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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 col23.z GAP library of groups Hans Ulrich Besche ## Bettina Eick, Eamonn O'Brien ## SMALL_GROUP_LIB[ 940 ] := [ 6476340209671, 97078844329225, 91457075261904327, 2296943346, 6079013933168647, 268566423861011716551, 303945903761079, 103303865015, 7020653081, 97294402487223, 183 ]; PROPERTIES_SMALL_GROUPS[ 940 ] := 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[ 944 ] := [ 516211523079297022904217, 9603399226736208904, 546834237949523399161, 516210922869544168549369, 487303675991219344536248313, 487303675991853815744176121, 460014670136310523886479824281, 546834237948867042393, 516210922869543512192601, 546834237947554328857, 516211521175891275402009, 516210922869542199479065, 546834237957399680377, 504364625643475405767660729, 476120206607441147656763509337, 476120206607441147657419866105, 449457475037424443751978556519833, 546834237956743323609, 10173048794680804, 20313843561233572, 19186420093957171172, 10173052732821412, 9593226187776141732, 9056005516918040599556, 8548869207610017891471780, 8070132531983495658826775780, 516210922235082805973081, 579272299477182137, 546833603498006174393, 546833603496693460857, 599554036034203705, 534284560428134344527737, 534284560428115966538233, 504364625044534576294815225, 579272297508111833, 579272317855171641, 10754405646986, 10764250998506, 9593215430088525770, 10162306203270506, 613047723020345, 57 ]; PROPERTIES_SMALL_GROUPS[ 944 ] := rec( isNilpotent := [ 2, 19, -26, 37, -40, 42 ], isAbelian := [ 2, 19, 22, 37, 42 ], lgLength := rec( lgLength := [ 2, 3, 4, 5 ], pos := [ [ 41, -42 ], [ 10, -13, 18, -21, 27, -40 ], [ 3, -9, 14, -17, 22, -26 ], [ 1, -2 ] ] ), frattFacs := rec( frattFacs := [ 5, 9, 14, 18, 47, 51 ], pos := [ 1, 2, 18, 26, 36, 40 ] ) ); SMALL_GROUP_LIB[ 945 ] := [ 114618597363623, 120777152947, 121287701279, 114616813836575, 114617705650463, 121287693503, 114616813828799, 121287810143, 127411411, 127528051, 120522410707, 128398883, 1571 ]; PROPERTIES_SMALL_GROUPS[ 945 ] := rec( isNilpotent := [ 2, 9, -11, 13 ], isAbelian := [ 2, 9, 13 ], lgLength := rec( lgLength := [ 3, 4, 5 ], pos := [ [ 12, -13 ], [ 3, -11 ], [ 1, -2 ] ] ), frattFacs := rec( frattFacs := [ 4, 7, 11, 14 ], pos := [ 1, 2, 8, 11 ] ) ); SMALL_GROUP_LIB[ 948 ] := [ 376088382658580513, 396758795996705, 18024296912389, 1384897332709409, 1312886006792360363, 18988735818, 396726777967259, 1420794200876699, 426413445275, 35991072433836, 378962973943837061, 1460466049691, 20136196471, 1384897887929243, 155 ]; PROPERTIES_SMALL_GROUPS[ 948 ] := rec( isNilpotent := [ 6, 15 ], isSupersolvable := [ 1, -9, 12, -15 ], isAbelian := [ 6, 15 ], lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 7, -15 ], [ 1, -6 ] ] ), frattFacs := rec( frattFacs := [ 3, 5, 7, 9, 11, 13 ], pos := [ 1, 2, 3, 4, 5 , 6 ] ) ); SMALL_GROUP_LIB[ 950 ] := [ 146492135653629, 869050325555, 142383711578967201, 53958945, 917071379, 164603649, 871094208275, 153992239293, 827550033942419, 1043 ]; PROPERTIES_SMALL_GROUPS[ 950 ] := 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[ 952 ] := [ 77965648110612485, 233831385671946255, 223667645833878175839, 16389604663040, 222529350655649271823, 211715596648873657892959, 1323713027289120863, 1323713027288072287, 1260174803383448764511, 1323713027303800927, 1260174803383464493151, 1260174803383463444575, 1199686412822446448050271, 222607201280115868943, 245620726039823, 233831093627782415, 245620724991247, 245620740719887, 74223182502243077893, 81896572718853, 