col18.z

#############################################################################
##
#W  col18.z                GAP library of groups           Hans Ulrich Besche
##                                               Bettina Eick, Eamonn O'Brien
##

SMALL_GROUP_LIB[ 760 ] :=
[ 53763157193932011, 304437711445097993, 232053513441830655911,
23590532798460, 40788355011749756139, 588955644529181384021927,
1019661811370588807, 1019661811368699239, 774942978661979213735,
1019661811397042759, 774942978662007557255, 774942978662005667687,
588956663785123128320423, 231372214052386661693, 400574633491997,
304437123254685725, 400574631602429, 400574659945949, 40859881788394600167,
70740834275271, 53763002424992199, 70740832385703, 70740860729223,
176360667983235889473959, 305333562944619143, 232053510500784198791,
305333562942729575, 305333562971073095, 30960572958, 30988916478,
17905294380881502, 774976906904747342471, 53668903478590119,
774941637534889651559, 1341657616011335, 526539460679, 93117911349,
401751180564551, 71 ]; 

PROPERTIES_SMALL_GROUPS[ 760 ] := rec(
isNilpotent := [ 4, 29, -31, 39 ], 
isAbelian := [ 4, 29, 39 ], 
lgLength := rec( lgLength := [ 3, 4, 5 ], pos := [ [ 35, -39 ], [ 7, -34 ], [
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[ 765 ] :=
[ 33625073, 4415 ]; 

PROPERTIES_SMALL_GROUPS[ 765 ] := rec(
lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 2 ], [ 1 ] ] ),
frattFacs := rec( frattFacs := [ 3 ], pos := [ 1 ] ) );

SMALL_GROUP_LIB[ 770 ] :=
[ 11874880359, 12110240359, 9142708960359, 16640359, 46400359, 25920395,
35763680359, 15680593, 35651040539, 19820000935, 27538847280359, 359 ]; 

PROPERTIES_SMALL_GROUPS[ 770 ] := rec(
isNilpotent := [ 12 ], 
isAbelian := [ 12 ], 
lgLength := rec( lgLength := [ 4 ], pos := [ [ 1, -12 ] ] ),
frattFacs := rec( frattFacs := [ ], pos := [ ] ) );

SMALL_GROUP_LIB[ 774 ] :=
[ 33456058931054423, 43228384077143, 960608299153903, 50626852061015,
856295033444421439, 1599415231, 43225291051319, 43228427640887,
33456058974618167, 56159891255, 65420298551, 1692766111, 50626895624759,
1238056783279, 39185307301958327, 1847 ]; 

PROPERTIES_SMALL_GROUPS[ 774 ] := rec(
isNilpotent := [ 6, 16 ], 
isAbelian := [ 6, 16 ], 
lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 7, 10, -11, 14, -16 ], [ 1,
-6, 8, -9, 12, -13 ] ] ),
frattFacs := rec( frattFacs := [ 3, 5, 7, 9, 11, 13 ], pos := [ 1, 2, 3, 4, 5
, 6 ] ) );

SMALL_GROUP_LIB[ 776 ] :=
[ 2491004297545777247, 33832956681216, 1931025889688558764127,
1933016063491414425695, 3210049096777823, 2491000079945564255,
3210049011843167, 3210049606385759, 43571487648, 44166030240,
26220343021544352, 1499551830721723930509407, 2490223953089396831,
4133939576927, 95 ]; 

PROPERTIES_SMALL_GROUPS[ 776 ] := rec(
isNilpotent := [ 2, 9, -11, 15 ], 
isAbelian := [ 2, 9, 15 ], 
lgLength := rec( lgLength := [ 2, 3, 4 ], pos := [ [ 14, -15 ], [ 4, -11, 13
], [ 1, -3, 12 ] ] ),
frattFacs := rec( frattFacs := [ 4, 7, 11, 14, 17 ], pos := [ 1, 2, 3, 8, 11
] ) );

