col2.z

#############################################################################
##
#W  col2.z                 GAP library of groups           Hans Ulrich Besche
##                                               Bettina Eick, Eamonn O'Brien
##

SMALL_GROUP_LIB[ 1064 ] :=
[ 175472014858665197, 596446440531372953, 637285813210923292619,
4389260038143947, 3330143116865206955, 3330143116863317387,
3543272279172558573515, 3330143116891660907, 3543272279172586917035,
3543272279172585027467, 3770041705042428320326091, 634618387185728382917,
560569102647461, 596445852340949669, 560569100757893, 560569129101413,
186701993178841904873, 164917145259977, 175471798172361161, 164917143370409,
164917171713929, 678072100879123216050635, 598952824591712939,
637285809093446915243, 598952824589823371, 598952824618166891, 4117506610571,
4117534954091, 4665795767071134155, 245502287654683032, 3129831094800491,
526539460715, 155035275575, 562922079639659, 107 ]; 

PROPERTIES_SMALL_GROUPS[ 1064 ] := rec(
isNilpotent := [ 4, 27, -29, 35 ], 
isSupersolvable := [ 1, -29, 31, -35 ], 
isAbelian := [ 4, 27, 35 ], 
lgLength := rec( lgLength := [ 3, 4, 5 ], pos := [ [ 30, -35 ], [ 5, -29 ], [
1, -4 ] ] ),
frattFacs := rec( frattFacs := [ 4, 7, 10, 13, 17, 20, 23, 26, 29 ], pos := [
1, 2, 3, 4, 11, 16, 21, 26, 29 ] ) );

SMALL_GROUP_LIB[ 1068 ] :=
[ 32886394673089, 2855664927190679, 3049856229678911663, 8198135419055,
3048014409787322007, 3255279379351824371887, 2921191900053679, 98410489687488
, 2673202036911, 32623435241, 2855665826726063, 175 ]; 

PROPERTIES_SMALL_GROUPS[ 1068 ] := rec(
isNilpotent := [ 4, 12 ], 
isSupersolvable := [ 1, -7, 9, -12 ], 
isAbelian := [ 4, 12 ], 
lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 7, -12 ], [ 1, -6 ] ] ),
frattFacs := rec( frattFacs := [ 3, 5, 7, 9 ], pos := [ 1, 2, 3, 4 ] ) );

SMALL_GROUP_LIB[ 1071 ] :=
[ 36173848341, 3993047391, 35656181, 4447 ]; 

PROPERTIES_SMALL_GROUPS[ 1071 ] := rec(
isNilpotent := [ 2, 4 ], 
isAbelian := [ 2, 4 ], 
lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 3, -4 ], [ 1, -2 ] ] ),
frattFacs := rec( frattFacs := [ 3, 5 ], pos := [ 1, 2 ] ) );

SMALL_GROUP_LIB[ 1078 ] :=
[ 29975649800955, 49730900559, 32446772050500595, 56340559, 46400559,
25920595, 49956320559, 27776480955, 53854367280559, 559 ]; 

PROPERTIES_SMALL_GROUPS[ 1078 ] := 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[ 1089 ] :=
[ 6195251199, 5161199, 103396029931199, 619531199, 318172641199, 1199 ]; 

PROPERTIES_SMALL_GROUPS[ 1089 ] := rec(
isNilpotent := [ 1, -2, 4, 6 ], 
isSupersolvable := [ 1, -2, 4, 6 ], 
isAbelian := [ 1, -2, 4, 6 ], 
lgLength := rec( lgLength := [ 2, 3, 4 ], pos := [ [ 5, -6 ], [ 2, -4 ], [ 1
] ] ),
frattFacs := rec( frattFacs := [ 5, 10, 11, 15 ], pos := [ 1, 2, 3, 4 ] ) );

SMALL_GROUP_LIB[ 1092 ] :=
[ 9772050455057819, 10012772920644359, 10671310655535764231,
189648347190121223, 10680793277045789447, 10807192613547004679,
14606827326658805, 207095879578296832775, 10681033681516024583,
10807433018017239815, 11663426142702695404295, 11801454218162022437639,
35668733711771, 13384597887221, 39066100378096391, 38950350069945095,
49024315544987, 22288244791541, 53766389178880775, 4464197628913,
53534676565683671, 24338813918451281, 58712898043932724439, 1112983981271,
[ ( 1, 2)( 3, 4)( 5, 8)( 6, 9)( 7,12)(13,14), 
  ( 2, 3, 5, 9, 6,11, 8,13,10, 7,12,14, 4), 
  ( 3, 6, 9, 4, 7,12)( 5,10, 8,14,11,13) ],
58406247708315211163, 63779622726813874967303, 58586124004031058695,
63779778037015915909895, 63779651637679414694663, 63976047295736636035847,
69647517616304436902417159, 69647379588228977575383815, 10012447679054039,
189888426036560087, 10807432693157855447, 10681033356656640215,
35661375996119, 35881510699223, 38941340886171863, 173670849183959,
39065775407235287, 38950025099083991, 13377240170777, 189648241589551319,
39065995541938391, 38950245233787095, 42659825307017085143,
42533425970515869911, 53507860980159899, 58430813801990116103,
58430582089376918999, 63806448671721072774359, 289420775129303,
57920158827239, 316403512400019671, 22288483419713, 316047683699048663,
442446914146074839, 345512635562591060183, 9172943063, 13249806617,
9064396357847, 8958397907159, 13359929456880, 9896704401928907,
14678058054392645, 10807954636054434119, 10681959683642593607, 44877349079,
20416168217, 49236328120535, 4108714837, 49024331219687, 22288260466241,
53766389186592983, 215 ]; 

