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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 col13.z GAP library of groups Hans Ulrich Besche ## Bettina Eick, Eamonn O'Brien ## SMALL_GROUP_LIB[ 1550 ] := [ 1015019451542819, 4512673622819, 3001308360866193, 18654547862819, 4777868769961863573, 12857942819, 1940604482819, 1967133602819, 3007774775522819, 518402819, 12052802819, 1270083573, 18680271842819, 1934707706193, 28954553978162819, 2819 ]; PROPERTIES_SMALL_GROUPS[ 1550 ] := rec( isNilpotent := [ 6, 16 ], isAbelian := [ 6, 16 ], lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 7, 10, -11, 14, -16 ], [ 1, -6, 8, -9, 12, -13 ] ] ), frattFacs := rec( frattFacs := [ 3, 5, 7, 9, 11, 13 ], pos := [ 1, 2, 3, 4, 5 , 6 ] ) ); SMALL_GROUP_LIB[ 1554 ] := [ 12057815459303, 12186783094247, 18737586990527975, 148368785303015, 18839023193089511, 18740130842863079, 4013717891585, 230565001068049895, 18839152160724455, 18740259810498023, 29275841616887477735, 29122162904635602407, 7954662887, 2794883585, 12123226424807, 12059589133799, 30152467943, 4353567233, 46932582741479, 913718845, 46805308164503, 6688015966553, 72933331116572135, 1511 ]; PROPERTIES_SMALL_GROUPS[ 1554 ] := rec( isNilpotent := [ 24 ], isAbelian := [ 24 ], lgLength := rec( lgLength := [ 4 ], pos := [ [ 1, -24 ] ] ), frattFacs := rec( frattFacs := [ ], pos := [ ] ) ); SMALL_GROUP_LIB[ 1564 ] := [ 2815817333971, 3942045217153, 6225795801646959, 46896411759, 4402990387121363, 158309533711053802351, 64719265679199, 2526217055, 1806582749, 3980669105247, 351 ]; PROPERTIES_SMALL_GROUPS[ 1564 ] := 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[ 1566 ] := [ 1701235964856501501222509, 18683391479387652359, 2662684627493495359998853261, 12830129531650311, 11930632505051399, 12813217557010695, 20065496528834578695, 693710419212798093, 442420493541517, 691944702507591821, 2166478826755781200013, 1138943101139939445701, 18683391480420274439, 31422567578237814495495, 1696948689185777836313541, 1086354043961512193645, 692829563803373165, 1783585010746802381327301, 1138942732601456106437, 8177299853575, 8181671287047, 12813779337842951, 7615519021319, 284177619909, 11930633537673479, 442421560584333, 18683391480936585479, 692829530759466605, 29258191126709054642439, 22791 ]; PROPERTIES_SMALL_GROUPS[ 1566 ] := rec( isNilpotent := [ 4, 20, -22, 30 ], isAbelian := [ 4, 20, 30 ], lgLength := rec( lgLength := [ 3, 4, 5 ], pos := [ [ 23, 28, -30 ], [ 5, -7, 10, 14, 16, -22, 24, -27 ], [ 1, -4, 8, -9, 11, -13, 15 ] ] ), frattFacs := rec( frattFacs := [ 4, 7, 10, 13, 17, 20, 23, 26, 29, 32 ], pos := [ 1, 2, 3, 4, 7, 11, 15, 17, 19, 22 ] ) ); SMALL_GROUP_LIB[ 1572 ] := [ 230325331310101, 29673325567227029, 46646510458646410259, 57469587370259, 30132805510080259, 689791567097100, 18873108800259, 155371856771, 29673329851360259, 259 ]; PROPERTIES_SMALL_GROUPS[ 1572 ] := rec( isNilpotent := [ 4, 10 ], isSupersolvable := [ 1, -5, 7, -10 ], isAbelian := [ 4, 10 ], lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 5, -10 ], [ 1, -4 ] ] ), frattFacs := rec( frattFacs := [ 3, 5, 7, 9 ], pos := [ 1, 2, 3, 4 ] ) ); SMALL_GROUP_LIB[ 1575 ] := [ 317445613523699, 1426902261323, 602867216363, 891846635, 201550943855, 1582593816850401, 508835717541181643, 22295356619, 48673842125231723, 383202923, 1004820942513, 979013668084331, 1643 ]; PROPERTIES_SMALL_GROUPS[ 1575 ] := rec( isNilpotent := [ 2, 4, 8, 13 ], isSupersolvable := [ 1, -5, 8, 10, 13 ], isAbelian := [ 2, 4, 8, 13 ], lgLength := rec( lgLength := [ 3, 4, 5 ], pos := [ [ 9, -13 ], [ 3, -8 ], [ 1 , -2 ] ] ), frattFacs := rec( frattFacs := [ 5, 9, 14, 18, 15, 19, 23, 27 ], pos := [ 1, 2, 3, 4, 5, 6, 7, 8 ] ) ); SMALL_GROUP_LIB[ 1580 ] := [ 89927079613959, 2307163283535785, 3650054650284102215, 7485961940807, 141963185742407175, 17719739432255358555719, 7098119664330551, 1460466049847, 58039613817, 2310158208713783, 311 ]; PROPERTIES_SMALL_GROUPS[ 1580 ] := 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[ 1590 ] := [ 191154891615, 11464619247, 304159833013087, 3977529869, 303763016994839, 17875789892327, 483614568913159007, 2911 ]; PROPERTIES_SMALL_GROUPS[ 1590 ] := rec( isNilpotent := [ 8 ], isAbelian := [ 8 ], lgLength := rec( lgLength := [ 4 ], pos := [ [ 1, -8 ] ] ), frattFacs := rec( frattFacs := [ ], pos := [ ] ) ); SMALL_GROUP_LIB[ 1596 ] := [ 789425065502704205, 793282579090289747, 1259926160349253420115, 4495775763311213651, 1263076644382265195603, 1260080023266510388307, 236822620416512369, 7175256242848275563603, 1263080498366563021907, 1260083877250808214611, 2015870322555612637135955, 2011087715254867964691539, 494690718282317, 148448817545585, 791404997784087635, 789527415631359059, 840559421784653, 247267237794161, 1345291730299438163, 49503176486029, 1341534213134163755, 394638772966666367, 2147085613328793293519, 12352516052687, 793278994774413743, 4499626160390787503, 1263080494785149522351, 1260083873669394715055, 494634845639087, 497049501911471, 789427424286333359, 2816903638389167, 791401415524061615, 789523833371333039, 148392944898683, 4495774589902707119, 791403830180333999, 789526248027605423, 1263076643214661441967, 1260080022098906634671, 4694482888741295, 939318583285367, 7498124854912217519, 247269049884059, 7492396879124592047, 10489016818026215855, 11967007268680674785711, 317326492079, 100615717499, 495876820894127, 494700390973871, 148261491571068 , 791401466013452297, 237613179567708509, 1263088955718688139387, 1260098897905458440315, 526539461039, 155035275899, 842912400660911, 31200548743, 840559540821623, 247267356831131, 1345291730358009263, 431 ]; PROPERTIES_SMALL_GROUPS[ 1596 ] := rec( isNilpotent := [ 24, 64 ], isSupersolvable := [ 1, -51, 57, -64 ], isAbelian := [ 24, 64 ], lgLength := rec( lgLength := [ 4, 5 ], pos := [ [ 25, -64 ], [ 1, -24 ] ] ), frattFacs := rec( frattFacs := [ 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49 ], pos := [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24 ] ) ); SMALL_GROUP_LIB[ 1602 ] := [ 79045877306066969, 4282130115346159, 146817398541382704169, 2732811763439, 2673202044655, 32623442985, 4282130954919663, 49283445114905, 6859977379784924911, 7919 ]; PROPERTIES_SMALL_GROUPS[ 1602 ] := 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[ 1608 ] := [ 3074595173366729443661801, 1487703317082261047273, 53152318001966520745, 3450672265322812659689, 5548683221170439500748003, 6639900182915792099, 3846526734835756054853492645, 1487635959779802630533, 2392118616195844745956229, 1487635959778550297957, 1487635959797335286597, 3556714083790430173379, 3556714083789177840803, 5719196249567150568213731, 3556714083807962829443, 5719196249567169353202371, 5719196249567168100869795, 9196467569306808258823638755, 1189138393957939589, 1189138411490595653, 3074701278425408587075493, 137689751272101776580160152, 230481653017220696959312265106, 5548678793195539415605157, 2145938916357458309, 3450670890618558712709, 2145938915105125733, 2145938933890114373, 85468828161163559100517, 33055010269989445, 53152256463577664581, 