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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 col24.z GAP library of groups Hans Ulrich Besche ## Bettina Eick, Eamonn O'Brien ## SMALL_GROUP_LIB[ 988 ] := [ 584832323999, 903771245069, 903025365278183, 53856558, 577333712429471, 10834606374803169767, 11099396335319, 917070551, 594584381, 913984881623, 215 ]; PROPERTIES_SMALL_GROUPS[ 988 ] := 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[ 990 ] := [ 12860983309001319, 14309303502506003191, 14166197676197552403191, 4884480201319, 14616179401319, 4874253001913, 14505779219401139, 1613907578403911, 1633151141501203191, 1604217620093209131, 1616922670253694601391, 1638601391, 4881625601139, 4884486401319, 4832004115201319, 4835283875203119, 4783683703728003119, 5734401139, 14758401139, 4928001193, 14652230401139, 1651201391, 14616185601319, 4874259201913, 14505779222401139, 1626950403911, 14470058825603119, 4825522198409113, 14360721678360001139, 1139 ]; PROPERTIES_SMALL_GROUPS[ 990 ] := rec( isNilpotent := [ 12, 30 ], isAbelian := [ 12, 30 ], lgLength := rec( lgLength := [ 4, 5 ], pos := [ [ 13, 16, -21, 26, -30 ], [ 1 , -12, 14, -15, 22, -25 ] ] ), 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[ 992 ] := [ 21490217467606355795127000029, 747719893784220332490000, 21663525672799558110000029, 21490194101359866164478000029, 21147749361879417233691137982000029, 21147772309402934342717036478000029, 20978567366984381895844763818647000029, 21663525672799553007000029, 21490194101359866159375000029, 21513326685574197027087000029, 21318272548478560034638938000029, 22969187066289021882642000029, 22785456679023832198870131000029, 22785479811608046529737843000029, 22785433569688280989851162000029, 22603150101130774763656863987000029, 21663525672799557381000029, 21490194101359866163749000029, 21663525672799555923000029, 21513326732541193232655000029, 21490194101359866162291000029, 21318341923029554295134031000029, 21318295657767144247498995000029, 21318295657790651442370803000029, 21147749292481641036110079063000029, 21686821302917537334000029, 21490264035312003372150000029, 22603173025521731189243445207000029, 22785433569688280989801590000029, 22603150101130774763656814415000029, 22603150101130704313162557822000029, 22446362132935850613077081488908000029, 22266791235872363808172485774049509000029, 22266791235872363808172485774050238000029, 22088656905985384897707105908793443991000029, 21686821302917536605000029, 21663525672799573419000029, 22785433569688280989850433000029, 22785433569688280989101021000029, 22969187066289021182073000029, 22603150101130704313162555635000029, 22603150101130704313161806223000029, 22603150101130704313162557093000029, 3009680769049515783000, 753749886771027783000, 746966143897467507783000, 3009680769059721783000, 746967658964933241783000, 740991916933370578953783000, 735063981597143759556027783000, 740991916933369080129783000, 735063981597143758057203783000, 735063981597143758067409783000, 2985604840993886523783000, 743228299699581740787783000, 743228300457878349555783000, 737282471046812377683075783000, 753749886781233783000, 746966143897477713783000, 729915570518050078409178360783000, 724076245953905677777912807377783000, 718283635986274432355685512070531783000, 21490217396918893814031000029, 21341220072019105165006671000029, 21341220048723475047044943000029, 21861714927928086000029, 21663525601709291862000029, 21663525601709268534000029, 21513326685503106765942000029, 21513326662019608663158000029, 21536459246233939530870000029, 23154445929259541565000029, 22969210385378940410493000029, 22969233704492556473547000029, 23341175309148516000029, 23154422445761461380000029, 23154445952956356516000029, 23154445952956355058000029, 