SMALL_GROUP_LIB[ 780 ] :=
[ 4995760267056251, 5085010946609903, 3896775728608105199, 6413161321595,
35032520053883, 9560276982003, 27408284438549231, 3192216217201,
27325499648565335, 7457052206896719, 21378462619652213951, 4077114612,
[ ( 1, 4, 3)( 6,14, 9,17,12, 7,15,10,18,13, 8,16,11), 
  ( 1, 2, 5)( 6,16,13,10, 7,17,14,11, 8,18,15,12, 9) ],
21286494444161979515, 75457667489002345199, 13006534298979991643017967,
13006534299021331038786287, 58856975556333099864815, 16615081291000673260271,
19966974180065471, 6405803606207, 6519939858623, 4995867045593279,
27296776090932347, 7444293646670067, 16675048962611576885999,
16675049003950972654319, 75480032101890052847, 21299007772004504303,
21298924987214520407, 5809027855352141391, 13006538223081324153818303,
13006538190836595454528703, 58874392795105758956735, 16613226062126363593919,
124063192055999, 41384400519623, 96940928145162431, 15912157447743,
96769430749937855, 161258782094327999, 75613924044549882047, 9172943039,
6372185434992, 5043565337175371, 44877349055, 12262441239, 35138534179007,
4108714549, 35032535728583, 9560292656703, 27408284446261439, 191 ]; 

PROPERTIES_SMALL_GROUPS[ 780 ] := rec(
isNilpotent := [ 12, 53 ], 
isSupersolvable := [ 1, -12, 14, -43, 46, -53 ], 
isSolvable := [ 1, -12, 14, -53 ], 
isAbelian := [ 12, 53 ], 
lgLength := rec( lgLength := [ 4, 5, false ], pos := [ [ 20, -23, 36, -53 ],
[ 1, -12, 14, -19, 24, -35 ], [ 13 ] ] ),
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[ 783 ] :=
[ 247360359821, 315342021, 319644613, 246733391045, 22791 ]; 

