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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 col6.z GAP library of groups Hans Ulrich Besche ## Bettina Eick, Eamonn O'Brien ## SMALL_GROUP_LIB[ 276 ] := [ 33470741701, 697933190921, 192635714225723, 120174274, 763914438187, 66577450060, 2526216747, 127435727, 697936704299, 43 ]; PROPERTIES_SMALL_GROUPS[ 276 ] := 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[ 280 ] := [ 30144584469531, 50193070279277, 14194653849396023, 35927430300, 8400353043532827, 16458887449920398135, 209937453296855, 209937453289079, 58782489989368631, 209937453405719, 58782489989485271, 58782489989477495, 16459097200087413047, 14053810573504913, 179255602481, 50192178565937, 179255594705, 179255711345, 8440305636962775, 107655687543, 30143947559799, 107655679767, 107655796407, 3974501833327577399, 50695161971927, 14194649390443223, 50695161964151, 50695162080791, 127409898, 127526538, 10024115650986, 58801396459711703, 40061058200424, 30001320906519, 58781740878128759, 749765652503, 638005271, 383201313, 181039712279, 23 ]; PROPERTIES_SMALL_GROUPS[ 280 ] := rec( isNilpotent := [ 4, 29, -31, 40 ], isSupersolvable := [ 1, -32, 34, -40 ], isAbelian := [ 4, 29, 40 ], lgLength := rec( lgLength := [ 3, 4, 5 ], pos := [ [ 33, 36, -40 ], [ 7, -32, 34, -35 ], [ 1, -6 ] ] ), 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[ 294 ] := [ 15311267211187079, 58917036167, 197119219, 293800986503, 86385862881287, 668807, 14991343638726599, 588778055, 218495303, 58353654599, 173433540167, 176164720199, 51792365903687, 50989398974279, 829511, 199978055, 209267783, 3359303, 998708039, 705235, 980128703, 293634440135, 71 ]; PROPERTIES_SMALL_GROUPS[ 294 ] := rec( isNilpotent := [ 6, 23 ], isSupersolvable := [ 1, -6, 8, -23 ], isAbelian := [ 6, 23 ], lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 7, 9, -14, 16, -17, 19, -20 , 22, -23 ], [ 1, -6, 8, 15, 18, 21 ] ] ), frattFacs := rec( frattFacs := [ 3, 5, 7, 9, 11, 13 ], pos := [ 1, 2, 3, 4, 5 , 6 ] ) ); SMALL_GROUP_LIB[ 296 ] := [ 2646611354518307, 256277534256, 782860163260711715, 783387557108386595, 8941096493603, 2646579547630115, 8941094813987, 8941106571299, 861644268, 873401580, 75601980157932, 2644798118347043, 30152466467, 35 ]; PROPERTIES_SMALL_GROUPS[ 296 ] := 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[ 297 ] := [ 1536051911, 5131191, 5201191, 1525851191, 1119 ]; PROPERTIES_SMALL_GROUPS[ 297 ] := rec( isAbelian := [ 1, -2, 5 ], lgLength := rec( lgLength := [ 2, 3, 4 ], pos := [ [ 5 ], [ 2, -4 ], [ 1 ] ] ), frattFacs := rec( frattFacs := [ 4, 8 ], pos := [ 1, 4 ] ) ); SMALL_GROUP_LIB[ 300 ] := [ 1525300726989, 1383134239335503, 414971876239189023, 5117056115, 124888380232387732559, 37425883631332414432287, 11329231246532639, 3035065682416, 4610446270495, 5083631677, 1383239583506463, 16785439, 2991093701626987551, 684917671750992975, 33234408178767, 15183512691, 4605765420111, 5083628785, 4555266000071, 1381730825241631, 16778364, [ ( 1, 4, 2, 5, 3)( 6, 9, 7,10, 8), ( 1, 4, 3)( 6, 7, 8, 9,10) ], 18492777126378635219665951, 37306291975581238756431, 61645312866147271933983, 9970312340996127, 2283058910920735, 4534973891699, 1362050316174415, 414482656821183567, 414482681987007567, 1361999816754375, 408162109962290207, 124345257580247614495, 124345250030500414495, 75548459039, 25216811063, 37764087611423, 22664761212959, 1381679656173599, 110786248735, 10116858352, 9970449069097231, 50462751, 15351349279, 16908349, 15183577143, 4605765451807 , 31 ]; PROPERTIES_SMALL_GROUPS[ 300 ] := rec( isNilpotent := [ 4, 12, 21, 49 ], isSupersolvable := [ 1, -7, 9, -12, 16, -21, 28, -40, 44, -49 ], isSolvable := [ 1, -21, 23, -49 ], isAbelian := [ 4, 12, 21, 49 ], lgLength := rec( lgLength := [ 3, 4, 5, false ], pos := [ [ 25, -27, 36, 38, -43, 45, -46, 48, -49 ], [ 7, -15, 17, -18, 20, -21, 23, -24, 29, -31, 33, -35, 37, 44, 47 ], [ 1, -6, 16, 19, 28, 32 ], [ 22 ] ] ), frattFacs := rec( frattFacs := [ 5, 9, 13, 17, 26, 30, 34, 38, 42, 46, 50, 54 , 23, 27, 31, 35, 39, 43, 47, 51, 55 ], 