col1.z

#############################################################################
##
#W  col1.z                 GAP library of groups           Hans Ulrich Besche
##                                               Bettina Eick, Eamonn O'Brien
##

SMALL_GROUP_LIB[ 16 ] :=
[ 149511, 9219, 16905, 279051, 9221, 140301, 2245212, 35922525, 574759519,
513, 520, 139787, 8716, 0 ]; 

PROPERTIES_SMALL_GROUPS[ 16 ] := rec(
isAbelian := [ 1, -2, 5, 10, 14 ], 
lgLength := rec( lgLength := [ 1, 2, 3, 4 ], pos := [ [ 14 ], [ 2, -4, 10,
-13 ], [ 5, -9 ], [ 1 ] ] ),
frattFacs := rec( frattFacs := [ 5, 10, 23 ], pos := [ 1, 9, 13 ] ) );

SMALL_GROUP_LIB[ 24 ] :=
[ 5358129, 213076, 3317376488, 128017073, 221729, 5333665, 221713, 221825,
8210, 8322, 4923570, 5790338948, 420868, 8705, 1 ]; 

PROPERTIES_SMALL_GROUPS[ 24 ] := rec(
isNilpotent := [ 2, 9, -11, 15 ], 
isSupersolvable := [ 1, -2, 4, -11, 14, -15 ], 
isAbelian := [ 2, 9, 15 ], 
lgLength := rec( lgLength := [ 2, 3, 4 ], pos := [ [ 14, -15 ], [ 3, -13 ], [
1, -2 ] ] ),
frattFacs := rec( frattFacs := [ 4, 7, 11, 14, 17 ], pos := [ 1, 2, 3, 8, 11
] ) );

SMALL_GROUP_LIB[ 32 ] :=
[ 572653583, 67665939, 17891335, 554762263, 67665945, 555778609, 17784406585,
569100501563, 17784406325, 569100501303, 569100501309, 2166390811,
19346260023, 19346784311, 619031068735, 17891341, 554762269, 18710018966396,
598720606913405, 19159059421217663, 557059, 1064977, 34619411, 34619413,
34095125, 1125138455, 557104, 17858610, 571506739, 17858612, 571490358,
18287722551, 571523126, 570982454, 18271469623, 557065, 17334297, 17334537,
554713688, 17750835801, 568026743387, 17750835804, 17734582904, 567506649722,
16385, 16400, 17317907, 540692, 17318224, 17734058326, 0 ]; 

PROPERTIES_SMALL_GROUPS[ 32 ] := rec(
isAbelian := [ 1, 3, 16, 21, 36, 45, 51 ], 
lgLength := rec( lgLength := [ 1, 2, 3, 4, 5 ], pos := [ [ 51 ], [ 2, 21, -35
, 45, -50 ], [ 3, -15, 36, -44 ], [ 16, -20 ], [ 1 ] ] ),
frattFacs := rec( frattFacs := [ 6, 12, 28, 74 ], pos := [ 1, 20, 44, 50
] ) );

SMALL_GROUP_LIB[ 36 ] :=
[ 425337683, 319541, 22151964, 11813699, 8259, 320021, 11576083, 8214,
14981017363, 894467, 615180, 8707, 320259, 3 ]; 

PROPERTIES_SMALL_GROUPS[ 36 ] := rec(
isNilpotent := [ 2, 5, 8, 14 ], 
isSupersolvable := [ 1, -2, 4, -8, 10, 12, -14 ], 
isAbelian := [ 2, 5, 8, 14 ], 
lgLength := rec( lgLength := [ 2, 3, 4 ], pos := [ [ 10, -11, 13, -14 ], [ 3,
-5, 7, -9, 12 ], [ 1, -2, 6 ] ] ),
frattFacs := rec( frattFacs := [ 5, 9, 14, 18, 22, 15, 19, 23 ], pos := [ 1,
2, 3, 4, 5, 6, 7, 8 ] ) );

SMALL_GROUP_LIB[ 40 ] :=
[ 656679683, 5506352, 25403106051, 26241280771, 16392707, 656026115, 16392451
, 16394243, 131340, 133132, 215091980, 635117827, 401411, 3 ]; 