PROPERTIES_SMALL_GROUPS[ 783 ] := 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[ 784 ] :=
[ 73211053665657731224379363, 23635507464037759428,
45000309856271886550715480897507, 93381446002102259313059,
73212183830560924351672739, 57398354408510056975700509091,
57398354408510059372896240035, 93381446002102259266403,
73212183830560924351626083, 93381446002102259173091,
73212183832437928608861923, 73212183830560924351532771,
93382887541371889408163, 436488743190168888169420309859171,
556745845905827663478434714915, 342207174661092408324827850386470883,
436488743190168888169420309905827, 93382887541371889361507, 30339594084220925
, 421024623075416957, 330083573318152865789, 30147818426025366,
23605359645613362582, 18506962308719453173590, 14509458450036019109375382,
11375415424828238949535095318, 73212183830558527157388131,
119108987241500835107, 93382887538974695263523, 93382887538974695170211,
1155337304257757389859, 710135007529225345842946211,
710135006087686076211358115, 556745845902912673469605411235,
119108987241500695139, 119110825939551630371, 38697588648185, 268534846094009
, 165056822041930276217, 210531660333011897, 118087090440366316181,
93241439995650938223587, 30147329202973128, 165177065429383744008,
151924725603247139, 48923108387, 57311205362481685036056951779,
825284650263809148323, 647023165811452206742499, 647023163932050755128739,
507266160522732416686375907, 508078373720600226246471971,
507266161994306151631101347, 398333444996950579565030415779,
507266161994303754435370403, 397696671003534145702462084067,
312293420877609254381171569251299, 397696671003536025103915144163,
825286527268066337507, 825284650263810454691, 647023167690853661108963,
647023165809055012317923, 647023165811452208048867, 150621287104094909,
118086821269532732093, 92580278100455162481341, 92580278100797619014333,
72582938031025650848383229, 150621287104048253, 118086821269532685437,
150621287103768317, 118087089412997738237, 118086821269532405501,
150621287105214653, 129498849597009012596285, 101527098084055308672881789,
101527098084055308672928445, 79597244897899362242300231933,
150621287105167997, 118930408145523508643, 93241438111455095147939,
73101288950956897291951523, 73101288950959294487682467,
57311410537552089243756270563, 118930408145523461987, 93241438111455095101283
, 118930408145523368675, 93241439988459352337123, 93241438111455095007971,
118930408145524815011, 710134866081674830503145763,
556745735008033069442544150371, 556745735008033069442544197027,
436488656246297926445282655278051, 118930408145524768355, 38452976560044,
76759187292972, 60217605685309356, 38452977213228, 30108876227667756,
23605359009825845484, 18506601463591645030188, 14509175547455737849353132,
35226562911850146659895851617598435, 57310743853713962933461611683,
44931623181311746938180397116131, 35226392574405685888081258417910051,
27617491778334057736255704906315586979,
21652113554213901265224472644858021188579,
35226392646655224537480621881535203, 57311205362479800844225592291,
44931985004184161983646285071331, 73101027248063366161556195,
57311205362479800844226898659, 73101027248063366161649507,
57311205362479800844226991971, 73101027248063366162955875,
648059150151426828518819, 647023163929653560890787,
508078373718720824792012195, 398333444995477128825829854179,
825284647866614817059, 508078373718720824790519203, 1052658986783037731,
826606058863820822819, 648059150151426831411491, 1052658986782944419,
825284647866616216739, 648059150151426831318179, 825284647866613277411,
1052658986784344099, 825284647866614723747, 647023163929653559257827,
1054344460041289763, 826606058863823622179, 118086820927077457913,
192118139083193, 150620944650267065, 150620944650173753, 268730605338809,
165177103734998859065, 165177103734996059705, 129498849328523038381625,
192118138943225, 192118141882553, 93241438109057900863331, 151696943085885731
, 118930405748330670371, 118930405748330577059, 1473644227223863331,
905784267958919770061987, 905784267958919767262627,
710134866079795429048685987, 151696943085745763, 151696943088685091,
48922408722, 48923855058, 30108827304651666, 38404055736786,
21652260230738689093160918223134485887971,
16975349947929508762736775781750519949619491,
13308648595489280086734238656789952541527081955, 496132450401430247765,
44931869134422011351878498406243, 73100438588918489761253411,
35226676242928570107200982529583843, 120397052593970568,
93240865735445957539427, 1342674436128803, 244635697187, 193487976972323, 35
]; 

PROPERTIES_SMALL_GROUPS[ 784 ] := rec(
isNilpotent := [ 2, 19, -26, 37, -40, 43, 46, 96, -103, 156, -159, 172 ], 
isSupersolvable := [ 1, -43, 45, -46, 48, -103, 118, -159, 169, -172 ], 
isAbelian := [ 2, 19, 22, 37, 43, 46, 96, 99, 156, 172 ], 
lgLength := rec( lgLength := [ 2, 3, 4, 5, 6 ], pos := [ [ 169, 171, -172 ],
[ 45, -46, 59, -63, 87, -90, 95, -98, 105, -106, 110, 113, -114, 117, -135,
146, -159, 165, -168, 170 ], [ 10, -13, 18, -21, 27, -40, 44, 48, -58, 71,
-74, 79, -86, 91, -94, 99, -103, 107, -109, 111, -112, 115, -116, 136, -145,
161, -164 ], [ 3, -9, 14, -17, 22, -26, 42, -43, 47, 64, -70, 75, -78, 104,
160 ], [ 1, -2, 41 ] ] ),
frattFacs := rec( frattFacs := [ 9, 17, 26, 34, 99, 107, 28, 36, 44, 333, 341
, 349, 70, 78, 86, 94, 102, 295, 303, 311, 327, 335, 343, 351, 359 ],
pos := [ 1, 2, 18, 26, 36, 40, 41, 42, 43, 44, 45, 46, 47, 63, 79, 95, 103,
104, 109, 110, 117, 135, 145, 155, 159 ] ) );