col7.z

#############################################################################
##
#W  col7.z                 GAP library of groups           Hans Ulrich Besche
##                                               Bettina Eick, Eamonn O'Brien
##

SMALL_GROUP_LIB[ 1323 ] :=
[ 1177731637436001295439, 231273203848271, 890197760710016495,
1177742333111568557039, 1177742333117811254255, 890197760710008719,
1177742333111568549263, 890205845130422063, 174795593615, 8259216006959,
10926948771102095, 224177933504855, 296592142864165199, 299714078285703503,
8277816533327, 672694835069231, 127465775, 1561142511284975,
2065391542070956367, 2065399801159373135, 1561142511393839,
2065391542071073007, 2065391548313770223, 2732513010159506044751,
2732513018418594461519, 2732523945192569845583, 169445651303, 224176149977447
, 224177041791335, 169445643527, 224176149969671, 169445760167,
224181501233903, 296592130378887407, 296592136621584623, 224181501226127,
296592130378879631, 224181501342767, 226541240781551, 299714065800425711,
226541240773775, 299714065800417935, 226541240890415, 6242706575, 6242823215,
8265331247759, 169453100591, 128398895, 169446133295, 171229761071, 1583 ]; 

PROPERTIES_SMALL_GROUPS[ 1323 ] := rec(
isNilpotent := [ 2, 9, -11, 15, 17, 44, -46, 51 ], 
isAbelian := [ 2, 9, 15, 17, 44, 51 ], 
lgLength := rec( lgLength := [ 2, 3, 4, 5 ], pos := [ [ 47, 49, -51 ], [ 16,
-26, 33, -46, 48 ], [ 3, -11, 13, -15, 27, -32 ], [ 1, -2, 12 ] ] ),
frattFacs := rec( frattFacs := [ 7, 13, 20, 26, 21, 27, 33, 39, 76, 82, 59,
65, 71, 77, 83 ], pos := [ 1, 2, 8, 11, 12, 13, 14, 15, 16, 17, 26, 32, 38,
43, 46 ] ) );

SMALL_GROUP_LIB[ 1326 ] :=
[ 6051581657535, 356324999675, 8024395216847295, 75497979, 505414079,
371196411, 673675477439, 35654641, 667971226399, 489864302363,
893296930455999, 447 ]; 

PROPERTIES_SMALL_GROUPS[ 1326 ] := rec(
isNilpotent := [ 12 ], 
isAbelian := [ 12 ], 
lgLength := rec( lgLength := [ 4 ], pos := [ [ 1, -12 ] ] ),
frattFacs := rec( frattFacs := [ ], pos := [ ] ) );

SMALL_GROUP_LIB[ 1330 ] :=
[ 917071415, 272099075, 1220346840887, 164604297, 1218304428443, 358556031167
, 1623076046493623, 1079 ]; 

PROPERTIES_SMALL_GROUPS[ 1330 ] := rec(
isNilpotent := [ 8 ], 
isAbelian := [ 8 ], 
lgLength := rec( lgLength := [ 4 ], pos := [ [ 1, -8 ] ] ),
frattFacs := rec( frattFacs := [ ], pos := [ ] ) );

SMALL_GROUP_LIB[ 1332 ] :=
[ 21132688210903119864455, 15868093995098874503, 2350025341853528993509,
61567887768073446023, 3364554164901545684286973, 49154462073567575,
109169527173308069453144711, 15865381712759133527, 81996025166965852250759,
436160348914855823762180062717, 2538234800048748075517, 11913148788020567,
5274376691153122512, 21266272260227489626979, 46222063383123287,
1764283295070212437, 2525940246415318587901, 36655321486679,
28144054612739668036461191, 21129172842634784318087, 15865381526825688947,
15868093998847777415, 21132688210906868767367, 11912962854575987,
46222063201771379, 1322562700053361, 61567887771822348935,
1761652054338473701, 82008426826432225356119, 329895777053015,
37494113100911602749542670983, 21129170130352444577111,
81959104484947779215219, 109169527173308073202047623, 15868018927852979543,
43961940590509856087, 77998393944506729642621795, 130215126638031034211,
11911174930171223, 11913152415991127, 15865381716387104087,
61558577873067794291, 81996025166969601153671, 109218705522388039794043223,
3125556546655574821867237, 193807756302525053657164900870487,
154039664675597120846995794263, 48859278476969303, 65180830410859218263,
1322620687069525, 65080617390987707735, 86820866145121140376919,
9163769906519, 3959750888130672, 15965669768496273251, 34681463637335,
998417500669, 46222067011093847, 1322566509375829, 61567887773696755031, 1367
]; 

