col11.z

#############################################################################
##
#W  col11.z                GAP library of groups           Hans Ulrich Besche
##                                               Bettina Eick, Eamonn O'Brien
##

SMALL_GROUP_LIB[ 500 ] :=
[ 1589809005115474162751, 4236666481871, 199123534354642374823512093759,
3179618010226995263, 8472506431, 6358598838068431, 12625274604751,
2109861161272527, 1054934598838592719, 3177504082755818559, 2160697804948543,
8472497395, 8472757491, 16785688759539, 6295692670799055,
1592789066326638535887, 1588594741388673483983, 794821658710934716884175,
7867487018322756342847, 795871304535263676179519, 263732594779726286652479,
397189579811170822391829567, 270086969512639335466047,
397189056571851688380437567, 540173947793050534975, 6610349001609279,
1055182054221086783, 12717197041727, 25249845311, 4219723776063,
2109869199138879, 6355008161550399, 4321393606719, 16781375, 18874431,
33573310527, 25249842419, 12709160748239, 6355001802982463, 16778492,
12591393015027, 6299970860942543, 3177189516672959695, 3177189558615999695,
3149985849804031039, 1588594779726284555327, 1588594758754764555327,
794374965318335334417471, 794374965339516569617471, 125880107071,
63543756849215, 31771879225065535, 50462783, 25417678911, 12709999640639, 63
]; 

PROPERTIES_SMALL_GROUPS[ 500 ] := rec(
isNilpotent := [ 2, 5, 12, -14, 34, -36, 40, 56 ], 
isAbelian := [ 2, 5, 12, 34, 40, 56 ], 
lgLength := rec( lgLength := [ 2, 3, 4, 5 ], pos := [ [ 51, -52, 55, -56 ], [
26, -27, 30, 32, -36, 39, -40, 45, -50, 53, -54 ], [ 4, -5, 8, 10, -14, 17,
19, -25, 28, -29, 31, 37, -38, 41, -44 ], [ 1, -3, 6, -7, 9, 15, -16, 18 ]
] ),
frattFacs := rec( frattFacs := [ 7, 13, 20, 26, 32, 21, 27, 33, 58, 64, 70,
76, 82, 88, 94, 100, 77, 83, 89, 95 ], pos := [ 1, 2, 3, 4, 5, 9, 11, 14, 18,
21, 23, 25, 27, 31, 33, 36, 37, 38, 39, 40 ] ) );

SMALL_GROUP_LIB[ 510 ] :=
[ 505413951, 102760947, 258405826879, 35652593, 257264976671, 51509202707,
131788223021375, 319 ]; 

PROPERTIES_SMALL_GROUPS[ 510 ] := rec(
isNilpotent := [ 8 ], 
isAbelian := [ 8 ], 
lgLength := rec( lgLength := [ 4 ], pos := [ [ 1, -8 ] ] ),
frattFacs := rec( frattFacs := [ ], pos := [ ] ) );

SMALL_GROUP_LIB[ 513 ] :=
[ 85395335964767, 27734355631, 43580445078835295, 166460239439,
85393294286543, 85394315493071, 166460134463, 85393294181567, 166460869295,
53859151, 54593983, 27627275215, 84952158995519, 325851695, 6191 ]; 

PROPERTIES_SMALL_GROUPS[ 513 ] := 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[ 516 ] :=
[ 14880633025612829, 28841890146845, 826967512981, 33774102561821,
17427589608779363, 1596303534, 28839198528083, 35415282599507, 56558186579,
1649099452140, 14952976195644689, 65420296787, 1692764347, 33774149235539, 83
]; 

PROPERTIES_SMALL_GROUPS[ 516 ] := 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[ 520 ] :=
[ 3317792308282947, 12153888387436619, 6348767134153466927, 2128124986992,
6313380188385775691, 3281266723739590222895, 1720831889515300419,
11631633956527624971311, 1716673256323354041541679, 1716673270654344574559279
, 43016556414081071, 43016556413832239, 22368609517408183343,
43016556417564719, 22368609517411915823, 22368609517411666991,
11631676949234215953455, 6319994437693744571, 23372690725307,
12153835391441339, 23372690476475, 23372694208955, 1725241403663854131,
6380323708467, 3317771927182899, 6380323459635, 6380327192115,
3301358772201633948719, 12209166594644015, 6348766869161072687,
12209166594395183, 12209166598127663, 4077112884, 4080845364,
1104507937760820, 1716691593293990466997295, 22370699807365109807,
6348643912084737071, 12134757704519099, 3309294085329459,
3301291416547653110831, 3301291444107250289711, 22368526839014280239,
6313435466592734255, 82723796287535, 44877348911, 12262441095, 23478704603183
, 47 ]; 

PROPERTIES_SMALL_GROUPS[ 520 ] := rec(
isNilpotent := [ 4, 33, -35, 49 ], 
isAbelian := [ 4, 33, 49 ], 
lgLength := rec( lgLength := [ 3, 4, 5 ], pos := [ [ 45, -49 ], [ 11, -44 ],
[ 1, -10 ] ] ),
frattFacs := rec( frattFacs := [ 4, 7, 10, 13, 17, 20, 23, 26, 29, 32, 35, 38
, 41, 44, 47 ], pos := [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 17, 22, 27, 32, 35
] ) );

SMALL_GROUP_LIB[ 522 ] :=
[ 86409532933837, 4444583683399, 51722774126526469, 315934725, 8516674375,
334374405, 4444592288583, 165249057485, 2320089187040071, 839 ]; 

