col11.z

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

SMALL_GROUP_LIB[ 1470 ] :=
[ 599355171509831597159, 407751195275493479, 880457198631601860364391,
830216442164327, 1383257615088743, 562480786221, 2033415099269220455,
187664149723, 2034773259838523855, 826847158798773, 2989120240684006993511,
127464551, 1789979572757028640463, 2627688019365242093615975, 187926884711,
406623393929300327, 410477635190458727, 276618385152359, 279240317983079,
1928061499705703, 1311608402279, 276242036705699, 189964818851,
597736389075060446567, 603402123728963294567, 406629026625070439,
410483267886228839, 2834250415253443943, 276632653925735, 279254586756455,
1928075768479079, 135364967, 188184674663, 189968302439, 638005607,
940865145191, 383201709, 939081517475, 1383088298038631, 128398171,
937297890119, 1383075812644559, 562481253621, 1380452096186483,
2033139826771131239, 359 ]; 

PROPERTIES_SMALL_GROUPS[ 1470 ] := rec(
isNilpotent := [ 12, 46 ], 
isSupersolvable := [ 1, -12, 15, -46 ], 
isAbelian := [ 12, 46 ], 
lgLength := rec( lgLength := [ 4, 5 ], pos := [ [ 13, -14, 16, -21, 24, -31,
33, -34, 36, -37, 39, -40, 42, -43, 45, -46 ], [ 1, -12, 15, 22, -23, 32, 35,
38, 41, 44 ] ] ),
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[ 1476 ] :=
[ 5413122673863170496041, 142648451858739264079, 8594444908642510950403161,
102148080128001679, 210512361632366899264079, 1375118796735998705975808003161
, 5848360152498585603161, 10967615085061057600, 96645166284801679,
3667427296051262441, 5822792178516377603161, 68786995201679,
96645165977665639, 2481363456126401, 142648451865088064079,
3662488082946496041, 210549115542801715201679, 619079372801679,
142623551953408065639, 210512361632373248064079, 310716245769353871462401679,
7978990322004177820096041, 677037139093053106401204736001679,
482855904869176003208908801679, 101594497024001679, 150161457034035201679,
2481461657662441, 149953587304857601679, 221638310653267148801679,
7430648629886400, 65444249601679, 1690828803161, 96645172428801679,
2481369907262441, 142648451868262401679, 1679 ]; 

PROPERTIES_SMALL_GROUPS[ 1476 ] := rec(
isNilpotent := [ 4, 12, 18, 36 ], 
isSupersolvable := [ 1, -7, 9, -21, 25, -29, 31, -36 ], 
isAbelian := [ 4, 12, 18, 36 ], 
lgLength := rec( lgLength := [ 3, 4, 5 ], pos := [ [ 26, -31, 34, -36 ], [ 7,
-13, 16, -19, 21, -25, 32, -33 ], [ 1, -6, 14, -15, 20 ] ] ),
frattFacs := rec( frattFacs := [ 5, 9, 13, 17, 22, 26, 30, 34, 38, 42, 46, 50
, 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 ] ) );

SMALL_GROUP_LIB[ 1480 ] :=
[ 6517283071366012611, 76003647809939658467, 112646140434726387379343,
271614140170103951, 112470154705861577627363, 9636891690009527066307,
246739607492291202679883099279, 246739607572580489080862862479,
527709444359980175326375055, 166455989705984661702503567,
240919359628625528975, 240919359628565062799, 356560652376227518737551,
240919359629472055439, 356560652376228425730191, 356560652376228365264015,
527709765516942500944948367, 112485344533954454895443, 51353774409078611,
76003611155645962067, 51353774348612435, 51353775255605075,
9645571607663473384755, 4403570804259123, 6517278118761347379,
4403570743792947, 4403571650785587, 166716287572313301746789519,
76112256814543816847, 112646140251451896268943, 76112256814483350671,
76112256815390343311, 183275458569359, 183276365561999, 401717862870638275727
, 246739867614172095822249698447, 356564772407300649339023,
112645912990231978878095, 75993348227663180627, 6511413800333038899,
166715951008305002109576335, 166715951062554519948076175,
356560435378252789687439, 112470263314866121319567, 162783265937817743,
34681463636111, 2979773154543, 51427088317218959, 143 ]; 

PROPERTIES_SMALL_GROUPS[ 1480 ] := 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[ 1482 ] :=
[ 797471599643, 807789480731, 1181839269711131, 12108348385307,
1192582259929115, 1183501691482139, 637840895105, 17944568616110363,
1192592577810203, 1183512009363227, 1767406885623943451, 1753949483185525019,
550914587, 443419265, 804730899995, 798603660827, 917070875, 594584705,
1365358167323, 57110815, 1355146105103, 876898965665, 2023466617165211, 539 ]
; 