77965527865102085, 81896571670277, 81896587398917, 212931596889428971225183, 234945002036265055, 223667643789489471583, 234945002035216479, 234945002050945119, 17180919280, 17196647920, 15586556596192752, 211847801410857200537615, 201552002361911083619319903, 223665893784041816159, 62329905664618496, 233749326022575375, 222390332614564118623, 1390453383495775, 257832255583, 86033563893, 246789022154847, 95 ]; PROPERTIES_SMALL_GROUPS[ 952 ] := rec( isNilpotent := [ 4, 29, -31, 42 ], isSupersolvable := [ 1, -34, 36, -42 ], isAbelian := [ 4, 29, 42 ], lgLength := rec( lgLength := [ 3, 4, 5 ], pos := [ [ 35, 38, -42 ], [ 7, -31, 34, 36, -37 ], [ 1, -6, 32, -33 ] ] ), frattFacs := rec( frattFacs := [ 4, 7, 10, 13, 17, 20, 23, 26, 29, 32, 35 ], pos := [ 1, 2, 3, 4, 5, 6, 13, 18, 23, 28, 31 ] ) ); SMALL_GROUP_LIB[ 954 ] := [ 3424923223166693, 182337211419895, 3772193043272494829, 3758175981, 191154891511, 3977524461, 182337313782519, 3582925949669, 173950058165814007, 2807 ]; PROPERTIES_SMALL_GROUPS[ 954 ] := 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[ 966 ] := [ 2667347511399, 116498320823, 2576649790683495, 149924791, 2526217319, 607192503, 2446888252775, 127438147, 2435853859999, 580156545743, 2363702512913895, 615 ]; PROPERTIES_SMALL_GROUPS[ 966 ] := rec( isNilpotent := [ 12 ], isAbelian := [ 12 ], lgLength := rec( lgLength := [ 4 ], pos := [ [ 1, -12 ] ] ), frattFacs := rec( frattFacs := [ ], pos := [ ] ) ); SMALL_GROUP_LIB[ 968 ] := [ 13108828765988474700099, 1538428109509090, 12689524392228030076300099, 13542178476871400099, 13109012801888277800099, 13542178476871300099, 13542368596808800099, 1603994100909, 17447323600909, 16348576538626300909, 13989853613600099, 1639200099, 13834462835709009, 13527016790445100099, 1589248909900, 12674983048223853945900099, 152001264089800099, 147137223775091500099, 152001264091200099, 147137223775093000099, 142428832614424641900099, 13391742584437100909, 14291776200909, 13834444814600909, 14291776100909, 14291777600909, 13094152061427733100099, 13974190509000099, 13527016592200200099, 13974190508900099, 13974190510400099 , 1638500990, 1640000990, 1536807733100990, 11876867777949732543388845100099, 12674990570767360776000099, 11496790519188234115234662779500099, 13094121295173036900099, 157025958400099, 14758400099, 14435961600099, 99 ]; PROPERTIES_SMALL_GROUPS[ 968 ] := rec( isNilpotent := [ 2, 8, -10, 12, 15, 32, -34, 42 ], isSupersolvable := [ 1, -15, 17, -34, 39, -42 ], isAbelian := [ 2, 8, 12, 15, 32, 42 ], lgLength := rec( lgLength := [ 2, 3, 4, 5 ], pos := [ [ 39, 41, -42 ], [ 11, -12, 17, -21, 27, -34, 36, -38, 40 ], [ 3, -10, 14, -16, 22, -26, 35 ], [ 1, -2, 13 ] ] ), frattFacs := rec( frattFacs := [ 7, 13, 20, 26, 69, 75, 22, 28, 34, 53, 59, 65, 71, 77 ], pos := [ 1, 2, 7, 10, 11, 12, 13, 14, 15, 16, 21, 26, 31, 34 ] ) ); SMALL_GROUP_LIB[ 975 ] := [ 20841548447, 10660599, 21899423, 227763895575, 20859750957215, 2207 ]; PROPERTIES_SMALL_GROUPS[ 975 ] := rec( isNilpotent := [ 2, 6 ], isSupersolvable := [ 1, -3, 6 ], isAbelian := [ 2, 6 ], lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 3, -6 ], [ 1, -2 ] ] ), frattFacs := rec( frattFacs := [ 3, 5 ], pos := [ 1, 2 ] ) ); SMALL_GROUP_LIB[ 976 ] := [ 699581656945131638400059, 12160927069270344000, 682186873472079374044800059 , 716784481493971200059, 699580896890387155200059, 682791694904399112403200059, 682791694905176264505600059, 666404694227452673325225600059, 716784481493193600059, 699580896890386377600059, 716784481491638400059, 699581654613684662400059, 699580896890384822400059, 