col12.z

#############################################################################
##
#W  col12.z                GAP library of groups           Hans Ulrich Besche
##                                               Bettina Eick, Eamonn O'Brien
##

SMALL_GROUP_LIB[ 532 ] :=
[ 143348617625, 487118979701, 261325734452603, 53854614, 2717333153387,
917070443, 272098103, 491205378923, 107 ]; 

PROPERTIES_SMALL_GROUPS[ 532 ] := 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[ 536 ] :=
[ 181771642179377777, 5226800036436, 97429251616497416945, 339124413231713,
181770991402857185, 339124394256977, 339124527080129, 9734043858, 9866867010,
2796316464515442, 632086405697, 65 ]; 

PROPERTIES_SMALL_GROUPS[ 536 ] := rec(
isNilpotent := [ 2, 8, -10, 12 ], 
isAbelian := [ 2, 8, 12 ], 
lgLength := rec( lgLength := [ 2, 3, 4 ], pos := [ [ 11, -12 ], [ 3, -10 ], [
1, -2 ] ] ),
frattFacs := rec( frattFacs := [ 4, 7, 11, 14 ], pos := [ 1, 2, 7, 10 ] ) );

SMALL_GROUP_LIB[ 540 ] :=
[ 198678808206087212864277, 2035205235720368407, 107292065587020226933641333,
1259408965317061, 1096293022857091395863, 1552780085719983175463130189941,
198703186403007245402229, 1356372026657363792, 3768898228895831,
367923718899950518485, 198689010346332683845749, 2332167323765,
3768898228867399, 6269084595392839, 3385282549719781703, 681317057373999557,
1259408967348677, 677562139282510277, 365884791417956536773,
371310242364499988765, 2035205235721384215, 1828052577038559088919,
197581186397070018777373, 367244911430625432341, 680080957731509013,
200506909581096773242973, 371309090067789385821, 2332167254385, 2332171440497
, 1254744634962289,
[ ( 2, 5)( 3, 4)( 6, 9,12, 7,10,13, 8,11,14), 
  ( 1, 4, 3, 2, 5)( 6,10,14, 7,11,12, 8, 9,13) ],
2030172265267614023, 2035172637996486983, 1098993200807563776327,
1775258166726523335774493, 1096969325587389755671, 593457004738425061380375,
958637577269357659804963101, 958639409411026795636740189,
200500784131466950611037, 198676804343827044766485,
216158464567631160161341533, 58468011679160551197223161949,
696362211887579229, 6269084607987799, 3387810516018659415,
365899836572520448093, 375405647170525741149, 695193323690786909,
688833821412458709, 365891051135783928021, 16434843957785043435613,
396324706464279576669, 197605514525279994249309, 203083576743426457370717,
202718363166456738480221, 2511799957071312, 1356371992297743824,
2511799957067216, 1356371992297739728, 2511799957194192, 6979323986007,
11609365807191, 6269041708662871, 1261698186018933, 2332169355381,
1254744768118901, 677564428617580661, 687611559580041309, 3768898229911639,
3385282549784248407, 365891085920212910173, 680083169104920789,
1259409503682773, 371309091815776075869, 687609425046536285, 4294983773,
4362076253, 2323644432477, 6979323957587, 2332169343345, 3768898229899591,
1259408968389061, 2035205235721900311, 680080957196735253,
1099010827867666518103, 4294971740,
[ ( 1, 2, 3)( 4, 5, 6)( 7, 9, 8,10,11), 
  ( 1, 2, 3)( 4, 6, 5)( 7,11, 8, 9,10) ],
3759580297302355, 2031424677732159815, 1096969325587390271767,
592363435817623665512535, 367241154117535535557, 320471527523672415977083159,
991529480629893008462103, 594917147335751649202965,
174125474470151978492318453847, 1606275540347193232275017815, 11609315475543,
6296864464830551, 6962160861301, 18793166286094423, 3400306860738740311,
3400404219061076055, 3778115253829845, 10200906494655856727,
3385305871405547607, 991557870304019350290519, 2040182261028487381,
5508489507298958639191, 4651452728688, 12886999127, 4297064541, 6979325001815
, 2332170387573, 3768898230419543, 1259408968909013, 2035205235722158167, 87
]; 