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[ 304 ] := [ 14840769322977354737, 2880024304178664, 48818312654065361, 14840589329227899089, 4511593338832298149073, 4511593339420513109201, 1371524375184319999924721, 48818312652175793, 14840589329226009521, 48818312648396657, 14840767558355149169, 14840589329222230385, 48818312676740177, 5038618310118470777489, 1531739966276353706151857, 1531739966276353708041425, 465648949748011864689310193, 48818312674850609, 9473362400484, 18853869534372, 5741009005438692, 9473373737892, 2870550970033572, 872647512620243076, 265284843523989335460, 80646592430979622770660, 14840588741041282481, 160582933537937, 48817724495792273, 48817724492013137, 179344371068945, 16574401746553273937, 16574401746500366033, 5038618131301096444625, 160582927869233, 160582986445841, 30960571986, 30988915506, 2870520000008850, 9442435835826, 526539460625, 17 ]; PROPERTIES_SMALL_GROUPS[ 304 ] := 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[ 306 ] := [ 3183043940113, 154587496735, 1103341869990385, 33686001, 505413919, 35652081, 154588414239, 10371469073, 47304807022879, 287 ]; PROPERTIES_SMALL_GROUPS[ 306 ] := 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[ 308 ] := [ 7920970905, 14249290509, 4458460650059, 5130590, 86779840059, 46400059, 25920095, 14474720059, 59 ]; PROPERTIES_SMALL_GROUPS[ 308 ] := rec( isNilpotent := [ 4, 9 ], isAbelian := [ 4, 9 ], lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 5, -9 ], [ 1, -4 ] ] ), frattFacs := rec( frattFacs := [ 3, 5, 7, 9 ], pos := [ 1, 2, 3, 4 ] ) ); SMALL_GROUP_LIB[ 312 ] := [ 252021598648337099, 810358411559627, 400698637895233, 4382081982989003, 1367226422168675351, 1280137378032, 425199844327363773131, 78630722206752973979, 807762245032091, 252021546416756891, 807762244783259, 807762248515739, 1364811990462694091, 425449898275480298519, 5173307544803351 , 5173307544554519, 1614072063294268439, 5173307548286999, 1614072063298000919, 1614072063297752087, 503590483857053721623, 2597981755547, 2597985239195, 252815262783906971, 39253642635061668672, 12214231401232964802948, 1367193085643990171, 14044827064475, 4382028986996891, 14044826815643, 14044830548123, 125014161014794801, 1284244348465, 400686410522161, 1284244099633, 1284247832113, 426574594253263021079, 4382134997391383, 1367226263174731799, 4382134997142551, 4382135000875031, 4077112596, 4080845076, 398134262375700, 1362820016615574683, 1367185560896130071, 77636182803139971792, 24222489085176976985328, 2590878597143, 15494050602419915, 258007482192496331 , 4374399132748955, 1363621468878720023, 16580763058199, 10192158743, 2556575616240, 826947358951115, 44877348887, 4108714117, 14044842491927, 23 ] ; PROPERTIES_SMALL_GROUPS[ 312 ] := rec( isNilpotent := [ 6, 42, -44, 61 ], isSupersolvable := [ 1, -24, 27, -46, 49, 52, -55, 58, -61 ], isAbelian := [ 6, 42, 61 ], lgLength := rec( lgLength := [ 3, 4, 5 ], pos := [ [ 49, 54, -55, 58, -61 ], [ 8, -12, 15, -48, 50, -53, 56, -57 ], [ 1, -7, 13, -14 ] ] ), frattFacs := rec( frattFacs := [ 4, 7, 10, 13, 16, 19, 23, 26, 29, 32, 35, 38 , 41, 44, 47, 50, 53, 56 ], pos := [ 1, 2, 3, 4, 5, 6, 7, 12, 13, 14, 21, 24, 25, 26, 31, 36, 41, 44 ] ) ); SMALL_GROUP_LIB[ 315 ] := [ 213706847, 665203, 705299, 275 ]; PROPERTIES_SMALL_GROUPS[ 315 ] := rec( isNilpotent := [ 2, 4 ], isAbelian := [ 2, 4 ], lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 3, -4 ], [ 1, -2 ] ] ), frattFacs := rec( frattFacs := [ 3, 5 ], pos := [ 1, 2 ] ) ); SMALL_GROUP_LIB[ 324 ] := [ 25466735817778565467928399, 2303853676463831, 1485950078920212988, 78601036474625185347343, 7110653904655, 748681409580811479, 741840889256919255, 719576453678125736535, 240358680937548268759, 242595552174519936599, 2303853676495575, 77876235399235891291735, 746412977514766423, 241830914488384544855, 481450086198193316055, 78353216307762574058071, 241837804148511367383, 78353216300739497222743, 78359933705878052598607, 241849364810640159055, 78598804168392182920527, 78353214011720170795087, 25386441344360643705238095, 155509110651275061538895 , 8225206994835599378133087055, 7110653903323, 21156807639259, 6868721951900123, 7110653904091, 2289632368723163, 7110654230619, 2303678522655067, 2303700265927003, 746398712712200667, 863531529999785960336000772207439, 741018462665111347983, 77875536940588435611919, 242636686769068516623, 78353216420543727493135, 25386442122538686225408271, 25386442124821207873052943, 4586265668272572, 1485949903363426748, 4586265668272508, 1485949903363426684, 4586265668272380, 1485950076772731132, 1485949903363426556, 1485950076772735164, 1485978256053164220, 481456954961475721468, 4586265668274364, 5920882723718809724, 2962734407988926524, 9144242534467644, 959926004373256259836, 959925976367922010300, 2962734581398227132, 4586265668274300, 4586265668278332, 2310745085756687, 2289632370802959, 2220914980483555855, 741847780667999503, 748751704236811791, 7110653936399, 240358751232205055503, 2303743761604623, 746391711381512207, 1485957056171106575, 241830914530129011215, 746412975770853647, 241830914508452848143, 241851647240347644687, 746448656807260431, 242588901754280146191, 241830907443567194127, 78353214025804442300943, 479966390898991869967, 25386441342085183252263695, 21944599311, 65297973519, 21199758295823, 21944599823, 7066765755663, 21947744271, 7110120178191, 7110187287055, 2303699731874575, 2310745085756507, 7110653935963, 2289632368967771, 21156807671899, 741847780666164315, 6854675798262107, 746455094224020055, 2303853676511447, 741840889256796247, 2303853684875351, 240356454622191346263, 240356454622191477335, 746448027668996311, 241849350634025840975, 746448596617949263, 21944598749, 21944664157, 7066764771549, 7066764771933, 241844602573858848983, 242588845484046049367, 78598785936263673307351, 228476044699931034545026127, 157683354242016200585295, 2353035280531983, 21156807868687, 2289762427355151, 741882982629556239, 741890070861726223, 6717468538447315983, 760277051340701967, 240370269491070484495, 2346512366649359, 247067019691730620943, 240370269536167612431, 77880706866753103942159, 14155138515260, 4586265131405628, 4586265131405500, 9144241997594748, 28222968414268, 9144241997594940, 2962734407452053692, 14155138515068, 4586265131405436, 14155138519100, 7131927462927, 21944631823, 7066766852111, 65298006031, 2289653644313615, 21156406002191, 2303873742070287, 7110653952271, 2289632369762319, 7110662316047, 741840909323264527, 741840909324313103, 2303851940045071, 746448613051265295, 2303853684879375, 67109135, 68157455, 21811429647, 21811430415, 21944631389, 7110653952091, 2303853676519511, 746448596609593423, 67108958, 24675464984170254868242298919 , 746433958580895835, 725488178091953021015, 705172975439628661420111, 8225834051926837478875459663, 65297219599, 21330217304079, 6910990872911887, 6911555661168655, 20732927520522255, 725547467232743239695, 43687919676, 67141647, 21944647695, 7110653960207, 2303853676523535, 15 ]; PROPERTIES_SMALL_GROUPS[ 324 ] := rec( isNilpotent := [ 2, 5, 26, -34, 81, -89, 105, -108, 151, -154, 159, 176 ], isSupersolvable := [ 1, -2, 4, -34, 36, -41, 61, -108, 114, -125, 136, -159, 165, -170, 172, -176 ], isAbelian := [ 2, 5, 26, 29, 81, 84, 105, 151, 159, 176 ], lgLength := rec( lgLength := [ 2, 3, 4, 5, 6 ], pos := [ [ 168, -171, 175, -176 ], [ 36, -37, 46, -48, 52, 59, 69, 74, -75, 81, -83, 116, 119, -135, 138 , 144, 149, -154, 158, -160, 163, -167, 172, -174 ], [ 14, 19, -20, 26, -28, 35, 38, -45, 49, -51, 53, -58, 60, 62, -63, 68, 70, -73, 76, -80, 84, -89, 92 , 98, 103, -108, 112, -115, 117, -118, 136, -137, 139, -143, 145, -148, 155, -157, 161, -162 ], [ 3, -5, 7, -8, 13, 15, -18, 21, -25, 29, -34, 61, 64, -67 , 90, -91, 93, -97, 99, -102, 109, -111 ], [ 1, -2, 6, 9, -12 ] ] ), frattFacs := rec( frattFacs := [ 9, 17, 26, 34, 42, 27, 35, 43, 76, 84, 92, 100, 108, 116, 101, 109, 117, 125, 294, 302, 310, 318, 326, 334, 342, 350, 358, 366, 415, 423, 431, 439, 447 ], pos := [ 1, 2, 3, 4, 5, 18, 25, 34, 35, 41, 60, 73, 80, 89, 95, 102, 104, 108, 111, 113, 118, 122, 125, 135, 141, 148 , 150, 154, 155, 156, 157, 158, 159 ] ) );