716784481503302400059, 705888204327869924851200059, 688946887424001493249891200059, 688946887424001493250668800059, 672412162125825457857731548800059, 716784481502524800059, 12459916368212400, 24881620694612400, 24296896084406612400, 12459921033812400, 12148467164553812400, 11856903946837632212400, 11572338251671373808212400, 11294602133630817924201812400, 682186872712027006684800059, 665814387766178204614108800059, 698961960524772432000059, 682186872712027016016000059, 698961960524773987200059, 682186872712027017571200059, 698961960524783318400059, 699580896113246716800059, 734408839411200059, 716783704365196800059, 716783704363641600059, 759252422246400059, 723246110214046329600059, 723246110214024556800059, 705888203569369462022400059, 734408837078400059, 734408861184000059, 12740976003540, 12752640003540, 12148454419689603540, 12447189388803540, 716634497504419200059, 751771238400059, 59 ]; PROPERTIES_SMALL_GROUPS[ 976 ] := rec( isNilpotent := [ 2, 20, -27, 45, -48, 51 ], isAbelian := [ 2, 20, 23, 45, 51 ], lgLength := rec( lgLength := [ 2, 3, 4, 5 ], pos := [ [ 50, -51 ], [ 11, -14, 19, -22, 30, -31, 34, -49 ], [ 4, -10, 15, -18, 23, -29, 32, -33 ], [ 1, -3 ] ] ), frattFacs := rec( frattFacs := [ 5, 9, 14, 18, 22, 51, 55, 59 ], pos := [ 1, 2, 3, 19, 27, 34, 44, 48 ] ) ); SMALL_GROUP_LIB[ 980 ] := [ 367699326111609, 604565403205622795, 592491953280557229551, 125745797921, 359852170001878905, 16929304010961379279373807, 17627346937834249103, 616903467842447, 375199869525, 604583625766438799, 127464335, 625162539425, 616160459417867, 375199847247, 614410720570031, 603849515659866863, 127410618 , 591758181755561437451, 367196151960399, 2518717827382373039, 17274799277074946265839, 568338308522311776062624495, 579922059956055620252399, 4370530037903, 2622574817483, 17987087951014031, 4283133293214863, 603835519543649423, 638005391, 628730284175, 383201493, 626946656459, 616172945052815, 143 ]; PROPERTIES_SMALL_GROUPS[ 980 ] := rec( isNilpotent := [ 4, 11, 17, 34 ], isSupersolvable := [ 1, -17, 19, -21, 24, -34 ], isAbelian := [ 4, 11, 17, 34 ], lgLength := rec( lgLength := [ 3, 4, 5 ], pos := [ [ 24, 26, -28, 30, -31, 33 , -34 ], [ 7, -11, 13, -14, 16, -19, 21, -23, 25, 29, 32 ], [ 1, -6, 12, 15, 20 ] ] ), frattFacs := rec( frattFacs := [ 5, 9, 13, 17, 22, 26, 30, 34, 38, 42, 46, 23 , 27, 31, 35, 39, 43 ], pos := [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17 ] ) ); SMALL_GROUP_LIB[ 984 ] := [ 1629426719644096001, 63421919802675264039, 62407237171170816000079, 1654234419326400, 62390856884381798464039, 61355838372531267481600079, 66667614896332800079, 66667614896230400079, 65600933199728128000079, 66667614897766400079, 65600933199729664000079, 65600933199729561600079, 64551318268674115481600079, 1579302283364648145856000, 62407101455232512001639, 64453044019201639, 63421851017420801639, 64453043916801639, 64453045452801639, 1603350931140096062401, 1655924531262401, 1629421687808062401, 1655924428862401, 1655925964862401, 61408721173560815104000079, 63421988595507200079, 62407236964812595200079, 63421988595404800079, 63421988596940800079, 1677824003160, 1679360003160, 1626116563251203160, 61392557621266258841664039, 60374082484731274979225600079, 62407085084495155200079, 3150594336372473858497600, 3100184827241081416908926400, 133409171977011264039, 63405343073996801639, 62353494281047347200079, 67751496908800079, 3306946560126400, 65444249600079, 1690828801561, 64453050368000079, 79 ]; PROPERTIES_SMALL_GROUPS[ 984 ] := 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 ] ) );