col3.z

#############################################################################
##
#W  col3.z                 GAP library of groups           Hans Ulrich Besche
##                                               Bettina Eick, Eamonn O'Brien
##

SMALL_GROUP_LIB[ 150 ] :=
[ 20062781, 9162470431, 1374781979679, 132127, 9741398894623, 2247290449951,
432979999, 401439, 60960799, 139325, 59650103, 9145563167, 31 ]; 

PROPERTIES_SMALL_GROUPS[ 150 ] := rec(
isNilpotent := [ 4, 13 ], 
isSupersolvable := [ 1, -4, 8, -13 ], 
isAbelian := [ 4, 13 ], 
lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 5, -7, 9, -10, 12, -13 ], [
1, -4, 8, 11 ] ] ),
frattFacs := rec( frattFacs := [ 3, 5, 7, 9 ], pos := [ 1, 2, 3, 4 ] ) );

SMALL_GROUP_LIB[ 152 ] :=
[ 21267650826305, 8277678036, 3232528169451713, 139908863537, 21266630354609,
139908758561, 139909493393, 53852994, 54587826, 1250011693026, 917070353, 17
]; 

PROPERTIES_SMALL_GROUPS[ 152 ] := 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[ 156 ] :=
[ 535102288283, 3453145499, 1688762161, 18357186971, 2864029466903, 10637844,
443893502308763, 3435208727, 2853821051291, 444420453171479, 21649711127,
26542103, 3345300720, 560219537099, 117448727, 11280517, 18357497879, 23 ]; 

PROPERTIES_SMALL_GROUPS[ 156 ] := rec(
isNilpotent := [ 6, 18 ], 
isSupersolvable := [ 1, -12, 15, -18 ], 
isAbelian := [ 6, 18 ], 
lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 8, 11, -18 ], [ 1, -7, 9,
-10 ] ] ),
frattFacs := rec( frattFacs := [ 3, 5, 7, 9, 11, 13 ], pos := [ 1, 2, 3, 4, 5
, 6 ] ) );

SMALL_GROUP_LIB[ 162 ] :=
[ 9715170314653540303, 14018937295, 2284237363535, 2243044071503,
1085577358228623, 363386305534287, 370183455120783, 14018941135,
58868718496136591, 2270647888911, 367803162459151, 728960773729359,
59584112483662991, 367844946160719, 59584112399252623, 59604544452042447,
367915529416271, 59963417495609167, 59584098568011279, 9652623995531984527,
117364873763583503, 1563725085060996562639, 86507727, 255336527, 41533579471,
86507855, 13845930319, 86532111, 14014767247, 14015291535, 2270473773263,
14100207887, 86511759, 13845944335, 255340559, 2243125336335, 41364762767,
2271153757327, 14018943055, 2243044064271, 14019005455, 363373221919887,
363373221928079, 2271068359759, 367915357445711, 2271081991695, 524367,
532495, 85467215, 85467407, 528399, 86513679, 14018944015, 2271081930255, 15
]; 

PROPERTIES_SMALL_GROUPS[ 162 ] := rec(
isNilpotent := [ 2, 23, -31, 47, -50, 55 ], 
isAbelian := [ 2, 23, 26, 47, 55 ], 
lgLength := rec( lgLength := [ 2, 3, 4, 5 ], pos := [ [ 54, -55 ], [ 11, 16,
-17, 23, -25, 34, 40, 45, -53 ], [ 4, -5, 10, 12, -15, 18, -22, 26, -33, 35,
-39, 41, -44 ], [ 1, -3, 6, -9 ] ] ),
frattFacs := rec( frattFacs := [ 5, 9, 14, 18, 22, 51, 55, 59, 63 ], pos := [
1, 2, 15, 22, 31, 37, 44, 46, 50 ] ) );