23154469460151226866000029, 22969233681009058393362000029, 22969210361895442330308000029, 45916757245108777200111000029, 22785456702272447926362159000029, 22785456678976794111631407000029, 22785479834856662257229871000029, 23154445929259542294000029, 22969187066217930808662000029, 22969187066217930785334000029, 22969210361871745539414000029, 22969210385355243642198000029, 22969233681009058372950000029, 22969210408862438514006000029, 22785456678953310613551222000029, 21838231429829676000029, 21663502118211193452000029, 21663502118211170124000029, 21490217396942590703340000029, 21490217396966287472364000029, 21318295657767073157217438000029, 21318295657790580352088517000029, 23154422445761443884000029, 22969187042734432686924000029, 22785433569688233595591404000029, 22603150101130727749266399390000029, 22970702785119490290888000029, 22786937162838543633935112000029, 22604641665535835294082745896000029, 22786937162838543633891372000029, 22604641665535835294082725484000029, 22604641665535835294082724026000029, 22423804532211548611739279905164000029, 22604641665535835294082680286000029, 22423804532211548611739279883294000029, 22244414095953856222845374859007806000029, 21838231429827489000029, 21663502118211191265000029, 21838231429824573000029, 21663525601709291133000029, 21513326661995911891947000029, 21663502118211188349000029, 21663502118211186891000029, 21838231429870500000029, 21838231429847172000029, 21686821231827275460000029, 21686821231827274002000029, 22969187066217942100872000029, 22604617239042648886019200314000029, 22785433569688209910017633000029, 23341175309146329000029, 23154445929259585305000029, 45916757245108777243851000029, 23341175309192256000029, 23154445929259586034000029, 23154445929259607904000029, 22969210361848048790802000029, 22785433569688209910019820000029, 22423780301130307694941651443870000029, 22603150101130704242082724293000029, 45549376922003008097738799000029, 22969187042734432659951000029, 22969210361848048770390000029, 22785456678953286916782198000029, 23154422445761441697000029, 22786912539357508946988936000029, 22785433569688209910018362000029, 22604617239042648886019199585000029, 21838231429868313000029, 21861714927993696000029, 759825434763026100, 1517357653497026100, 1505977829450667026100, 1505977829452125026100, 1505219532843357026100, 1494682996086697743026100, 759825502560026100, 753748358010642026100, 747718372604582379026100, 753748358012100026100, 747718371840172662026100, 741736624866906416463026100, 747718373368996470026100, 747717614307975798026100, 741735873394967127375026100, 759825444969026100, 752990061366153026100, 752990062089321026100, 746966141607408048026100, 740990412472134464649026100, 735062489172354973891131026100, 740990412472134466836026100, 740989661000195221488026100, 735061743712191199161762026100, 21663502094514468897000029, 22014298802376000029, 21838207733151048000029, 21838207733148132000029, 23529375134208000029, 23154422422075959780000029, 23341151612469888000029, 23154422422075872300000029, 22969187042710747185324000029, 22969187042710735983510000029, 23341151613125988000029, 23154422422064765256000029, 22785433546369072585943646000029, 22014298797273000029, 22014298889856000029, 764412633000870, 764435232000870, 752989296944043000870, 759061046916000870, 752989297781664000870, 740989660241896225974000870, 21490175257612697406368700000, 22168318464000029, 29 ]; PROPERTIES_SMALL_GROUPS[ 992 ] := rec( isNilpotent := [ 2, 44, -62, 149, -172, 188, -193, 196 ], isSupersolvable := [ 1, -193, 195, -196 ], isAbelian := [ 2, 45, 58, 149, 164, 188, 196 ], lgLength := rec( lgLength := [ 2, 3, 4, 5, 6 ], pos := [ [ 194, -196 ], [ 37, 44, 63, -93, 117, -125, 129, -135, 139, -142, 147, -163, 