PROPERTIES_SMALL_GROUPS[ 1092 ] := rec(
isNilpotent := [ 24, 77 ], 
isSupersolvable := [ 1, -24, 26, -64, 70, -77 ], 
isSolvable := [ 1, -24, 26, -77 ], 
isAbelian := [ 24, 77 ], 
lgLength := rec( lgLength := [ 4, 5, false ], pos := [ [ 34, -49, 54, -77 ],
[ 1, -24, 26, -33, 50, -53 ], [ 25 ] ] ),
frattFacs := rec( frattFacs := [ 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25,
27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49 ], 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 ] ) );

SMALL_GROUP_LIB[ 1098 ] :=
[ 368421504010563719, 87836063043719, 8036245768532461, 430267464003719,
10201097655351367141, 404792643719, 335540413443719, 335553477123719,
368421504192003719, 81285123719, 391910403719, 7050247141, 430267645443719,
7306329812461, 472434406675203719, 3719 ]; 

PROPERTIES_SMALL_GROUPS[ 1098 ] := rec(
isNilpotent := [ 6, 16 ], 
isAbelian := [ 6, 16 ], 
lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 7, 10, -11, 14, -16 ], [ 1,
-6, 8, -9, 12, -13 ] ] ),
frattFacs := rec( frattFacs := [ 3, 5, 7, 9, 11, 13 ], pos := [ 1, 2, 3, 4, 5
, 6 ] ) );

SMALL_GROUP_LIB[ 1100 ] :=
[ 17463545290867503039, 7949770854703039, 6579799859220109033,
17862090765103039, 7294811326668822900393, 20275200500339, 7946094605200339,
14436352400339, 7961557791967027834509033, 9153512593920428236950900393,
6871301331488400393, 16238195600339, 5981636218400933, 6631641258416400393,
18022800339, 7946094297703309, 7989420140903039, 8740743340153703039,
5424844903309, 16238195303309, 5414924903903, 17901740051303039,
5974466579309033, 19692112732182500339, 450560100339, 71971392971065703039,
79168528223691078503039, 7989345139200339, 5421888000339, 5461203200339,
5963666656000339, 3686400339, 5949203264103903, 71981305290976103039,
7229056967516793709033, 87471584857900277859300339, 7229056976527993709033,
87471584857999401059300339, 32716612444384109033, 395818629514485808100339,
59488729600339, 65718696435200339, 5431404800933, 65437802563200339,
72290566250588800339, 14758400339, 4928000393, 16274246400339, 5431315200933,
17901920278400339, 339 ]; 

PROPERTIES_SMALL_GROUPS[ 1100 ] := rec(
isNilpotent := [ 6, 15, 25, 51 ], 
isAbelian := [ 6, 15, 25, 51 ], 
lgLength := rec( lgLength := [ 3, 4, 5 ], pos := [ [ 29, 32, 42, -46, 49, -51
], [ 7, -8, 11, -16, 19, -20, 23, -25, 28, 30, -31, 35, -41, 47, -48 ], [ 1,
-6, 9, -10, 17, -18, 21, -22, 26, -27, 33, -34 ] ] ),
frattFacs := rec( frattFacs := [ 5, 9, 13, 17, 21, 25, 30, 34, 38, 42, 46, 50
, 54, 58, 62, 31, 35, 39, 43, 47, 51, 55, 59, 63, 67 ], 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
] ) );