PROPERTIES_SMALL_GROUPS[ 40 ] := rec(
isNilpotent := [ 2, 9, -11, 14 ], 
isAbelian := [ 2, 9, 14 ], 
lgLength := rec( lgLength := [ 2, 3, 4 ], pos := [ [ 13, -14 ], [ 4, -12 ], [
1, -3 ] ] ),
frattFacs := rec( frattFacs := [ 4, 7, 11, 14, 17 ], pos := [ 1, 2, 3, 8, 11
] ) );

SMALL_GROUP_LIB[ 48 ] :=
[ 61763227873, 1260388776, 276070751805136, 1286607041, 61684585153,
2964411389633, 2964412962497, 142291823498977, 1286607009, 61684585121,
1286606945, 61758509665, 61684585057, 1286607425, 8411174942337,
403736398149281, 403736398149313, 19379347112081121, 1286607393, 26214500,
50856484, 2466775652, 26214692, 1234174756, 59240893188, 2843562494756,
136490999368548, 16352318614672076712, 340673304472416136, 275708419185700,
2493562920, 3081530597768, 147913464963496, 61683012769, 26742913, 1285035137
, 1285035073, 76034049, 175231218753, 175231217857, 8411099444417, 26742817,
26743809, 524322, 524802, 1233650274, 25690754, 5743925468164, 52101124,
119795621392, 528385, 1 ]; 

PROPERTIES_SMALL_GROUPS[ 48 ] := rec(
isNilpotent := [ 2, 20, -27, 44, -47, 52 ], 
isSupersolvable := [ 1, -2, 4, -27, 34, -47, 51, -52 ], 
isAbelian := [ 2, 20, 23, 44, 52 ], 
lgLength := rec( lgLength := [ 2, 3, 4, 5 ], pos := [ [ 50, -52 ], [ 3, 11,
-14, 19, -22, 34, -49 ], [ 4, -10, 15, -18, 23, -33 ], [ 1, -2 ] ] ),
frattFacs := rec( frattFacs := [ 5, 9, 14, 18, 22, 51, 55, 59, 63 ], pos := [
1, 2, 3, 19, 27, 30, 33, 43, 47 ] ) );

SMALL_GROUP_LIB[ 54 ] :=
[ 75104412647, 467047, 25674567, 467495, 24356615, 1315620679, 1366049703,
25290119, 8231, 9223, 451623, 8711, 467719, 25289607, 7 ]; 

PROPERTIES_SMALL_GROUPS[ 54 ] := rec(
isNilpotent := [ 2, 9, -11, 15 ], 
isAbelian := [ 2, 9, 15 ], 
lgLength := rec( lgLength := [ 2, 3, 4 ], pos := [ [ 14, -15 ], [ 5, 7, -13 ]
, [ 1, -4, 6 ] ] ),
frattFacs := rec( frattFacs := [ 4, 7, 11, 14, 17 ], pos := [ 1, 2, 6, 8, 11
] ) );

SMALL_GROUP_LIB[ 56 ] :=
[ 10673942837, 38492676, 597482846645, 190483493, 10669307045, 190482197,
190491269, 664878, 673950, 2118735822, 8439127992, 3359237, 5 ]; 

PROPERTIES_SMALL_GROUPS[ 56 ] := rec(
isNilpotent := [ 2, 8, -10, 13 ], 
isSupersolvable := [ 1, -10, 12, -13 ], 
isAbelian := [ 2, 8, 13 ], 
lgLength := rec( lgLength := [ 2, 3, 4 ], pos := [ [ 11, -13 ], [ 3, -10 ], [
1, -2 ] ] ),
frattFacs := rec( frattFacs := [ 4, 7, 11, 14 ], pos := [ 1, 2, 7, 10 ] ) );

SMALL_GROUP_LIB[ 60 ] :=
[ 8266033, 24256787, 1456877831, 131356, [ (1,2,3,4,5), (1,2,3) ], 1424171283
, 85919707399, 39739399, 16134256, 401415, 139277, 24260615, 7 ]; 

