, 18, 22, 51, 55, 59, 63 ], pos := [ 1, 2, 3, 19, 27, 28, 35, 45, 49 ] ) ); SMALL_GROUP_LIB[ 660 ] := [ 5719246860901309, 2153010080103019, 1419535471532903019, 3262464101309, 9750131301309, 3252236901903, 6458957843301039, 1086272103901, 6435132230503019, 2146492435309013, 4262912434198500139, 1638501390, [ (1,5,11,9,10)(2,7,6,3,4), (1,2,8)(3,7,9)(5,6,10) ], [ (1,4,3,2,5)(6,7,8,9,10,11,12,13,14,15,16), (1,3)(4,5)(6,10,14,7,11,15,8,12, 16,9,13) ], 5721406323200319, 2176763606413009, 3259609600139, 3262470400319, 2150811667200319, 5734400139, 2142151488101903, 15550550794464101039, 1414533145004909013, 10263355673911369700139, 35699161600139, 11909593600319, 23611161075200139, 5411699200913, 23561494595200139, 39262573408000139, 15583366340700800139, 2167622413900, 14758400139, 4928000193, 9786182400139, 1651200391, 9750137600319, 3252243200913, 6458957846400139, 139 ]; PROPERTIES_SMALL_GROUPS[ 660 ] := rec( isNilpotent := [ 12, 40 ], isSupersolvable := [ 1, -12, 15, 17, -31, 33, -40 ], isSolvable := [ 1, -12, 15, -40 ], isAbelian := [ 12, 40 ], lgLength := rec( lgLength := [ 4, 5, false ], pos := [ [ 15, -20, 25, -40 ], [ 1, -12, 21, -24 ], [ 13, -14 ] ] ), frattFacs := rec( frattFacs := [ 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25 ] , pos := [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 ] ) ); SMALL_GROUP_LIB[ 664 ] := [ 827976966799861889, 15417216924116, 549775431060134844673, 1246949010925169 , 827975045779715825, 1246948965712993, 1246949282198225, 23193852930, 23510338162, 10221534524469410, 1876486152785, 81 ]; PROPERTIES_SMALL_GROUPS[ 664 ] := rec( isNilpotent := [ 2, 8, -10, 12 ], isAbelian := [ 2, 8, 12 ], lgLength := rec( lgLength := [ 2, 3, 4 ], pos := [ [ 11, -12 ], [ 3, -10 ], [ 1, -2 ] ] ), frattFacs := rec( frattFacs := [ 4, 7, 11, 14 ], pos := [ 1, 2, 7, 10 ] ) ); SMALL_GROUP_LIB[ 666 ] := [ 9556125894960983, 14350427473751, 384306547746133, 20077622421335, 294156442177143805, 863325181, 6356749713429423959, 9544671558813527, 14348757935447, 14350450988375, 9556125918475607, 21714077015, 30152467799, 913713661, 20077645935959, 575396176213, 13371754048470359, 1367 ]; PROPERTIES_SMALL_GROUPS[ 666 ] := rec( isNilpotent := [ 6, 18 ], isAbelian := [ 6, 18 ], lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 9, 12, -13, 16, -18 ], [ 1, -8, 10, -11, 14, -15 ] ] ), frattFacs := rec( frattFacs := [ 3, 5, 7, 9, 11, 13 ], pos := [ 1, 2, 3, 4, 5 , 6 ] ) );