col8.z

#############################################################################
##
#W  col8.z                 GAP library of groups           Hans Ulrich Besche
##                                               Bettina Eick, Eamonn O'Brien
##

SMALL_GROUP_LIB[ 360 ] :=
[ 72941629123561870085, 603956712027746579, 26622482823630598746141,
559745907864004, 216620058419121910035, 84169286558624286569443357,
9765387610299021667774493, 75350146740525240349, 27126052826766912827421,
27126076695274566357021, 75350146740525244445, 75350213041935515677,
27126076695274566361117, 26332122893077909706560, 219425470003640692807,
1677678652448839, 609515194277847111, 1677678652444743, 1693097585164359,
26260385276168877846725, 202615636242800837, 72945514655920627909,
202615636242796741, 202626429495738565, 9584102409100384244772893,
73951341175681622045, 26622506691944978751517, 73951341175681617949,
73951407477091893277, 1559073149041, 4642859794545, 601719261697831025,
1677657177624899, 561292098179521, 603964442969919751, 202069870453478149,
217427223047405318167, 1554778231152, 233805570397736176488477,
18776544982074183401620304, 6759556193557925054392443344, 3008577775731745091
, 601722406689591367, 233803573773955415707677, 209305962674159645,
1117911318012368, 4660041646103, 562821107613749, 205420391621492765,
4295000093,
[ ( 1,21,14)( 2,19,17)( 3,23,11)( 4,16,15)( 5,20, 7)( 6,24,13)( 8,18,12)
    ( 9,22,10)(25,27,26), 
  ( 1,17,21,13, 6, 4,12,16, 7, 5)( 2,15,19,11, 3, 8,14,18,10, 9)(20,24)
    (22,23)(25,27,26) ],
601722385214771523, 216820452144226259207, 78055362795403084312599,
26187845546321227305733, 47135814524669815284051991,
10144281333369829756658790423, 2787841815879751, 2787841815875655,
1003623111362359367, 2787841816002631, 1003623111362486343,
1003623111362482247, 361304320148093677639, 1010284219099783191,
1010284219099779095, 363702319059405123607, 1010284219099906071,
363702319059405250583, 363702319059405246487, 130932834861569326329879,
1671468146499781, 601728564615721157, 1671468146622661, 601728564615848133,
216622283293534073029, 3007467719943528471, 3007467719943524375,
1082688379368800006167, 3007467719943651351, 1082688379368800133143,
1082688379368800129047, 389767816572957130633239, 363702272673758846999,
363702272673758842903, 363702272673758969879, 130932818162736480002071,
47135814538585316048646167, 73144785814546908608, 603948873712545875,
4660041621587, 1677635702890579, 4660041617491, 4660041744467,
202060528898682993, 1559075233905, 561279213379697, 1559075229809,
1559075356785, 217427176339635580999, 1677678653481031, 603964378545528903,
1677678653476935, 1677678653603911, 72745139485075976389, 561304984101061,
202069831798890693, 561304984096965, 561304984223941, 78273800227679396048919
, 603964507394940951, 217427222854131916823, 603964507394936855,
603964507395063831, 4294971484, 4295098460, 558178244898908,
[ (1,2,3,4,5), (2,3,4,5,6) ],
[ (1,3)(2,5,4)(6,7,8), (1,4,2) ],
[ (2,3)(4,5,7)(6,8), (1,2,3)(5,8,7) ],
[ (1,3)(4,8,5,6,7), (1,2,3)(4,5,7) ],
[ ( 1, 2)( 7, 9,10), (1,2)(3,5,4)(6,9,8) ],
3393944781795139583361438469, 6108913881524238592415691714583,
2199168749184287409750176528085015, 603942732999692359, 217427154822141841431
, 219423784787600478231, 78273776246300294516759, 130935225512865529077783,
3651941382448839033253522837527, 26187447548157183000773,
47136677790300149774942231, 6109007893014188464250017161239,
1221829600720733026706670104773, 2199242841484383451761220507021335,
8357160335441943, 144880748319896764880, 52157069407037505143152,
52157069394633639592784, 28073813880477260669911408, 8357160276721987,
5014292740964801, 9025723813776589063, 1671453097332819, 602279034452185159,
216820452208651276311, 72744015407845740741, 130932818124081951412247,
28178559259360637612462103, 7743844909079, 2806344543371287, 4642878521397,
8354076474474519, 1010284090251280407, 3105311687024, 12886999063, 4297064477
, 4660042661911, 1559076274229, 1677678653997079, 23 ]; 

PROPERTIES_SMALL_GROUPS[ 360 ] := rec(
isNilpotent := [ 4, 30, -32, 38, 50, 115, -117, 162 ], 
isSupersolvable := [ 1, -13, 15, -39, 43, -45, 47, -50, 52, -54, 58, -88, 90,
-117, 126, -129, 137, 145, -147, 151, -155, 157, -162 ], 
isSolvable := [ 1, -50, 52, -117, 123, -162 ], 
isAbelian := [ 4, 30, 38, 50, 115, 162 ], 
lgLength := rec( lgLength := [ 3, 4, 5, 6, false ], pos := [ [ 137, 152, -155
, 157, 160, -162 ], [ 45, 47, -50, 65, -94, 105, -117, 127, -136, 140, -142,
145, 147, -151, 156, 158, -159 ], [ 7, -33, 36, -44, 46, 52, 54, -64, 95,
-104, 123, -126, 138, -139, 143, -144, 146 ], [ 1, -6, 34, -35, 53 ], [ 51,
118, -122 ] ] ),
frattFacs := rec( frattFacs := [ 7, 13, 19, 25, 38, 44, 50, 56, 62, 68, 74,
80, 33, 39, 45, 51, 57, 63, 220, 226, 232, 238, 244, 250, 256, 262, 268, 274,
280, 286, 119, 125, 131, 137, 143, 149, 155, 161, 167, 173, 179, 185, 191,
197, 203, 209, 215, 221, 227 ], pos := [ 1, 2, 3, 4, 5, 6, 13, 14, 19, 24, 29
, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50,
51, 52, 53, 54, 55, 56, 57, 64, 71, 76, 83, 88, 89, 94, 99, 104, 109, 114,
117 ] ) );

