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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 col9.z GAP library of groups Hans Ulrich Besche ## Bettina Eick, Eamonn O'Brien ## SMALL_GROUP_LIB[ 380 ] := [ 61544599959, 348234891245, 133109170036055, 53853966, 23304232051095, 168239654931521879, 1165099230791, 917070407, 164602677, 350278878023, 71 ]; PROPERTIES_SMALL_GROUPS[ 380 ] := rec( isNilpotent := [ 4, 11 ], isAbelian := [ 4, 11 ], lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 7, -11 ], [ 1, -6 ] ] ), frattFacs := rec( frattFacs := [ 3, 5, 7, 9 ], pos := [ 1, 2, 3, 4 ] ) ); SMALL_GROUP_LIB[ 390 ] := [ 8401232063, 8698171583, 3275604209855, 23888063, 117448895, 32514327, 45961261247, 11280949, 45685223879, 12475774527, 17925194889407, 191 ]; PROPERTIES_SMALL_GROUPS[ 390 ] := rec( isNilpotent := [ 12 ], isAbelian := [ 12 ], lgLength := rec( lgLength := [ 4 ], pos := [ [ 1, -12 ] ] ), frattFacs := rec( frattFacs := [ ], pos := [ ] ) ); SMALL_GROUP_LIB[ 392 ] := [ 15317868231805900355, 19678765308150, 6004933494182966852675, 39076194438608867, 15318707893309660643, 39076194438601091, 39078336448274723 , 50833430681, 349718601785, 53739485781474137, 30755922365829096, 99684155112227, 127464227, 98236868054045, 39058771070624579, 50196452940, 6001779701934198711107, 685454402006243, 268698129877191491, 685454402115107, 268698129877308131, 105329666916146884931, 38508503173263833, 250600713593, 98235976340345, 250600705817, 250600822457, 15311035818197453123, 99639691773155, 39058764828044003, 99639691765379, 99639691882019, 127409970, 127526610, 19627167597042, 922257476101259105775543107, 6001649650563688742435, 361528625176228301335179577667, 78458984771976, 15310662504951572099, 1748597207075, 638005283, 254168451107, 35 ]; PROPERTIES_SMALL_GROUPS[ 392 ] := rec( isNilpotent := [ 2, 8, -10, 13, 16, 33, -35, 44 ], isSupersolvable := [ 1, -10, 12, -16, 18, -35, 41, -44 ], isAbelian := [ 2, 8, 13, 16, 33, 44 ], lgLength := rec( lgLength := [ 2, 3, 4, 5 ], pos := [ [ 39, 41, 43, -44 ], [ 11, -13, 18, -22, 28, -35, 37, -38, 40, 42 ], [ 3, -10, 15, -17, 23, -27, 36 ], [ 1, -2, 14 ] ] ), frattFacs := rec( frattFacs := [ 7, 13, 20, 26, 69, 75, 81, 22, 28, 34, 53, 59, 65, 71, 77 ], pos := [ 1, 2, 7, 10, 11, 12, 13, 14, 15, 16, 17, 22, 27, 32, 35 ] ) ); SMALL_GROUP_LIB[ 396 ] := [ 102772246138509011, 2319536960301019, 43046120919882100191, 653721901901, 110496274976400191, 515807660919100, 5857293200119, 259525856800911, 108702325168400191, 1638800191, 5857292901109, 653734501901, 2319536966501019 , 258888518509011, 918536793315300119, 1638501190, 40597346348870509011, 176835124944337404900119, 7151680000119, 2847626124800119, 1948121600911, 8484459360000119, 1127659964099200119, 1302547211900, 14758400119, 1651200191 , 5857299200119, 653740800911, 2319536969600119, 119 ]; PROPERTIES_SMALL_GROUPS[ 396 ] := rec( isNilpotent := [ 4, 10, 16, 30 ], isSupersolvable := [ 1, -5, 7, -16, 19, -23, 25, -30 ], isAbelian := [ 4, 10, 16, 30 ], lgLength := rec( lgLength := [ 3, 4, 5 ], pos := [ [ 20, -25, 28, -30 ], [ 5, -11, 14, -19, 26, -27 ], [ 1, -4, 12, -13 ] ] ), frattFacs := rec( frattFacs := [ 5, 9, 13, 17, 22, 26, 30, 34, 38, 42, 23, 27 , 31, 35, 39, 43 ], pos := [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16 ] ) ); SMALL_GROUP_LIB[ 405 ] := [ 2772418180565, 6845107573, 20401112437, 8276049677685, 6845113717, 2758727984501, 6845186421, 2772284033397, 2772300810613, 1122781811002741, 16778589, 16793949, 6811567453, 6811570525, 37962734775812949, 343 ]; PROPERTIES_SMALL_GROUPS[ 405 ] := rec( isNilpotent := [ 1, -14, 16 ], isSupersolvable := [ 1, -14, 16 ], isAbelian := [ 1, -2, 5, 11, 16 ], lgLength := rec( lgLength := [ 2, 3, 4, 5 ], pos := [ [ 15, -16 ], [ 2, -4, 11, -14 ], [ 5, -10 ], [ 1 ] ] ), frattFacs := rec( frattFacs := [ 5, 10, 23 ], pos := [ 1, 10, 14 ] ) ); SMALL_GROUP_LIB[ 408 ] := [ 2880961122463745, 43017189985357839, 17551134369248182303, 7043755810560, 17536595737382490127, 7144429885136605020191, 48723123291291679, 48723123290243103, 19879034905034752031, 48723123305971743, 19879034905050480671, 19879034905049432095, 8110646241855955533855, 481912776993955508224, 17550894589763649807, 105432993497359, 43016897941209359, 105432992448783, 105433008177423, 1175411104574082817, 7061062553345, 2880909596430081, 7061061504769, 7061077233409, 7160862465967510257695, 43017482107093023, 17551133493090582559, 43017482106044447, 43017482121773087, 17180918256, 17196646896, 2866856330265072, 7154905202012680359951, 2919193154863904888717343, 17550860131759030303, 955626429158208368896, 389895583487520382394112, 145970735146340367, 42981859580182799, 17510857561808568351, 119417941786655, 14071923482368, 257832255519, 17314087153, 105433058508831, 31 ]; PROPERTIES_SMALL_GROUPS[ 408 ] := rec( isNilpotent := [ 4, 30, -32, 46 ], isSupersolvable := [ 1, -13, 15, -35, 39, -41, 43, -46 ], isAbelian := [ 4, 30, 46 ], lgLength := rec( lgLength := [ 3, 4, 5 ], pos := [ [ 41, 43, -46 ], [ 7, -32, 35, -40, 42 ], [ 1, -6, 33, -34 ] ] ), frattFacs := rec( frattFacs := [ 4, 7, 10, 13, 17, 20, 23, 26, 29, 32, 35, 38 ], pos := [ 1, 2, 3, 4, 5, 6, 13, 14, 19, 24, 29, 32 ] ) ); SMALL_GROUP_LIB[ 414 ] := [ 20755948357387, 1045516855855, 9809201904784723, 120408531, 2526217231, 127436211, 1045520135439, 50025847499, 432848969633167, 527 ]; PROPERTIES_SMALL_GROUPS[ 414 ] := 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[ 420 ] := [ 67689574879145, 23601863014223, 9552454894511951, 54408617897, 268436983721 , 161164513263, 113496695957327, 53892043165, 112745788664051, 67690586630817 , 47668625050612379, 127410114, [ ( 1, 3, 2)( 6, 8,10,12, 7, 9,11), ( 1, 4, 2, 5, 3)( 6, 8,10,12, 7, 9,11) ], 198240974757705551, 83261163321370044239, 68545489268795, 161196355643, 56216623163, 22743962929211, 67475340480495, 198331244152481615, 28362091480279713, 83298965234136347291, 1124327485499, 375203819639, 473821362671675, 267931349181, 472219917990971, 786850072307771, 199004973862100027, 159252539, 107401367628, 23225510828957, 638005307, 383201349, 270221101115, 128397451, 268437473399, 161165002941, 113496696198203, 59 ]; PROPERTIES_SMALL_GROUPS[ 420 ] := rec( isNilpotent := [ 12, 41 ], isSupersolvable := [ 1, -12, 14, -31, 34, -41 ], isSolvable := [ 1, -12, 