PROPERTIES_SMALL_GROUPS[ 522 ] := 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[ 525 ] :=
[ 353054075, 666501, 705371, 7666078881, 195140099291, 347 ]; 

PROPERTIES_SMALL_GROUPS[ 525 ] := 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[ 528 ] :=
[ 155228552823309090001, 1392361972171277010009, 735170349213156103000019,
293437702169019000, 1700479912382982000019, 1700479912382981000019,
897853393804988935000019, 897853375534600742000019, 897853375534600741000019,
474066582282335949351000019, 476018778818233767524000019,
474066591910865146470000019, 476018788446762964517000019,
251337915216027460834918000019, 251337915216027460834917000019,
474066591910830543462000019, 250307160528918559068775000019,
476018798093527946789000019, 251337925393364551734823000019,
132706419234062499352417895000019, 250307160528936829456999000019,
251337920299872641095207000019, 1700479912382979000019,
1700479912383010000019, 1700479912383009000019, 897853412075377187000019,
897853393770385955000019, 897853393804988963000019, 897853375534600739000019,
86305520454038717388190000, 2637049102858001009, 1392355858973226001009,
735167103058838186001009, 735167103070372522001009,
388168230421167866539001009, 2637049102857001009, 1392355858973225001009,
2637049102851001009, 1392361937568291001009, 1392355858973219001009,
2637049102882001009, 897846938210142888001009, 474063183374965541545001009,
474063183374965541546001009, 250305360821981816031915001009,
2637049102881001009, 293993447946009001, 155226885587498009001,
81960670913888938009001, 81960670917034666009001, 43275234244197089963009001,
293993447945009001, 155226885587497009001, 293993447939009001,
155228543386147009001, 155226885587491009001, 293993447970009001,
244642840254089896009001, 129171419654161173161009001,
129171419654161173162009001, 68202509577397101136555009001,
293993447969009001, 1392368085369606000019, 735170330873561894000019,
388169944329804055398000019, 388169944329838658406000019,
204953730606154845782887000019, 1392368085369605000019,
735170330873561893000019, 1392368085369603000019, 735170349109347107000019,
735170330873561891000019, 1392368085369634000019,
1420719219164864055140000019, 750139747719048254719845000019,
750139747719048254719846000019, 396073786795657478525683559000019,
1392368085369633000019, 555745283001900, 1108344865001900, 585760768035001900
, 555745297001900, 292881956913001900, 154641674277168001900,
81650804017074481001900, 43111624521014055219001900,
6394018032482109694095311321091000, 12109882637276722905661912091000,
86304590857803006849090100, 3376041521155783082495580445177019000,
6394018032492013413817522680019000, 45568823982292073546689001900,
25561508566397325692173010090, 48411948042419195148010090,
5096712527944193010009, 901550717424113158000019, 897853375499997766000019,
476018778799963379270000019, 897853375499997765000019,
476018778799963379269000019, 474066582264030958151000019,
251337915206380695852615000019, 1700479877780004000019,
901550717424113188000019, 476018778799963379238000019, 3220605768196000019,
1707482419303940000019, 1700479877780036000019, 901550717424113220000019,
3220605768194000019, 1700479877780034000019, 901550717424113218000019,
3220605768193000019, 1707482419303937000019, 1700479877779971000019,
3220605768224000019, 1700479877780002000019, 1700479877780001000019,
897853375499997731000019, 3233868158464000019, 3220605768256000019,
1707482419304000000019, 586317574145019000, 82269658607130648019000,
43438379744493705241019000, 1392355847438917000109, 4994368004000109,
2637037568580000109, 2637037568578000109, 6099568128000109,
1700467674449474000109, 1700467674449414000109, 897846932120012358000109,
4994368001000109, 4994368064000109, 155226882441797000901, 556794372000901,
293990302276000901, 293990302274000901, 1661994496000901,
463338709452354000901, 463338709452294000901, 244642838593144390000901,
556794369000901, 556794432000901, 735170330838958917000019,
2637060637444000019, 1392368050766660000019, 1392368050766658000019,
9651759351552000019, 2690756096868484930000019, 2690756096868484870000019,
1420719219146593666886000019, 2637060637441000019, 2637060637504000019,
1048577000190, 1048608000190, 292880908323000190, 554696740000190,
86304590879973815424001900, 163455664503784320009100,
86304590875553006528001900, 9652864598528001009, 6099571200000019,
1110540288001900, 309577899836352190000, 9437696000019, 1049088000091,
4994368256000019, 19 ]; 

PROPERTIES_SMALL_GROUPS[ 528 ] := rec(
isNilpotent := [ 4, 79, -86, 156, -159, 170 ], 
isSupersolvable := [ 1, -29, 31, -86, 96, -122, 126, -159, 164, 167, -170 ], 
isAbelian := [ 4, 79, 82, 156, 170 ], 
lgLength := rec( lgLength := [ 3, 4, 5, 6 ], pos := [ [ 164, 166, -170 ], [
23, -30, 38, -41, 46, 54, -57, 62, 70, -73, 78, -81, 96, -122, 126, -163, 165
], [ 5, -22, 31, -37, 42, -45, 47, -53, 58, -61, 63, -69, 74, -77, 82, -95,
123, -125 ], [ 1, -4 ] ] ),
frattFacs := rec( frattFacs := [ 5, 9, 13, 17, 22, 26, 30, 34, 38, 42, 127,
131, 135, 139, 143, 147, 151, 155, 159 ], pos := [ 1, 2, 3, 4, 29, 30, 46, 62
, 78, 86, 89, 92, 95, 122, 125, 135, 145, 155, 159 ] ) );