PROPERTIES_SMALL_GROUPS[ 1332 ] := rec(
isNilpotent := [ 6, 18, 30, 61 ], 
isSupersolvable := [ 1, -12, 15, -36, 39, -44, 48, -53, 56, -61 ], 
isAbelian := [ 6, 18, 30, 61 ], 
lgLength := rec( lgLength := [ 3, 4, 5 ], pos := [ [ 38, -39, 49, -56, 59,
-61 ], [ 8, 11, -18, 21, 24, -25, 28, -30, 32, -33, 35, -37, 40, -42, 44, -48
, 57, -58 ], [ 1, -7, 9, -10, 19, -20, 22, -23, 26, -27, 31, 34, 43 ] ] ),
frattFacs := rec( frattFacs := [ 5, 9, 13, 17, 21, 25, 30, 34, 38, 42, 46, 50
, 54, 58, 62, 66, 70, 74, 31, 35, 39, 43, 47, 51, 55, 59, 63, 67, 71, 75 ],
pos := [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19,
20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30 ] ) );

SMALL_GROUP_LIB[ 1340 ] :=
[ 39103762398231, 846833682390365, 1136503987840379927, 3254565693719,
52346183483198487, 4699601486411453657111, 2617288862639879, 632086405895,
29752390341, 848135785686023, 263 ]; 

PROPERTIES_SMALL_GROUPS[ 1340 ] := 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[ 1350 ] :=
[ 19330285422576831714403285, 42998067497540992983391,
35333444663759671450518415139293, 7972855165837663, 31850420368313499999,
264204346926304395615, 356675868350608317694303, 10606373887244583413,
7845036941140445, 10575075172085154293, 28542127808306461360629,
42998255220253580140895, 57848146427101796749853047,
481512422461473002989879647, 130054592681999581796754047351,
14318667322129326351317, 10590765194942096341, 78094997678317285575873184119,
96337168804276785791271287, 5905580106079, 144959445467487,
195695353008300383, 521538281467217681595494875531207007,
231119621198762158064689503, 52930227016562663775, 23511789146776023,
31819249428414357855, 14318729942649422840789, 19330391501900791825646453,
26076770618895391180749480437, 145277268812127, 23575522167554399,
5811092881789, 31827076701369205087, 7845011172377077,
42966553958533182587231, 10590765194407322581, 58004847845301211772158303,
4295033183, 385361025971473842164998495, 520237385061489974761527984479,
702320893540126699298281532178783, 520238055562630299876161487199,
386324556601997639668740864754015, 386324556601997248579756309225823,
286166523741845646109998186847, 171199719406490302300511,
231119853583836673584677215, 171199719406490302292319,
231120117764590588610486623, 171199891543582619730271,
214366839317980325888381, 289395243052048311466082685, 52930227016563171679,
71455806182703500099935, 1263646374205624035797089205895549,
936034351348245031009201701245, 231119621198762158065197407,
312011802338179364628469645663, 39207575379525983, 52930226801818485087,
39207575379517791, 52930226801818476895, 39207575383703903, 17416094499191,
29003920441719, 39155305583493495, 23569814155968863, 195706906473398623,
264204323836560163167, 7856573224387061, 5811092857333, 7833389007634933,
21142316895033164277, 10637776935766753757, 23511789147791831,
52859662593636696535, 28542159211354975142365, 14361218470335265653117,
31819249428414865759, 356675837179668419314015, 19273138186703295269847421,
10606420238532150229, 7845011707659221, 14360999118405474485085,
10637765528398857053, 19387644936245611799134589, 14361218465494839722365,
107374190943, 107378377055, 145062524625247, 285452611830722739044703,
211975065350890122209132895, 423736133825695728691708255,
126814606967744495967, 39207575380033887, 171199719406490302808415,
52930227016563425631, 231119621198762158065451359, 29042619187551,
12886999391, 17459045204319, 4297064829, 17416095531383, 23569814156476767,
5811093897717, 23511789148307927, 31819249428415119711, 7845011172885461,
31740915538538005335, 42955986729321474425183, 351 ]; 

