sml1368.z

#############################################################################
##
#W  sml1368.z              GAP library of groups           Hans Ulrich Besche
##                                               Bettina Eick, Eamonn O'Brien
##

SMALL_GROUP_LIB[ 1368 ] :=
[ 1250602040183820106488545573, 914317194044003973759269,
125361449784330393122679907, 1553450244451314367660325,
177245381966062429925323815223, 1276476231169480644647,
1710827059279981934573756417195, 914182778589047228104811,
1250604575497063577742870635, 914182778589047194092587,
914184631212063788896235, 243837657577979066485707707162935,
130295241520636200216764599, 178243890400235932082377005367,
178243901738288787190796560567, 130295241520636200250776823,
130295249808686533951990903, 178243901738288787190830572791,
668361198842617135211, 670213821859177926635, 1254254229968250138820379819,
171619458933904503495731521848, 237181590403514913079605527228322,
2128588242925805886654448811, 1135563718858763305067,
1555985557692835225012331, 1135563718858729292843, 1137416341875324096491,
171495193208351316649505883163, 91638486684009487400923,
125361983339437890133526491, 91638486684009453388699, 91638876709908516278107
, 242471698040021373079025522524471, 129565337694481195046845687,
177245393304109186421070775543, 129565337694481195012833463,
129565345982531528748059767, 933087744416997287, 8343579807633075047,
15614383844374664281088039, 1025595350649459946937990185253,
749704338107266456562073893, 914182777909473299205929,
914318121033144017143667, 1250602041110809246531929971, 668360519268688236329
, 1135563041235231379241, 66889798170198047641, 1553451171440454411044723,
91505390881279669626979, 2125121205323670317666129447, 8355099408153769511,
342114500357063316535617041436, 468012636500754683606850455605020,
668262272496600900455, 5205638078001178949331305,
1254254228017369971070216553, 95178316405210580132983, 488575556535182183,
200278584360594904860, 916852507963356211947881, 830088969418990439,
66987197660439812503, 94711455404967875757175, 677623906165607,
1403014443156769711260674787181739, 749704203691820415916867691,
1025595353184773199325344958571, 749704203691820415882855467,
749704205544443432477659115, 914316167446305316704107,
914316167446305282691883, 1250784517065317126237162411,
914316167446306337070827, 1250784517065317127291541355,
1250784517065317127257529131, 1711073219345352600099983791019,
914049292171939798450283, 914051144794956359241707,
1710577249561994078685844505771, 324450067486549921471983826321715106,
180498022624122906192334914402, 1250602039253444808263144669,
668262265809321496733, 914182777233800912312477, 668262265809287484509,
668262265810341863453, 1250787186794015423630201771, 668361198851188215659,
914318119002224498169707, 668361198851154203435, 668361198852208582379,
1710823592236807699858566239147, 914182778589055799185259,
1250602041108778327012956011, 914182778589055765173035,
914182778589056819551979, 171244926966756333288678418531,
4450990777527465709965017736926759, 1268952576116851904363,
1268952576116817892139, 1735927125946383719304107, 1268952576117872271083,
1735927125946384773683051, 1735927125946384739670827,
2374748308296471412881822635, 1738594907154573358299623,
1738594907154573324287399, 2378397832993245405113447975,
1738594907154574378666343, 2378397832993245406167826919,
2378397832993245406133814695, 3253648235534765503200716062247,
66889905433086245851, 91505390560561197660187, 66889905434106612571,
91505390560562252039131, 125179374286775772172140571,
1735927130012129843255783, 1735927130012129809243559,
2374748313862471946377074215, 1735927130012130863622503,
2374748313862471947431453159, 2374748313862471947397440935,
3248655693363867500919200357927, 2378397827431310621007321575,
2378397827431310620973309351, 2378397827431310622027688295,
3253648227926038712638706950631, 4450990775802820964671362914393639,
488568869255778461, 488568870276145181, 914316263668705748358365,
125452820858121587213334648, 173378355558124933071473718114,
1553449314074065745286365, 830088969214922909, 1135562363612447512733,
830088969180910685, 830088970235289629, 91505097612896037054733,
48895912340530381, 66889691177842781389, 48895912306518157, 48895913360897101
, 2125121199751571171464270763, 1135563718867334385515,
1553451169407584495097707, 1135563718867300373291, 1135563718868354752235,
125179374286775510958260251, 66889905171872365531, 91505390560301038158811,
66889905171838353307, 66889905172892732251, 2907165808874444149199676595751,
1553451173473329564670439, 2125121205317571706013901287,
1553451173473329530658215, 1553451173473330585037159, 6098612740619687,
6098613794998631, 11421439186646028549671, 914049193245593782215527,
1710577249560043182914918558057, 250086301932535355124160092,
342118061043316084379892921948, 5205637734376409031389417,
668359779110144999783, 668164712508081824615, 1250421966054768078449650025,
3805290743008983625961, 320471695708610299294692231020210275,
8329718073344544494093064847277890065959, 3253658817998096560018939476455,
171245018604900863171473558363, 4450995768339917524169813158816103,
6088968720998226237302237813383242215,
438406214387442729313821447112927658011,
11395042199725394018542863465569640452546087, 1270902706651681948007,
182809721570921683975836, 250083702215910717344396892,
250083699091138489848480540, 342114504631369398440455224924,
488504244873757031, 488575564970213735, 668262272505035932007,
3805290990935784567017, 916852505859173852393705, 600835359745719246169,
10420152169769669445114419, 924463086699218600516147,
1259468742109138461565999667, 125179040180390365188931483,
3253648229186743932818909945255, 927595582963089767, 1270902705676483461479,
146402526088697239, 3805193484330675388775, 1738594903088835839435111,
365560118378855, 146402787302688348, 670213820116527722729, 606312244740455,
35681816052343, 830088977854021991, 48895920979629463, 1135563718871619920231
, 359 ]; 