33055009017656869, 33055027802645509, 8922282613014146605689312995, 3450673640119738646723, 5548683217046296683774659, 3450673640118486314147, 3450673640137271302787, 4124162854294691, 4124181639283331, 10670331960416782548707, 170778331677730076606988, 274611565777008035045720844, 1189102644872220803, 7115763776245766214473, 3081810409171206904435529, 2211885104244609155, 748914917769347, 99002320247420172, 1916548763335671759689, 1333844398706819, 20678515499203, 2145938994002073731, 131 ]; PROPERTIES_SMALL_GROUPS[ 1608 ] := rec( isNilpotent := [ 6, 39, -41, 54 ], isSupersolvable := [ 1, -21, 24, -41, 44, 47, -48, 51, -54 ], isAbelian := [ 6, 39, 54 ], lgLength := rec( lgLength := [ 3, 4, 5 ], pos := [ [ 44, 47, -48, 51, -54 ], [ 7, -43, 45, -46, 49, -50 ], [ 1, -6 ] ] ), 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, 18, 21, 22, 23, 28, 33, 38, 41 ] ) ); SMALL_GROUP_LIB[ 1610 ] := [ 2526218287, 607193471, 4068944263471, 367316293, 4063427067083, 968039504635, 6551040102027695, 1583 ]; PROPERTIES_SMALL_GROUPS[ 1610 ] := rec( isNilpotent := [ 8 ], isAbelian := [ 8 ], lgLength := rec( lgLength := [ 4 ], pos := [ [ 1, -8 ] ] ), frattFacs := rec( frattFacs := [ ], pos := [ ] ) ); SMALL_GROUP_LIB[ 1612 ] := [ 7359233156111, 19400213619929, 31480512300810359, 167132970359, 11859035170436111, 592416968043155850359, 227980370880359, 12052800359, 4587840881, 19528788960359, 359 ]; PROPERTIES_SMALL_GROUPS[ 1612 ] := 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[ 1617 ] := [ 40352046601955, 56341559, 15681595, 24945121955, 24873441955, 1559 ]; PROPERTIES_SMALL_GROUPS[ 1617 ] := rec( isNilpotent := [ 2, 6 ], isAbelian := [ 2, 6 ], lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 4, -6 ], [ 1, -3 ] ] ), frattFacs := rec( frattFacs := [ 3, 5 ], pos := [ 1, 2 ] ) ); SMALL_GROUP_LIB[ 1624 ] := [ 27797774790401548400859, 17117780436648638683, 3721575565232707397, 20092473323033770203, 32716509280921927079079, 93073634948797607, 52984125625518254295398619, 45143586246308147957048171, 17116856460678743915, 27797774782277376870251, 17116856460661533547, 17116856460919689067, 2755808971278187, 2755809212223339, 7267931720463696110443, 32616777291379525073115, 52969732653690199710684327, 107845038967660689575, 107845038967643479207, 175140343322789216375975, 107845038967901634727, 175140343322789474531495, 175140343322789457321127, 284427917556248967976817831, 32630163401190132130667, 12372204802754411, 20092465145991989099, 12372204785544043, 12372205043699563, 6043835510707964339893, 2291610374867637, 3721573591633185461, 2291610357657269, 2291610615812789, 53131610979309850704647335, 20145633726514215079, 32716509223681327364263, 20145633726497004711, 20145633726755160231, 57240875080871, 57241133236391, 151058681161001571495, 32625693119365061585771, 2755317684109479, 32716421301801549864103, 5498506051751, 5208003908181454912, 23033087027385729099035, 23097813116871726146843, 20084222603153419115, 32616830451782988307623, 66407019460296871, 7615518998695, 1412076274425, 12404914931433639, 167 ]; PROPERTIES_SMALL_GROUPS[ 1624 ] := rec( isNilpotent := [ 6, 40, -42, 56 ], isSupersolvable := [ 1, -46, 50, -56 ], isAbelian := [ 6, 40, 56 ], lgLength := rec( lgLength := [ 3, 4, 5 ], pos := [ [ 44, 46, -49, 52, -56 ], [ 8, -15, 18, -43, 45, 50, -51 ], [ 1, -7, 16, -17 ] ] ), frattFacs := rec( frattFacs := [ 4, 7, 10, 13, 16, 19, 23, 26, 29, 32, 35, 38 , 41, 44, 47, 50 ], pos := [ 1, 2, 3, 4, 5, 6, 7, 12, 15, 16, 17, 24, 29, 34, 39, 42 ] ) );