173, -193 ], [ 8, -16, 19, -31, 36, 38, -43, 45, -57, 94, -116, 126, -128, 136, -138, 143, -146 , 164, -172 ], [ 3, -7, 17, -18, 32, -35, 58, -62 ], [ 1, -2 ] ] ), frattFacs := rec( frattFacs := [ 6, 11, 17, 22, 58, 63, 209, 214 ], pos := [ 1, 2, 43, 62, 148, 172, 187, 193 ] ) ); SMALL_GROUP_LIB[ 996 ] := [ 23126978024341, 1869462034259621, 1861988466307294643, 23193859654, 1915530664502947, 46183696333900, 1876486152867, 24595430387, 1869462712435619, 163 ]; PROPERTIES_SMALL_GROUPS[ 996 ] := 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[ 999 ] := [ 21487990471114391, 861691808917, 21447557568789626519, 21509461515671, 21487926845580695, 21487958664226199, 21509459836055, 21487926843901079, 21509471593367, 861692221, 873449533, 859978557757, 21469026985016471, 21552880535, 48023 ]; PROPERTIES_SMALL_GROUPS[ 999 ] := rec( isNilpotent := [ 2, 10, -12, 15 ], isAbelian := [ 2, 10, 15 ], lgLength := rec( lgLength := [ 2, 3, 4 ], pos := [ [ 14, -15 ], [ 4, -13 ], [ 1, -3 ] ] ), frattFacs := rec( frattFacs := [ 4, 7, 11, 14, 17 ], pos := [ 1, 2, 3, 9, 12 ] ) ); SMALL_GROUP_LIB[ 1000 ] := [ 12966931472703284077137604671, 4316485296901387059, 12966931472707178543046452077196324927, 12966932005261532979540266823743, 12966931472703283007168575, 12966932005261532979007299647, 12966931472703283007164479, 12966932005261532446031935, 4316549506748623, 107378498842345679, 107378498949614036807887, 12966931472707178543046451476926527, 12966931472702749900863, 4316442230847, 12966510669180229997327, 12906419888903451443, 4307916729986390709007, 4307933806669180246774543, 12949665704689295953539135, 4359714465932392280127 , 4303600180310988, 8594272513201100, 34364041968184505292, 12889218373297171886899, 12966510587365502332632650511, 12949330696723845721833362191, 12966523450813925502332649427727, 64437437630868209295970316351, 12966514912715294228112003903551, 4307916626735679629452444708927, 12949665704172937806462608012259391, 4359713940893684636607619543103, 12949665708468021066579600012259391, 4359713949677322790017445951, 13224269265769184375122079807, 13224268733725321236543, 13224268733725815121948735, 13224269265769183881367615, 13224268733725321240639, 13224269265768690122815, 13224269265769183881371711, 4308174333385063805760365015103, 4308174333385063850319935, 4308174333385063850442815, 4308174333385063805804884031, 4308174333385063805805011007, 12966613645208848855937231, 12992297652718038839503, 12966510668968698063, 12966613645208744829135, 12906484100784335, 12992297652612915407, 4307916729879104094089423, 4307916729908994255, 4307916729879134085327, 17192835797645208848990154959, 17192835694669102915791, 17192835797645208879046863, 12966510668968693967, 12906484100780239, 12966613645104709839, 12992297547481295, 4307916729908990159, 4307916729909117135, 17192835694669102911695, 17192835797645238927567, 12949666236732128375082758207, 12949665704688225919039, 12949666236732127842050111, 4359714465395520321499199, 4359714465396564031, 4359714465395521495103, 12949665704688225914943, 12949666236731594801215, 4359714465396559935, 4359714465396686911, 4316442153203, 4316509245683, 17184185693262067, 21479131594995, 4316509372659, 17201348382703859, 21479152943607476467, 4316463628858568947, 17201348336943674585331, 4368312465428874631908072501568878424127, 64437733665784052495454271, 12966828393491941932028465215, 4307916635604468752179988009023, 12966828711302393183920045120098367, 4359713941194237363266846979526719, 4368303875829367394680918730618830911, 4368304387033417489750438720547991615, 12889218438582522063, 12966510587365503731306703, 12949330696723847254642895, 12966510565912037503865524431, 64437437630868208360132671, 12966514912715294227444600895, 