SMALL_GROUP_LIB[ 168 ] :=
[ 1830410557933757, 3747409959101, 3660769643545, 18130577377469,
3046092002763563, 21658407660, 307508823321440585, 10895323131113,
1830409690108649, 10895323123337, 10895323239977, 25280253275339,
25280253267563, 4247084392008491, 25280253384203, 4247084392125131,
4247084392117355, 713510179697996075, 22327213289, 22327322153,
629414627918153, 104533337189112264, 17270578686151910766, 3045787893854537,
107910491369, 18129685664489, 107910483593, 107910600233, 614945298936277,
21786750325, 3660387537781, 21786742549, 21786859189, 511743009412417835,
18131469665483, 3046089327438539, 18131469657707, 18131469774347, 127409826,
127526466, 3617324679522,
[ (3,4)(5,6), (1,2,3)(4,5,7) ],
11509314698901829264200, 14448163334472, 204798489053599836,
34406146498723232652, 64912306187, 75662134235357, 1863071209083101,
150466719755, 191102987, 43201216908, 3898132439261, 638005259, 128397343,
107910973451, 11 ]; 

PROPERTIES_SMALL_GROUPS[ 168 ] := rec(
isNilpotent := [ 6, 39, -41, 57 ], 
isSupersolvable := [ 1, -21, 24, -41, 47, 50, -51, 54, -57 ], 
isSolvable := [ 1, -41, 43, -57 ], 
isAbelian := [ 6, 39, 57 ], 
lgLength := rec( lgLength := [ 3, 4, 5, false ], pos := [ [ 43, -44, 47, 50,
-51, 54, -57 ], [ 7, -41, 45, -46, 48, -49, 52, -53 ], [ 1, -6 ], [ 42 ] ] ),
frattFacs := rec( frattFacs := [ 4, 7, 10, 13, 16, 19, 23, 26, 29, 32, 35, 38
, 41, 44, 47 ], pos := [ 1, 2, 3, 4, 5, 6, 11, 18, 21, 22, 23, 28, 33, 38, 41
] ) );

SMALL_GROUP_LIB[ 176 ] :=
[ 80954386035900009, 51334350109000, 459967706200009, 80951178050200009,
14247962460178200009, 14247962478200600009, 2507641396178143100009,
459967706100009, 80951178050100009, 459967705900009, 80954331969900009,
80951178049900009, 459967707400009, 17373673781701200009,
3057766585589803700009, 3057766585589803800009, 538166919063815826300009,
459967707300009, 291635500900, 578356900900, 102080513900900, 291636100900,
51042716100900, 8983519292000900, 1581099386530500900, 278273492020489100900,
80951160029300009, 2613261200009, 459949686800009, 459949686600009,
3186726400009, 98714037494600009, 98714037491800009, 17373670609757400009,
2613260900009, 2613264000009, 1638500090, 1640000090, 51041077100090,
289998800090, 14758400009, 9 ]; 

PROPERTIES_SMALL_GROUPS[ 176 ] := 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[ 180 ] :=
[ 100025241904325, 1646096682055, 18501356885349405, 3070233713,
294093108415559, 28549729257133937693, 106569246511133, 1096290600400,
9143717911, 555695153205, 102785312067613, 16781341, 9143714899, 3070362737,
1646096745543, 552792687813, 296298133816343, 16778332,
[ (1,5,2,4,3)(6,8,7), (1,4,2,5,3)(6,7,8) ],
1633857700947, 294636690277447, 53034604215632919, 17909395709166789,
16115327744418481175, 1728006428961561084951, 15150481431, 2763258724375,
9077129269, 8162871017495, 497386657841175, 6090326384, 50462743, 16908317,
9143779351, 3070427189, 1646096777239, 23 ]; 

PROPERTIES_SMALL_GROUPS[ 180 ] := rec(
isNilpotent := [ 4, 12, 18, 37 ], 
isSupersolvable := [ 1, -7, 9, -18, 20, -22, 26, -30, 32, -37 ], 
isSolvable := [ 1, -18, 20, -37 ], 
isAbelian := [ 4, 12, 18, 37 ], 
lgLength := rec( lgLength := [ 3, 4, 5, false ], pos := [ [ 27, -32, 35, -37
], [ 7, -13, 16, -18, 20, 22, -26, 33, -34 ], [ 1, -6, 14, -15, 21 ], [ 19 ]
] ),
frattFacs := rec( frattFacs := [ 5, 9, 13, 17, 26, 30, 34, 38, 42, 46, 50, 54
, 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[ 184 ] :=
[ 85786909203269, 22309848836, 15784284971307973, 466211137589,
85784152244405, 466210903333, 466212543125, 120173790, 121813582,
4082848527230, 2526216725, 21 ]; 

