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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 col15.z GAP library of groups Hans Ulrich Besche ## Bettina Eick, Eamonn O'Brien ## SMALL_GROUP_LIB[ 1660 ] := [ 115397433594775, 3114488171352877, 5176436334203610711, 9606728368983, 191403684019741591, 26371457459071784135255, 9570135803586375, 1876486153031, 70892698613, 3118331522778183, 327 ]; PROPERTIES_SMALL_GROUPS[ 1660 ] := 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[ 1665 ] := [ 12918425552567, 159094955231, 59621810249500343, 7793466335, 48095 ]; PROPERTIES_SMALL_GROUPS[ 1665 ] := rec( isNilpotent := [ 2, 5 ], isAbelian := [ 2, 5 ], lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 4, -5 ], [ 1, -3 ] ] ), frattFacs := rec( frattFacs := [ 3, 5 ], pos := [ 1, 2 ] ) ); SMALL_GROUP_LIB[ 1666 ] := [ 467953031319381, 839097910623, 785603467325081077, 570557791, 505415007, 169870837, 841380529503, 280685973333, 1401754687636831, 1375 ]; PROPERTIES_SMALL_GROUPS[ 1666 ] := 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[ 1668 ] := [ 49122170659675212797, 12724760672840189, 310298382141589, 42458742892332029 , 70821240631460752163, 77432698705955, 12724446959866643, 43077853050914579, 7706095792403, 929391135022188, 21267952596471334385, 25451006133011, 197294640091, 42458748332422163, 275 ]; PROPERTIES_SMALL_GROUPS[ 1668 ] := 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[ 1672 ] := [ 779498440784362737, 1472293810442307257, 2474839349687828764691, 10831390281465875, 14800525421008288499, 14800525421006398931, 24746478508369129984019, 14800525421034742451, 24746478508369158327539, 24746478508369156437971, 41376112065997625475768851, 2461674267732334767317, 880558040958389, 1472293222251861941, 880558039068821, 880558067412341, 1303320823519836010221, 466207039573965, 779498100263330253, 466207037684397, 466207066027917, 4137931381865454836099603, 1480167067798831859, 2474839343217492546803, 1480167067796942291, 1480167067825285811, 6470366451155, 6470394794675, 18099272561986359827, 8851986226925747, 526539460787, 278870004027, 885263877789875, 179 ]; PROPERTIES_SMALL_GROUPS[ 1672 ] := rec( isNilpotent := [ 4, 27, -29, 34 ], isAbelian := [ 4, 27, 34 ], lgLength := rec( lgLength := [ 3, 4, 5 ], pos := [ [ 30, -34 ], [ 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[ 1674 ] := [ 44855674030978129827959, 4483391698168227959, 3135782245780026983583931, 32375229341675427959, 5246629072501424333959853131, 20697646840227959, 26795504206062027959, 44857904020370132427959, 44857904032712199627959, 26795504206013427959, 44857904020370083827959, 26796836359180827959, 134471075393560618828771, 225106343035582176990028771, 225104475398132109841228771, 26796861831850227959, 44857905377996649627959, 225104571345387600241228771, 376824891807609708591140428771, 376828018232701120998231628771, 44855674030979587827959, 75092131330079226768027959, 16007686138827959, 26796837152430027959, 26796849494497227959, 16007686090227959, 26796837152381427959, 16007692262427959, 19340022510027959, 20672175628827959, 34605218733678027959 , 1119006267746453131, 667669181453131, 1116341189740853131, 3736393906414485653131, 1964763694277233228771, 32375229343133427959, 57929136181431696027959, 3128389855106690545228771, 1873221816248633583931, 1117676556778383931, 3289014608824257116428771, 