PROPERTIES_SMALL_GROUPS[ 1482 ] := rec(
isNilpotent := [ 24 ], 
isAbelian := [ 24 ], 
lgLength := rec( lgLength := [ 4 ], pos := [ [ 1, -24 ] ] ),
frattFacs := rec( frattFacs := [ ], pos := [ ] ) );

SMALL_GROUP_LIB[ 1484 ] :=
[ 27803567901621, 283525290124803, 421930311632863799, 1388863394359,
420618042797778435, 624198351516214575671, 1472379070210359, 191154889015,
18951711329, 284319031832887, 311 ]; 

PROPERTIES_SMALL_GROUPS[ 1484 ] := 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[ 1485 ] :=
[ 14478979994113119, 134086656311139, 19482624211319, 19482625611319,
28931106817811319, 90112111139, 90113611139, 133906433711139, 4096011139,
11139 ]; 

PROPERTIES_SMALL_GROUPS[ 1485 ] := rec(
isNilpotent := [ 2, 6, -8, 10 ], 
isAbelian := [ 2, 6, 10 ], 
lgLength := rec( lgLength := [ 3, 4, 5 ], pos := [ [ 9, -10 ], [ 3, -8 ], [ 1
, -2 ] ] ),
frattFacs := rec( frattFacs := [ 4, 7, 11, 14 ], pos := [ 1, 2, 5, 8 ] ) );

SMALL_GROUP_LIB[ 1494 ] :=
[ 51841530485840663, 2803231682281735, 89756977668226919383, 1921427062535,
1876486159591, 24595437111, 2803232315252199, 34655675994839,
4188031603262713447, 6887 ]; 

PROPERTIES_SMALL_GROUPS[ 1494 ] := 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[ 1496 ] :=
[ 346322489029226505, 577169834363621391, 868679050497853751455,
4812528038183071, 863253391558847795215, 1291432306743901980459167,
5883058512663150751, 5883058512662102175, 8801055537150297112735,
5883058512677830815, 8801055537150312841375, 8801055537150311792799,
13166379083579049152348319, 863445635373068192015, 385808458582287,
577169542319442191, 385808457533711, 385808473262351, 518098160856203267849,
231498873573129, 346322300064239369, 231498872524553, 231498888253193,
1299543854741593414172831, 580667810412232863, 868679047285233942687,
580667810411184287, 580667810426912927, 3212636586143, 3212652314783,
7194739050307125407, 1291426727289682043899919, 1931974389258323357105914015,
868674549600228475039, 577041045470054671, 863256889534895358111,
3932524266913951, 257832255647, 154753040633, 388144985800863, 159 ]; 