PROPERTIES_SMALL_GROUPS[ 1350 ] := rec(
isNilpotent := [ 4, 20, -22, 31, 39, 89, -91, 112 ], 
isSupersolvable := [ 1, -22, 26, -39, 65, -91, 101, -112 ], 
isAbelian := [ 4, 20, 31, 39, 89, 112 ], 
lgLength := rec( lgLength := [ 3, 4, 5, 6 ], pos := [ [ 94, -95, 100, 102,
109, 111, -112 ], [ 32, 37, -39, 43, -51, 55, 59, -64, 68, -70, 73, 81, 83,
-84, 87, -93, 96, -99, 101, 103, 105, -106, 108, 110 ], [ 5, -7, 10, 14, 16,
-25, 27, -28, 30, -31, 33, -36, 40, -42, 52, -54, 56, -58, 65, -67, 71, -72,
74, 77, 79, -80, 82, 85, -86, 104, 107 ], [ 1, -4, 8, -9, 11, -13, 15, 26, 29
, 75, -76, 78 ] ] ),
frattFacs := rec( frattFacs := [ 7, 13, 19, 25, 32, 38, 44, 50, 56, 62, 33,
39, 45, 51, 57, 63, 69, 75, 81, 142, 148, 154, 160, 166, 172, 178, 184, 125,
131, 137, 143, 149, 155, 161, 167, 173, 179, 185, 191, 197, 203, 209 ],
pos := [ 1, 2, 3, 4, 7, 11, 15, 17, 19, 22, 23, 24, 25, 26, 27, 28, 29, 30,
31, 32, 33, 34, 35, 36, 37, 38, 39, 43, 46, 51, 55, 59, 64, 67, 70, 74, 78,
82, 84, 86, 88, 91 ] ) );

SMALL_GROUP_LIB[ 1352 ] :=
[ 151400934158774877471887, 8385007444411535, 276746454165213029028365780111,
204695754373387575636231311, 111982939465580476559, 151402185187416390482063,
111982939465580227727, 111983864783136104591, 6200911604879, 931518467481743,
1702727254070683665551, 204694122903264075284425871, 82767031219740815,
4078854287, 82045026833090123, 111894440776107844751, 932892365251727,
110880091995203257931, 204530661840529746431861903,
204530661549897258422264975, 1948021893927337853740175, 1065713776298662031,
1440845026028958606479, 1065713776302145679, 1440845026028962338959,
1948022475191624871060623, 110924804631651297851, 60684145368635,
82044973837082171, 60684145119803, 60684148852283, 151281282998406861628559,
82762159366379663, 111894440087121647759, 82762159366130831,
82762159369863311, 688990178447, 688993910927, 1260339651420890255,
373862414900738175218274404164751, 204532031449424931763571855,
1441440324352370645135, 373865381021936784681106824858767,
505465994939075852641213718484034703, 82011904354669115,
151280075325836168580239, 151280075110871310584975, 1440844596099640249487,
61214376001679, 44877349007, 61214153048207, 143 ]; 

PROPERTIES_SMALL_GROUPS[ 1352 ] := 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 ] ) );