14, -41 ], isAbelian := [ 12, 41 ], lgLength := rec( lgLength := [ 4, 5, false ], pos := [ [ 16, -19, 24, -41 ], [ 1, -12, 14, -15, 20, -23 ], [ 13 ] ] ), 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[ 424 ] := [ 34407520842076979, 1594787884976, 14572553002124399411, 14588704802261654323, 81149125411379, 34407322485246515, 81149118099763, 81149169281075, 3750861660, 3802042972, 674591064016220, 34369229952954675, 191154888755, 51 ]; PROPERTIES_SMALL_GROUPS[ 424 ] := rec( isNilpotent := [ 2, 9, -11, 14 ], isAbelian := [ 2, 9, 14 ], lgLength := rec( lgLength := [ 2, 3, 4 ], pos := [ [ 13, -14 ], [ 4, -12 ], [ 1, -3 ] ] ), frattFacs := rec( frattFacs := [ 4, 7, 11, 14, 17 ], pos := [ 1, 2, 3, 8, 11 ] ) ); SMALL_GROUP_LIB[ 440 ] := [ 1119386438976503009, 959548723703009, 955203597309003, 2862714074103009, 1266596429843500039, 724173703900, 492530025187342700309, 2544060429000309, 1119386421262600309, 2544060428900309, 2544060430400309, 2181120200309, 2181121600309, 422193481729900309, 419017212326909003, 2027753667805254700039 , 10473988160200039, 10473988160100039, 4608554852416300039, 10473988161600039, 4608554852417800039, 4608554852417700039, 2027764135125057900039, 1259586274933100309, 6506099400309, 2862696053000309, 6506099300309, 6506100800309, 420285980686700903, 2170893000903, 955195406600903, 2170892900903, 2170894400903, 557302389563413100039, 2878627859400039, 1266596339733000039, 2878627859300039, 2878627860800039, 1638500390, 1640000390, 317916776300390, 5782745600039, 4609156079885000039, 5734400039, 952312640100903, 4608531063008100039, 23804377600039, 14758400039 , 4928000093, 6542150400039, 39 ]; PROPERTIES_SMALL_GROUPS[ 440 ] := rec( isNilpotent := [ 6, 39, -41, 51 ], isAbelian := [ 6, 39, 51 ], lgLength := rec( lgLength := [ 3, 4, 5 ], pos := [ [ 42, 44, 47, -51 ], [ 7, -14, 17, -41, 43, 45, -46 ], [ 1, -6, 15, -16 ] ] ), frattFacs := rec( frattFacs := [ 4, 7, 10, 13, 16, 19, 23, 26, 29, 32, 35, 38 , 41, 44, 47 ], pos := [ 1, 2, 3, 4, 5, 6, 11, 14, 15, 16, 23, 28, 33, 38, 41 ] ) ); SMALL_GROUP_LIB[ 441 ] := [ 57943285009775, 297275591, 131390662751, 669023, 297314471, 131129219375, 135225989423, 665275, 2049173279, 705311, 297333791, 306623519, 287 ]; PROPERTIES_SMALL_GROUPS[ 441 ] := rec( isNilpotent := [ 2, 4, 8, 13 ], isAbelian := [ 2, 4, 8, 13 ], lgLength := rec( lgLength := [ 2, 3, 4 ], pos := [ [ 9, 11, -13 ], [ 3, -4, 6 , -8, 10 ], [ 1, -2, 5 ] ] ), frattFacs := rec( frattFacs := [ 5, 9, 14, 18, 15, 19, 23, 27 ], pos := [ 1, 2, 3, 4, 5, 6, 7, 8 ] ) ); SMALL_GROUP_LIB[ 444 ] := [ 4251639501309491, 9577628968499, 384459108913, 13395705185843, 5947764030427463, 861645564, 2638741940844709427, 9576176099399, 5945028030023219, 2635354081980207431, 14157738565703, 21929066567, 766308095856, 4266594088382051, 30152466503, 913712365, 13395730378823, 71 ]; PROPERTIES_SMALL_GROUPS[ 444 ] := rec( isNilpotent := [ 6, 18 ], isSupersolvable := [ 1, -12, 15, -18 ], isAbelian := [ 6, 18 ], lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 8, 11, -18 ], [ 1, -7, 9, -10 ] ] ), frattFacs := rec( frattFacs := [ 3, 5, 7, 9, 11, 13 ], pos := [ 1, 2, 3, 4, 5 , 6 ] ) );