1964763138091348828771, 12342115827959, 12348288027959, 20672968829427959, 16006892889627959, 16007687596827959, 26795504207520027959, 26796861832579227959, 44855674030980316827959, 1617408027959, 11548915227959, 401241628771, 19340023968027959, 667670688053131, 32375229343862427959, 1117676510122383931 , 54196134023598177627959, 27959 ]; PROPERTIES_SMALL_GROUPS[ 1674 ] := rec( isNilpotent := [ 6, 44, -46, 60 ], isAbelian := [ 6, 44, 60 ], lgLength := rec( lgLength := [ 3, 4, 5 ], pos := [ [ 47, 52, -53, 58, -60 ], [ 7, -12, 17, 22, -31, 34, 38, 40, -46, 48, -51, 54, -57 ], [ 1, -6, 13, -16, 18, -21, 32, -33, 35, -37, 39 ] ] ), 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, 12, 17, 22, 28, 31, 35, 39, 41 , 43, 46 ] ) ); SMALL_GROUP_LIB[ 1683 ] := [ 6274748831, 4511 ]; PROPERTIES_SMALL_GROUPS[ 1683 ] := rec( lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 2 ], [ 1 ] ] ), frattFacs := rec( frattFacs := [ 3 ], pos := [ 1 ] ) ); SMALL_GROUP_LIB[ 1690 ] := [ 53881129143, 336133913343551, 568075193366806079, 10700351, 117449279, 198886109759, 32515767, 197781960287, 336121226312255, 575 ]; PROPERTIES_SMALL_GROUPS[ 1690 ] := rec( isNilpotent := [ 4, 10 ], isAbelian := [ 4, 10 ], lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 6, -7, 9, -10 ], [ 1, -5, 8 ] ] ), frattFacs := rec( frattFacs := [ 3, 5, 7, 9 ], pos := [ 1, 2, 3, 4 ] ) ); SMALL_GROUP_LIB[ 1692 ] := [ 16394259664521268736999, 435001549810511456563, 29865432668852463709769403, 269780944570401535, 17718544349769166562267, 28987904550565123852, 257092860508271647, 9689278784756159267, 17650959227238172725211, 158602201596959, 257092859890480009, 5719799660355341, 435001549823281161075, 9677886480100408551, 736022623661191855459199, 1427412605650815, 27706424388258066169445607, 2203323358303287354847581596543, 268505515340150943, 454859387320749267103, 5719997178752035, 454311584864884561055, 769622083510456560645279, 17132362843187772, 151878746208415, 3400860663899, 257092872866050207, 5719812635925539, 435001549829665918111, 2207 ]; PROPERTIES_SMALL_GROUPS[ 1692 ] := 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[ 1694 ] := [ 43402580995, 133100206600599, 225476909752920599, 5160599, 46400599, 78566880599, 25920995, 78341600959, 133094579760599, 599 ]; PROPERTIES_SMALL_GROUPS[ 1694 ] := rec( isNilpotent := [ 4, 10 ], isAbelian := [ 4, 10 ], lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 6, -7, 9, -10 ], [ 1, -5, 8 ] ] ), frattFacs := rec( frattFacs := [ 3, 5, 7, 9 ], pos := [ 1, 2, 3, 4 ] ) ); SMALL_GROUP_LIB[ 1700 ] := [ 254157468155354607667, 745245287772074047, 436807167873023977980915, 503799669064511, 1266666755341121761343, 18295153680938567661142410227, 734515082025048556170178611, 1307218743318694240376595678195, 2146033615729362179492862252549107, 2146033371943279185301739479761907, 265926636823520478195, 438378860380991, 149504392989511475, 256945305296635429875, 292061971263, 438378857247503, 87703367466755, 746238284275920959, 149387982188638259, 1268610055208881357631, 7301445452607 , 745098099240743695, 148978766227455747, 2156625017033475046256703, 2156625017529973265674303, 4305384807640576569407, 1266667748337625608255, 431730076490861051441203, 6232681166381781535291570389823, 6232681166382628064755677397823, 12476999038390187193472647999, 431730076636889939505203, 6232681166381784017782667477823, 