SMALL_GROUP_LIB[ 364 ] :=
[ 19397637941, 42648499163, 15725726892359, 10638420, 15500761199579,
5638256756916551, 251313020999, 117448775, 53747849, 43200884807, 71 ]; 

PROPERTIES_SMALL_GROUPS[ 364 ] := 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[ 368 ] :=
[ 88632655135884453813, 11497294262285656, 240849585926931541,
88631936576183843413, 32616814949607478404693, 32616814951549531858517,
12002987902171825550838197, 240849585921777909, 88631936576178689781,
240849585911470645, 88632649309785935925, 88631936576168382517,
240849585988775125, 35705232259249161518997, 13139525471404808854627061,
13139525471404808859780693, 4835345373476970774032165301, 240849585983621493,
31241744945620, 62230235250964, 22931851717789652, 31241775867412,
11466052594441236, 4219507394866516148, 1552778720260486706196,
571422569054806830414548, 88631934634207694069, 654472694218133,
240847644028086677, 240847644017779413, 716450829242389, 97025085715820495573
, 97025085715676193877, 35705231544573418360917, 654472678757237,
654472838519829, 84442260782, 84519565262, 11465968126403054, 31157395440974,
1773838905365, 21 ]; 

PROPERTIES_SMALL_GROUPS[ 368 ] := 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[ 372 ] :=
[ 1381861685610929, 3715580970929, 155546756101, 4486882410929,
1669148921610059, 415531770, 3714880320059, 4794655680059, 10160640059,
309834773100, 1386978415947029, 12052800059, 440640871, 4486894560059, 59 ];


PROPERTIES_SMALL_GROUPS[ 372 ] := 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[ 375 ] :=
[ 49809023, 23889860735, 131711, 147583, 196756095, 1081749631, 127 ]; 

PROPERTIES_SMALL_GROUPS[ 375 ] := rec(
isNilpotent := [ 1, 3, -5, 7 ], 
isSupersolvable := [ 1, 3, -5, 7 ], 
isAbelian := [ 1, 3, 7 ], 
lgLength := rec( lgLength := [ 2, 3, 4 ], pos := [ [ 7 ], [ 2, -6 ], [ 1 ]
] ),
frattFacs := rec( frattFacs := [ 4, 8, 11 ], pos := [ 1, 2, 5 ] ) );

SMALL_GROUP_LIB[ 376 ] :=
[ 14625158996424797, 866571406916, 5499019319361972445, 38896278160973,
14625051282265805, 38896273683517, 38896305025709, 2296936998, 2328279190,
324962773282502, 103303864877, 45 ]; 

PROPERTIES_SMALL_GROUPS[ 376 ] := 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[ 378 ] :=
[ 20734359878330183, 18543494182727, 2628760740670211299, 91358307542855,
993899797787066084179, 48540234067, 54852805798535, 20770669190941319,
20770670082755207, 54852805782983, 20770669190925767, 54948868854023,
7809954854710711963, 7809954902741259931, 20662265002866331, 18543494649287,
7008766248305927, 2952162808615395536539, 2952162808663426084507,
7810209706580364955, 6972358836913607, 2649276558880699655, 49057757831,
18541712530055, 18542604343943, 49057742279, 18541712514503, 49059717383,
241682590343, 337745645831, 127667620153991, 18396593241235, 48541167187,
18252250712467, 6899397118164115, 7155115828645531, 91358308009415,
48258361956824327, 2608173312746548891, 6936093472264675, 18349342222435,
2704618564902238171, 7155075443305243, 127417819, 129392923, 48287358427,
145119817991, 49058224391, 18445396101383, 18543494882567, 6972358837146887,
135364871, 638005511, 128397595, 241683056903, 48541649299, 91358308242695,
18349327292515, 34533447885421319, 263 ]; 

PROPERTIES_SMALL_GROUPS[ 378 ] := rec(
isNilpotent := [ 6, 44, -46, 60 ], 
isAbelian := [ 6, 44, 60 ], 
lgLength := rec( lgLength := [ 3, 4, 5 ], pos := [ [ 47, 52, -53, 58, -60 ],
[ 7, -12, 17, 22, -31, 34, 38, 40, -46, 48, -51, 54, -57 ], [ 1, -6, 13, -16,
18, -21, 32, -33, 35, -37, 39 ] ] ),
frattFacs := rec( frattFacs := [ 4, 7, 10, 13, 16, 19, 23, 26, 29, 32, 35, 38
, 41, 44, 47, 50 ], pos := [ 1, 2, 3, 4, 5, 6, 12, 17, 22, 28, 31, 35, 39, 41
, 43, 46 ] ) );