PROPERTIES_SMALL_GROUPS[ 540 ] := rec(
isNilpotent := [ 4, 12, 28, -30, 77, -79, 87, 119 ], 
isSupersolvable := [ 1, -7, 9, -30, 32, -40, 44, -56, 62, -87, 89, -92, 99,
-110, 112, -119 ], 
isSolvable := [ 1, -30, 32, -87, 89, -119 ], 
isAbelian := [ 4, 12, 28, 77, 87, 119 ], 
lgLength := rec( lgLength := [ 3, 4, 5, 6, false ], pos := [ [ 104, -112, 117
, -119 ], [ 46, 48, -64, 67, 71, 73, -80, 85, -87, 89, 92, 96, -103, 113,
-116 ], [ 7, -15, 18, 22, 24, -30, 32, -34, 37, 39, -45, 47, 65, -66, 68, -70
, 72, 81, -84, 90, -91, 93, -95 ], [ 1, -6, 16, -17, 19, -21, 23, 35, -36, 38
], [ 31, 88 ] ] ),
frattFacs := rec( frattFacs := [ 7, 13, 19, 25, 38, 44, 50, 56, 62, 68, 74,
80, 33, 39, 45, 51, 57, 63, 118, 124, 130, 136, 142, 148, 154, 160, 166, 172,
178, 184, 190, 196, 202, 208, 214, 220, 226, 143, 149, 155, 161, 167, 173,
179, 185 ], pos := [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 19, 23, 25,
27, 30, 31, 34, 38, 40, 41, 42, 43, 47, 49, 51, 54, 56, 61, 64, 68, 72, 74,
76, 79, 80, 81, 82, 83, 84, 85, 86, 87 ] ) );

SMALL_GROUP_LIB[ 546 ] :=
[ 11713683671, 12286660823, 6394553413847, 75477049559, 6405574680791,
6556291227863, 5853192473, 41210074460375, 6406147657943, 6556864205015,
3497441934569687, 3579733169270999, 23888087, 13271321, 11735580887,
12011618519, 117448919, 53747993, 64455782615, 11281237, 63903707879,
29059266113, 35193281034455, 215 ]; 

PROPERTIES_SMALL_GROUPS[ 546 ] := rec(
isNilpotent := [ 24 ], 
isAbelian := [ 24 ], 
lgLength := rec( lgLength := [ 4 ], pos := [ [ 1, -24 ] ] ),
frattFacs := rec( frattFacs := [ ], pos := [ ] ) );

SMALL_GROUP_LIB[ 550 ] :=
[ 12415801940339, 8505620339, 4691477000933, 25400660339, 2625683477060393,
5140393, 8495680339, 8618400339, 4671914720339, 16640339, 46400339, 15680393,
25513440339, 8525280933, 14032973360339, 339 ]; 

PROPERTIES_SMALL_GROUPS[ 550 ] := 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[ 552 ] :=
[ 25868659313232473, 541370705580329613, 298837712768809202251,
46778203508652, 592736080003708651, 592736079998555019, 327190320165156575819
, 592736080075859499, 327190320165233880299, 327190320165228726667,
180609056735166776905803, 7910713603354358376712, 298835559031281537561,
980737664153785, 541368763593862841, 980737659000153, 980737736304633,
14279359988642084821, 46863264194165, 25868406068696181, 46863259040533,
46863336345013, 164958414237614670915659, 541372647948144363,
298837706942726145259, 541372647942990731, 541372648020295211, 84442261266,
84519565746, 25775017974178770, 15721729997391960170332,
8678394962278766170979148, 1186720729504414125, 1073789984075819,
93479793103180, 1773838905387, 85096772047, 980737983678507, 43 ]; 

PROPERTIES_SMALL_GROUPS[ 552 ] := 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[ 558 ] :=
[ 3105817060500959, 5566891860959, 130055404706131, 6723882900959,
83309880131461771, 416341771, 937811520959, 5566903200959, 3105817071840959,
1762560959, 12052800959, 440641771, 6723894240959, 232696826131,
3751949905200959, 959 ]; 