12476999038392669684569735999, 1266219555441439993907, 3695534079668981557053358911, 3695534079671464048150446911, 36590704885070258955617087, 2153335177138602979099455, 1489753027380031, 2539588650958586687, 87876171730739, 2532583387265237823, 4317300709414244713279, 257832256319, 51673826291, 438963038847807, 87875232206643, 746241204886176575, 831 ]; PROPERTIES_SMALL_GROUPS[ 1700 ] := rec( isNilpotent := [ 4, 15, 21, 50 ], isAbelian := [ 4, 15, 21, 50 ], lgLength := rec( lgLength := [ 3, 4, 5 ], pos := [ [ 41, -45, 48, -50 ], [ 11 , -16, 19, -22, 28, -40, 46, -47 ], [ 1, -10, 17, -18, 23, -27 ] ] ), frattFacs := rec( frattFacs := [ 5, 9, 13, 17, 22, 26, 30, 34, 38, 42, 46, 50 , 54, 58, 62, 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, 19, 20, 21 ] ) ); SMALL_GROUP_LIB[ 1704 ] := [ 80096612310135967001, 5520277305010477443069, 9406555870574526520500139, 10006190570008500139, 5680096775919329400139, 5680096775917648700139, 9678884910194279384500139, 5680096775942859200139, 9678884910194304595000139, 9678884910194302914300139, 16492819886975076976253300139, 232978218059884872814477000, 9406549197825638064504969, 3239597281044604969, 5520275349934521404969, 3239597279363904969, 3239597304574404969, 136484486311345840838101, 47005175572938101, 80096529722195338101, 47005173892238101, 47005199102738101, 16028771193469840397840500139, 5520279260210804600139, 9406555864709258316600139, 5520279260209123900139, 5520279260234334400139, 5865295095100139, 5865320305600139, 17040560128049955700139, 272728870926400090871900, 464730008811416529384681100, 11363702896672985943069, 3333387759654400139, 140797160090281100, 1900239756800139, 27751718404831, 3239597385248000139, 139 ]; PROPERTIES_SMALL_GROUPS[ 1704 ] := rec( isNilpotent := [ 4, 28, -30, 39 ], isSupersolvable := [ 1, -11, 13, -30, 34, 36, -39 ], isAbelian := [ 4, 28, 39 ], lgLength := rec( lgLength := [ 3, 4, 5 ], pos := [ [ 34, 36, -39 ], [ 5, -33, 35 ], [ 1, -4 ] ] ), frattFacs := rec( frattFacs := [ 4, 7, 10, 13, 17, 20, 23, 26, 29, 32 ], pos := [ 1, 2, 3, 4, 11, 12, 17, 22, 27, 30 ] ) ); SMALL_GROUP_LIB[ 1708 ] := [ 56714217332405, 669079815858059, 1145555795210400359, 2833380000359, 1142652001871538059, 1951652381001236640359, 3457100528640359, 391910400359, 33592323545, 670699077120359, 359 ]; PROPERTIES_SMALL_GROUPS[ 1708 ] := 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[ 1710 ] := [ 906163382921516279, 908283309516884627, 1549541395705560963731, 529983617778935, 900557349606647, 158973078300321, 1541967284369726099, 90791010432375535, 159419906695302092623, 155615579383477523779, 272618194479630678856711, 2941078586003, 929072136473408754935, 929074256392264452755, 1588713355353976805530259, 906057519466169591, 529921938499667, 531160164851795, 906164559468589139, 529983734932151, 906163383038669495, 908283309573571667, 1549541395705617650771, 311521744979, 526539466835, 93117917505, 901733896679507, 31200553927, 900557466759863, 158973195453537, 1541967284426413139, 53032585277935, 1539954412832866751, 271844008626749601, 2636764064469053597267, 6227 ]; PROPERTIES_SMALL_GROUPS[ 1710 ] := rec( isNilpotent := [ 12, 36 ], isAbelian := [ 12, 36 ], lgLength := rec( lgLength := [ 4, 5 ], pos := [ [ 17, -19, 24, -27, 32, -36 ] , [ 1, -16, 20, -23, 28, -31 ] ] ), 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 ] ) );