SMALL_GROUP_LIB[ 1104 ] :=
[ 160407216201553164244369, 3362744944204262270998629,
3712473757216030828966774763, 10016378146857979627499,
3682401607619199356943787, 3682401607619199243563883,
4065371374827425539987785707, 4065371365771055440498918827,
4065371365771055440385538923, 4488169987811261031758871138283,
4496639530634320046485381415211, 4488169997800445458612822250923,
4496639540623504473325046659947, 4964290041820289338806262446527915,
4964290041820289338806262333148011, 4488169997800437255379033298347,
4954939677571682737552663322992619, 4496639550621737067041069529963,
4964290063886388681340751566671851, 5480576206169599430049599892101505003,
4954939677571691793922766326636523, 4964290052848339897878262318174187,
3682410655786068231495403, 3682401607619202531581099,
3682410655786071632892523, 4065381382108186128399984363,
4065371374819222309373470443, 4065381363995445922392696555,
4065381373051816025396340459, 390483934004428692830455111344,
3045964613525269188653, 3362741919945408698275885,
3712470409350538628778915885, 3712470409353273040041900077,
4098567331926016085328043016813, 3045964613525155808749,
3362741919945408584895981, 3048980669147547093101, 3362744936001030976180333,
3366077680198936317137005, 3045964613527990306349,
4065364697250197321704891309, 4488162625764220236415247543789,
4488162625764220236415360923693, 4954931538843699143395561391227501,
3048980669150948490221, 145296390253789859833, 160406821733009900541945,
177089565505896709295880185, 177089565506253371634530297,
195506880318903993657147572793, 145296390253676479929,
160406821733009787162041, 145689788812527274041, 160407215131568637956153,
160841920896512812863545, 145296390256510977529, 529986748821331299847414649,
585105370698749770535434104249, 585105370698749770535547484153,
645956329251419746686498194768441, 145689788815928671161,
3362747968463147362876843, 3712473748143254261900002731,
4098571027939345234428680918443, 4098571027939353437662469871019,
4524822414845046203273800150212587, 3362747968463147249496939,
3712473748143254261786622827, 3362757016630016237428459,
3712473757191421130774554347, 3712483755424014846797424363,
3362747968463150537514155, 13457062939821808717151174115627,
14856597485563276831701520325397355, 14856597485563276831701520438777259,
16401683624061857622206444938395770859, 3362757016630019638825579,
9072776570921688811, 18120943443537777259, 20014586130875810277099,
9072776571148448619, 10007305370290799475563, 11048065136999772506620203,
12197063911255811515980647275, 13465558558026423976186361880555,
263306607727465253533608131666873690664, 238502362071979396316694393361670120
, 353697621663697911404067956, 290690494931149926580814053249617471157448,
263306607727490875526099701407357676168, 390482185919359921817216371596,
233410939511616204720067470121502, 211422952456174100604913799134,
11041384294885347499711845, 4073043053102587117948485035,
4065371365762852210338123179, 4496639530625263676378976374187,
4065371365762852210224743275, 4496639530625263676378862994283,
4488169987802196458425706698731, 4964290041810291106212542908880875,
3682401599415968969388331, 4073043053102587121349882155,
4496639530625263676375348217259, 3335508688215126092075,
3689350591571638325193003, 3682401599415972597545259,
4073043053102587124978039083, 3335508688214899332267,
3682401599415972370785451, 4073043053102587124751279275,
3335508688214785952363, 3689350591571637985053291, 3682401599415965227851499,
3335508688218300729387, 3682401599415968742628523, 3682401599415968629248619,
4065371365762852206369826539, 3341803065283270770731, 3335508688221928886315,
3689350591571645127987243, 434837493627909113544, 177568900799626050616029832
, 196036066482770115802549976264, 3362741917211000496538937,
2759021022855080697, 3045961879120582228729, 3045961879120355468921,
3021286844856631801, 3682395556366732872656505, 3682395556366726069862265,
4065364694231407160158080889, 2759021022514940985, 2759021029657874937,
160406821376350622935797, 131608461465931957, 145296033598027030709,
145296033597800270901, 393874283467483061, 480060460532082999053365,
480060460532076196259125, 529986748427575950765225269, 131608461125792245,
131608468268726197, 3712473748135051031625827179, 3045967347964877138219,
3362747960259920603478315, 3362747960259920376718507, 10000991614883550707755
, 12189368604902848166819161259, 12189368604902848160016367019,
13457062939812752347044769074603, 3045967347964536998507,
3045967347971679932459, 8203233902332523, 8203237417109547,
10007297167056783763179, 9064573340874273067, 353697633222378096644223308,
320378280535773645294428, 353697632173314727004488012,
10001253886017627531693, 3021287193159696427, 393885255014043980,
480061641916563274605488, 2496694421061675, 118945496728015,
2759021051426816043, 43 ]; 

PROPERTIES_SMALL_GROUPS[ 1104 ] := rec(
isNilpotent := [ 4, 79, -86, 156, -159, 170 ], 
isSupersolvable := [ 1, -29, 31, -86, 96, -122, 126, -159, 164, 167, -170 ], 
isAbelian := [ 4, 79, 82, 156, 170 ], 
lgLength := rec( lgLength := [ 3, 4, 5, 6 ], pos := [ [ 164, 166, -170 ], [
23, -30, 38, -41, 46, 54, -57, 62, 70, -73, 78, -81, 96, -122, 126, -163, 165
], [ 5, -22, 31, -37, 42, -45, 47, -53, 58, -61, 63, -69, 74, -77, 82, -95,
123, -125 ], [ 1, -4 ] ] ),
frattFacs := rec( frattFacs := [ 5, 9, 13, 17, 22, 26, 30, 34, 38, 42, 127,
131, 135, 139, 143, 147, 151, 155, 159 ], pos := [ 1, 2, 3, 4, 29, 30, 46, 62
, 78, 86, 89, 92, 95, 122, 125, 135, 145, 155, 159 ] ) );