PROPERTIES_SMALL_GROUPS[ 558 ] := 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[ 560 ] :=
[ 25851633706198227603, 43065526788430352501, 24237300035112481045463,
15397041413939112, 14442471694211386563219, 56604685544434640886676439,
180500212060232402327, 180500212060232355671, 101080118757034374298583,
101080117798156083367319, 101080117798156083320663,
56604865966970710080111575, 56748946252079022121988375,
56604866502985387804794263, 56748946788093699840792407,
31779409901164253951101640087, 31779409901164253951101593431,
56604866502983675522129303, 31698725241670859881834992599,
56748947325065543572248407, 31779410502035748798880629719,
17796469544651982214179654390743, 31698725241671818760127370199,
31779410201331516309265269719, 180500212060232262359, 180500212060233708695,
180500212060233662039, 101080119715912667982551, 101080118755322092939991,
101080118757034375604951, 101080117798156083227351, 76902723986104589,
43065334327860160781, 24116694426865247815949, 24116694427207704348941,
13505348879236639104581453, 76902723986057933, 43065334327860114125,
76902723985777997, 43065525761061776717, 43065334327859834189,
76902723987224333, 33721939564598083853453, 18884286156175198265987789,
18884286156175198266034445, 10575200247458111300235181901, 76902723987177677,
46163629895295675, 25851496234362759867, 14476914464998702811835,
14476914465243314621115, 8107072100536483012034811, 46163629895249019,
25851496234362713211, 46163629894969083, 25851632972363820795,
25851496234362433275, 46163629896415419, 24082190232141694377531,
13486026529999522314507387, 13486026529999522314554043,
7552174856799732669561192699, 46163629896368763, 43280892907649172887,
24237299072809624784279, 13572888016789758865530263,
13572888016791471148195223, 7600817289403225532581811159,
43280892907649126231, 24237299072809624737623, 43280892907649032919,
24237300029975634356951, 24237299072809624644311, 43280892907650479255,
94325084608773352581165335, 52822047380913079108390594391,
52822047380913079108390641047, 29580346533311324302361644831703,
43280892907650432599, 27494367503868, 54841969181052, 30738947325357564,
27494368157052, 15369547047691644, 8606946394554265404,
4819889980884555474300, 2699138389295285206422012, 101096841592742685614807,
101096840635576677348503, 56614230755923675918723799,
101096840635576676042135, 56614230755923675917417431,
56614230754966509909151127, 31703969222781246285623870423,
14442471556748722591995, 8087784071635940722548987, 25790128035879364347,
14442471556748723711739, 25790128035879644283, 14442471556748723991675,
25790128035880764027, 56604685543472339366689751,
31698623904343553716795638743, 101079795615051192525527,
56604685543472339367996119, 101079795615051192618839,
56604685543472339368089431, 101079795615051193925207,
101337404019854604617111, 101080117796443802195351,
56748946251120143828211095, 101080117796443802148695,
56748946251120143828164439, 56604865966010119506562007,
31779409900627282107368737751, 180500210347951137047,
101337404019854606016791, 56748946251120143826718103, 322321801349912855,
180959650032659486999, 180500210347952630039, 101337404019854607509783,
322321801349819543, 180500210347952536727, 101337404019854607416471,
322321801349772887, 180959650032659347031, 180500210347949597399,
322321801351219223, 180500210347951043735, 180500210347950997079,
101080117796443800562391, 323142229405827095, 322321801352712215,
180959650032662286359, 43065333985404886961, 137325093804401,
76902381532277105, 76902381532183793, 192020341948529, 60217748879503031537,
60217748879500232177, 33721939372822373029361, 137325093664433,
137325096603761, 25851495989752209399, 82434203802039, 46163385286191543,
46163385286098231, 137129451946167, 43003910883850353975,
43003910883847554615, 24082190095159028831799, 82434203662071, 82434206601399
, 24237299071097343565655, 77287302684317975, 43280891195369400599,
43280891195369307287, 537109853797859351, 168437651085380018683031,
168437651085380015883671, 94325084607814474287388055, 77287302684178007,
77287302687117335, 48922408650, 48923854986, 15369498124675914,
27445446680970, 129257067924852283731, 180530072563741748375,
61450699165143912, 120512180381157155952, 46053823653689079,
180499635026910213719, 575571802226711, 244635697175, 146790973473,
138010018627607, 23 ]; 

PROPERTIES_SMALL_GROUPS[ 560 ] := rec(
isNilpotent := [ 4, 80, -87, 166, -169, 180 ], 
isSupersolvable := [ 1, -169, 171, 174, -180 ], 
isAbelian := [ 4, 80, 83, 166, 180 ], 
lgLength := rec( lgLength := [ 3, 4, 5, 6 ], pos := [ [ 173, 176, -180 ], [
25, -31, 39, -42, 47, 55, -58, 63, 71, -74, 79, -82, 88, -90, 97, -98, 101,
104, -105, 108, -172, 174, -175 ], [ 7, -24, 32, -38, 43, -46, 48, -54, 59,
-62, 64, -70, 75, -78, 83, -87, 91, -96, 99, -100, 102, -103, 106, -107 ], [
1, -6 ] ] ),
frattFacs := rec( frattFacs := [ 5, 9, 13, 17, 22, 26, 30, 34, 38, 42, 46,
131, 139, 143, 147, 151, 155, 159, 163 ], pos := [ 1, 2, 3, 4, 5, 6, 31, 47,
63, 79, 87, 94, 101, 108, 135, 145, 155, 165, 169 ] ) );