PROPERTIES_SMALL_GROUPS[ 184 ] := 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[ 189 ] :=
[ 24594600503, 127408867, 130100519, 24585319847, 24589964711, 130099223,
24585318551, 130108295, 665131, 674203, 126086827, 705287, 263 ]; 

PROPERTIES_SMALL_GROUPS[ 189 ] := rec(
isNilpotent := [ 2, 9, -11, 13 ], 
isAbelian := [ 2, 9, 13 ], 
lgLength := rec( lgLength := [ 2, 3, 4 ], pos := [ [ 12, -13 ], [ 3, -11 ], [
1, -2 ] ] ),
frattFacs := rec( frattFacs := [ 4, 7, 11, 14 ], pos := [ 1, 2, 8, 11 ] ) );

SMALL_GROUP_LIB[ 196 ] :=
[ 25899682770035, 134705129, 132141139811, 668771, 654968777, 132039612467,
665058, 5071949876421683, 4555408931, 3359267, 673567523, 35 ]; 

PROPERTIES_SMALL_GROUPS[ 196 ] := rec(
isNilpotent := [ 2, 4, 7, 12 ], 
isSupersolvable := [ 1, -7, 9, -12 ], 
isAbelian := [ 2, 4, 7, 12 ], 
lgLength := rec( lgLength := [ 2, 3, 4 ], pos := [ [ 9, 11, -12 ], [ 3, -4, 6
, -8, 10 ], [ 1, -2, 5 ] ] ),
frattFacs := rec( frattFacs := [ 5, 9, 14, 18, 15, 19, 23 ], pos := [ 1, 2, 3
, 4, 5, 6, 7 ] ) );

SMALL_GROUP_LIB[ 198 ] :=
[ 204790280911, 9180500119, 45197486660191, 5140191, 46400119, 5440191,
9180640119, 1029600911, 1817841200119, 119 ]; 

PROPERTIES_SMALL_GROUPS[ 198 ] := 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[ 200 ] :=
[ 82680889527708687, 677967305932, 3323258594887783361551,
16538982301460294671, 413404443650063, 82694911505426447, 413404443649039,
413474555650063, 3439334451, 16794013747, 671776589765683,
16616292974441210895, 2067020324879, 16785423, 2030211044547, 412804238740495
, 3389007088, 403341221958851, 80809223311789071, 16508918201897913359,
16508921557341113359, 10076816017423, 2015363492088847, 10076816031759,
2015363492104207, 403072698706185231, 406025488452659, 10150348851,
2030127171635, 10150347827, 10150363187, 82560764241726479, 2064017197071,
412803819325455, 2064017196047, 2064017211407, 16778300, 16793660,
674460879932, 660356726303585266764815, 412723293324303, 16510795186078155791
, 3302000528755531661327, 132096126953042561369590799, 2016713770035,
404046116750351, 82544591011775503, 82544607788991503, 50382635023, 50462735,
10318184463, 15 ]; 

PROPERTIES_SMALL_GROUPS[ 200 ] := rec(
isNilpotent := [ 2, 9, -11, 14, 17, 37, -39, 52 ], 
isSupersolvable := [ 1, -39, 41, -42, 45, -52 ], 
isAbelian := [ 2, 9, 14, 17, 37, 52 ], 
lgLength := rec( lgLength := [ 2, 3, 4, 5 ], pos := [ [ 49, 51, -52 ], [ 13,
-14, 22, -26, 32, -39, 41, -44, 46, -48, 50 ], [ 4, -12, 16, -17, 19, -21, 27
, -31, 40, 45 ], [ 1, -3, 15, 18 ] ] ),
frattFacs := rec( frattFacs := [ 7, 13, 20, 26, 32, 75, 81, 87, 22, 28, 34,
59, 65, 71, 77, 83, 89, 95, 101 ], pos := [ 1, 2, 3, 8, 11, 12, 13, 14, 15,
16, 17, 18, 19, 20, 21, 26, 31, 36, 39 ] ) );