PROPERTIES_SMALL_GROUPS[ 1368 ] := rec(
isNilpotent := [ 6, 39, -41, 53, 66, 162, -164, 211 ], 
isSupersolvable := [ 1, -21, 24, -53, 56, 59, -60, 63, -81, 84, -98, 101,
-134, 137, -165, 170, -171, 182, 187, -189, 198, -203, 206, -211 ], 
isAbelian := [ 6, 39, 53, 66, 162, 211 ], 
lgLength := rec( lgLength := [ 3, 4, 5, 6 ], pos := [ [ 182, 187, 199, -203,
206, 209, -211 ], [ 56, 59, -60, 63, -66, 83, -88, 108, -141, 152, -165, 169,
-171, 173, 176, -181, 185, -186, 188, -191, 196, -198, 204, -205, 207, -208 ]
, [ 7, -41, 44, 47, -48, 51, -55, 57, -58, 61, -62, 67, -82, 89, -107, 142,
-151, 166, -168, 172, 174, -175, 183, -184, 192, -195 ], [ 1, -6, 42, -43, 45
, -46, 49, -50 ] ] ),
frattFacs := rec( frattFacs := [ 7, 13, 19, 25, 31, 37, 44, 50, 56, 62, 68,
74, 80, 86, 92, 45, 51, 57, 63, 69, 75, 81, 87, 93, 99, 105, 111, 256, 262,
268, 274, 280, 286, 292, 298, 304, 310, 316, 322, 328, 173, 179, 185, 191,
197, 203, 209, 215, 221, 227, 233, 239, 245, 251, 257, 263, 269, 275, 281,
287, 293, 299, 305, 311 ], pos := [ 1, 2, 3, 4, 5, 6, 11, 18, 21, 22, 23, 28,
33, 38, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57,
58, 59, 60, 61, 62, 63, 64, 65, 66, 71, 78, 81, 82, 83, 88, 93, 98, 99, 100,
107, 114, 119, 126, 131, 134, 135, 136, 141, 146, 151, 156, 161, 164 ] ) );