PROPERTIES_SMALL_GROUPS[ 60 ] := rec(
isNilpotent := [ 4, 13 ], 
isSupersolvable := [ 1, -4, 6, -8, 10, -13 ], 
isSolvable := [ 1, -4, 6, -13 ], 
isAbelian := [ 4, 13 ], 
lgLength := rec( lgLength := [ 3, 4, false ], pos := [ [ 8, -13 ], [ 1, -4, 6
, -7 ], [ 5 ] ] ),
frattFacs := rec( frattFacs := [ 3, 5, 7, 9 ], pos := [ 1, 2, 3, 4 ] ) );

SMALL_GROUP_LIB[ 72 ] :=
[ 14878183004515, 2796552426, 1086274882571704, 1072579641613155,
206641305923, 14896939408195, 206641305891, 206901877507, 39321765, 113771141
, 589901071077, 2834305193, 204192356451, 38797612, 149167619499417164,
5551210572, 2869958915, 524547, 1058098627270755, 8196214851, 590130729059,
8196215299, 590130729539, 42489415750243, 15087151156632, 203957998181,
39325765, 2832732741, 39325733, 39326213, 14701514201699, 2835880003,
204187638339, 2835879971, 2835880451, 524326, 524806, 2756182630,
5485182275489618019, 1057720606902787, 395011278090722335331, 28774618045452,
2071772490948108, 24574980105, 14695814338595, 113790979, 77119500, 528387,
39327747, 3 ]; 

PROPERTIES_SMALL_GROUPS[ 72 ] := rec(
isNilpotent := [ 2, 9, -11, 14, 18, 36, -38, 50 ], 
isSupersolvable := [ 1, -2, 4, -14, 17, -18, 20, -24, 26, -38, 46, 48, -50 ],

isAbelian := [ 2, 9, 14, 18, 36, 50 ], 
lgLength := rec( lgLength := [ 2, 3, 4, 5 ], pos := [ [ 46, 49, -50 ], [ 17,
-18, 20, -25, 31, -38, 40, -41, 43, 45, 47, -48 ], [ 3, -11, 13, -16, 19, 26,
-30, 39, 42, 44 ], [ 1, -2, 12 ] ] ),
frattFacs := rec( frattFacs := [ 7, 13, 20, 26, 32, 21, 27, 33, 76, 82, 88,
94, 59, 65, 71, 77, 83, 89 ], pos := [ 1, 2, 3, 8, 11, 12, 13, 14, 15, 16, 17
, 18, 19, 24, 25, 30, 35, 38 ] ) );

SMALL_GROUP_LIB[ 80 ] :=
[ 26320432143363, 110125659328, 2070724866087939, 329001342979,
26313553500163, 2105614595708931, 2105614679595011, 168449174436764675,
329001341955, 26313553499139, 329001339907, 26320180497411, 26313553497091,
329001355267, 3462294017593347, 276983521456083971, 276983521456084995,
22158681716535254019, 329001354243, 1375734832, 2701149232, 217449516080,
1375740976, 108749939760, 8700010520624, 696000809886768, 55680064759098416,
2070717990575107, 165657432360639491, 25884060945411, 2070717990587395,
25884060947459, 2070717990589443, 25884060959747, 26313469629443, 4110553091,
328917487619, 328917485571, 6761611267, 43278590707715, 43278590679043,
3462287306692611, 4110550019, 4110581763, 16778252, 16793612, 108733156364,
1358974988, 121887296570112, 323557131267, 50462723, 3 ]; 

PROPERTIES_SMALL_GROUPS[ 80 ] := rec(
isNilpotent := [ 2, 20, -27, 45, -48, 52 ], 
isSupersolvable := [ 1, -48, 50, -52 ], 
isAbelian := [ 2, 20, 23, 45, 52 ], 
lgLength := rec( lgLength := [ 2, 3, 4, 5 ], pos := [ [ 49, 51, -52 ], [ 11,
-14, 19, -22, 30, -31, 34, -48, 50 ], [ 4, -10, 15, -18, 23, -29, 32, -33 ],
[ 1, -3 ] ] ),
frattFacs := rec( frattFacs := [ 5, 9, 14, 18, 22, 51, 55, 59 ], pos := [ 1,
2, 3, 19, 27, 34, 44, 48 ] ) );