PROPERTIES_SMALL_GROUPS[ 1496 ] := rec(
isNilpotent := [ 4, 29, -31, 41 ], 
isAbelian := [ 4, 29, 41 ], 
lgLength := rec( lgLength := [ 3, 4, 5 ], pos := [ [ 37, -41 ], [ 7, -31, 34,
-36 ], [ 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[ 1500 ] :=
[ 14524602612136850237, 98259280944428201545404735,
147388923214046689499287490687, 9697499283558527,
331625073187465575401780394015166783, 497437316247027207156803067269149986943
, 4076928950526825629407084671, 43496233404122294256, 65462526825629402890367
, 9683068195487997, 98193791407645951707152511, 6463925878911,
76173585147139060579997274869887, 33919576852835663911326015,
14737500061340537151, 43670160273732342223, 29023348879020495,
14524602397523710415, 87016757904273866559951, 65505955368566525595967,
14640953491470160191, 9683068195460045, 28997536129749965,
43496226940199654349, 65505472184530977231647, 43534959212969866039,
21786903596401656599327, 130525137088184530994008863,
98258934250348405067681919, 21961430238008719446143, 8053063716991,
8053600555135, 9671730016587903,
[ (1,2,3,4,5), ( 3, 4, 5)( 6, 7, 8, 9,10,11,12,13,14,15,16,17,18,19,20,21,
     22,23,24,25,26,27,28,29,30) ],
114260378111891186751899211377938559, 111253219937254869924180768044093759,
342555478619472122653411946856720367743, 52217967883699160865264369791,
22613051235224157421695, 43496239869120762319, 98257860432287233934954959,
98170887296250621792883151, 147386790576001439234069172687,
2446183598272184745792704831, 149343685253371917926477107519,
49021837354243345993260601663, 221082599367187286622634195358015,
49413216263490223852966383935, 221082599367187528214544595358015,
32942144195277842237886783, 65244359737965238301495,
147386790648662622419379884831, 147256330944375930389899252511,
221080185864002390622419396662047, 3669275332179658828532428902527,
224015527880059074387829109592191, 73532756031365018990187963486335,
331623899050780931131449205126402175, 74119824395235335779947946709119,
331623899050781293519314805126402175, 49413216292916763858344611967,
217462200032719044735, 21786903454668305203327, 362416979040122503391,
48337773876232439, 14737125926323093727, 87335504723040256721119,
2717952633645895664599167, 15703571135429345407, 326193300828603183562879,
65462469623038799052927, 32680355182002110529798271,
98193703952153854807441535, 32942144176111550504632447, 9825000420802687,
28997488881977328, 38674037319141360, 58011055984886171632,
23352420626634127574079, 29094125646184575, 19348829798527, 9683068733358207,
14524608750183055487, 43641645895660404863, 9760635841151103, 6455337976061,
19331717005565, 28997484653084925, 43670314789476303071, 29023305930391799,
14524602397524230367, 87016758058789610520799, 65462469623038751867007,
14640953491470418047, 4295000191, 4831838335, 6447282815103,
652580864121200609842434847, 538439775594097902392587325567,
362967706049211011391, 260933787834397439824335, 1957003234231662738960552255
, 48395798915846607, 19348829770227, 29087773389492687, 43631982738935386431,
6455337948145, 29023305930380231, 43631660401639822111,
65447974110008184672383, 1610612740223,
[ ( 1, 2, 3, 4, 5)( 6, 7, 8, 9,10), ( 1, 4, 3, 5, 2)(11,12,13,14,15) ],
807661718259803278718571795714175, 880651533940743412343802821088031,
1981465951369085919864756024939846045823,
1320977300911115118999208760637657215, 147256570120338138510379717071,
331330366803902405192154048076714303, 331330366803902405143674604723114303,
1104424275902434183183295808278847, 148724088773240633491228987711,
65592783501164577558847, 1656633627562634521108249351276069951,
1125899649238567647180712575199, 1688849476032178664691269535268991,
1125899301201416620933050531967, 652580864121844853780250751,
1304668939171463174291583, 159537653388084248799, 239306480402366345248895,
173955858556599140479, 1304668822821108339703935, 241978470544965759,
28997495323365875, 65447258223357658665423, 65447258255569913385423,
217461742709416923599, 147257939946499194604697948479,
147257939946547674048051548479, 490854407490223852429513023,
490854407490384913703113023, 1630789026860616455295295, 43496239826172122055,
98170887335034389882475295, 98170887383352771962475295,
326192614063637614039839, 220886909919748791907947443392639,
220886909919821511072977843392639, 736281611235335779947409838207,
736281611235577371857809838207, 2446183540290926187393060991, 19391811944575,
29087988169834623, 44211416562130223231, 32225158496503, 241611302188875999,
29087773421469919, 43631595762430247135, 1811968415988142571647,
43631982738967101567, 218157514955451269247, 98171960100075666992267391,
66317124843666975490175, 32264196980863, 19331650947056, 72594020528190916367
, 12886999167, 19391780487295, 29087988138377343, 4297064701, 19348830814455,
29087773390012639, 43631982738935644287, 127 ]; 

PROPERTIES_SMALL_GROUPS[ 1500 ] := rec(
isNilpotent := [ 4, 12, 31, -33, 95, -97, 111, 174 ], 
isSupersolvable := [ 1, -7, 9, -12, 16, -33, 40, -74, 80, -97, 104, -111, 134
, -163, 167, -174 ], 
isSolvable := [ 1, -33, 35, -111, 113, -174 ], 
isAbelian := [ 4, 12, 31, 95, 111, 174 ], 
lgLength := rec( lgLength := [ 3, 4, 5, 6, false ], pos := [ [ 123, 128, 132,
-133, 153, -154, 159, -163, 165, 169, -170, 173, -174 ], [ 37, -39, 62, -63,
66, 68, -79, 82, 84, -88, 91, 93, -97, 100, 102, 106, -107, 110, -111, 118,
-122, 124, -127, 129, -131, 138, -142, 147, -152, 155, -158, 164, 166, -168,
171, -172 ], [ 7, -15, 18, 20, -24, 27, 29, -33, 35, -36, 42, 44, -50, 53, 55
, -61, 64, -65, 67, 80, -81, 83, 89, -90, 92, 98, -99, 101, 103, -105, 108,
-109, 113, -117, 134, -137, 143, -146 ], [ 1, -6, 16, -17, 19, 25, -26, 28,
40, -41, 43, 51, -52, 54 ], [ 34, 112 ] ] ),
frattFacs := rec( frattFacs := [ 7, 13, 19, 25, 38, 44, 50, 56, 62, 68, 74,
80, 33, 39, 45, 51, 57, 63, 69, 75, 81, 136, 142, 148, 154, 160, 166, 172,
178, 184, 190, 196, 202, 208, 214, 220, 226, 232, 238, 244, 250, 256, 262,
268, 274, 280, 286, 292, 298, 161, 167, 173, 179, 185, 191, 197, 203, 209,
215, 221, 227, 233, 239 ], pos := [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13
, 14, 15, 19, 21, 24, 28, 30, 33, 34, 35, 36, 37, 38, 39, 43, 46, 48, 50, 54,
57, 59, 61, 63, 67, 69, 72, 74, 75, 78, 79, 83, 85, 88, 92, 94, 97, 98, 99,
100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111 ] ) );