4307916626735679629321310271, 12949665704172937806462007676991, 4359713940893684636275183679, 12949665708468021066578999676991, 4359713949677322455486527, 13224268733231431743, 4308174333385108357183, 12966510564802623, 12906378854463, 4307917162414143, 4307933807101673535, 12949665704155054143, 4359714466431039, 4295000127, 4831838271, 17184701055039, 12906419676287939, 12949433986373931791, 12949649057931857506367, 4303557301232, 12889218374158029763, 12893556354690642367247, 12949330713989721816584975, 12949330735464558296584975, 12893556569761931891060799, 12949330735679629451907838015, 12949330714204792971907838015, 12949648524303750044607116226623, 12949648524325332255269516226623, 64437501734953167, 64437501823463469263, 64437501735076047, 64437501823463596239, 64437501823551975600335, 64746645409000071231, 64746645409000067135, 64746645409509698187327, 64746645409000194111, 64746645409509698314303, 64746645409509698310207, 64746645409510207810318399, 64746645194761333907519, 64746645194761334030399, 64746645194761843519810842687, 12906398220793557235, 12906378830067, 12906398201553139, 12906378825971, 12906378952947, 12949433879103959871695, 12949433774776527, 12949433878999867599, 12949433774772431, 12949433774899407 , 12949649057395519786725439, 12949649056861790271, 12949649057394986721343, 12949649056861786175, 12949649056861913151, 4294971644, 4295098620, 4299266558406908, 12949330713933710849848611197711, 64746644893684103215259145233237553215, 64746644915266313791609475457877553215, 64746675151634488896775021363998783, 12949390830582433269682383, 64445997269311824079, 12949648584733840620299550694314047, 64746653569424084401397823, 12949648584733840620192176511914047, 64746653676798266801397823, 64746954122653684635746701375, 64746653569423869961535234111, 64746653676798052361535234111, 322229934332263347003455, 322186984809627210223679, 322187079096722587660677820479, 12949365142400205651430211791, 64746653741222454212912755213213759, 64746825711712792672010252813209663, 12949429566858028732910145620816079, 64746653741222625710956884800013217855, 322186984680325183, 12889220479717619 , 12949330713991120425167, 12949330735465956905167, 64437437399475163343, 12949648524303750044006748223, 12949648524325332254669148223, 64746644915266846400712767, 64746644915159472218312767, 322135496634308564095039, 64437413216319, 64746644899364927, 64746645194252222527, 12886999103, 12949329543231, 12949648523657279, 63 ]; PROPERTIES_SMALL_GROUPS[ 1000 ] := rec( isNilpotent := [ 2, 9, -11, 14, 21, -23, 77, -85, 113, -115, 119, 159, -161, 199 ], isSupersolvable := [ 1, -85, 87, -91, 94, -161, 166, -177, 183, -199 ], isAbelian := [ 2, 9, 14, 21, 77, 113, 119, 159, 199 ], lgLength := rec( lgLength := [ 2, 3, 4, 5, 6 ], pos := [ [ 183, 194, -195, 198, -199 ], [ 105, -106, 109, 111, -115, 134, -143, 154, -161, 168, -177, 179, -180, 182, 188, -193, 196, -197 ], [ 13, -14, 35, -46, 53, -55, 63, -64, 67, -85, 87, -93, 96, 98, -104, 107, -108, 110, 118, -119, 124, -133, 144, -153, 163, -167, 178, 181, 184, -187 ], [ 4, -12, 17, 19, -23, 26, 28, -34, 47, -52, 56, -62, 65, -66, 86, 94, -95, 97, 116, -117, 120, -123, 162 ], [ 1, -3, 15, -16, 18, 24, -25, 27 ] ] ), frattFacs := rec( frattFacs := [ 10, 19, 29, 38, 47, 111, 120, 129, 31, 40, 49, 86, 95, 104, 113, 122, 131, 140, 149, 366, 375, 384, 393, 402, 411, 420, 429, 438, 447, 456, 465, 474, 115, 124, 133, 142, 377, 386, 395, 404, 413, 422, 431, 440, 449, 458, 467, 476, 485, 494, 503, 512 ], pos := [ 1, 2, 3, 8, 11, 12, 13, 14, 18, 20, 23, 27, 30, 32, 34, 46, 66, 76, 85, 86, 89, 91, 92, 93, 97, 100, 102, 104, 106, 110, 112, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 133, 140, 143, 148, 153, 158, 161 ] ) );