col9.z

#############################################################################
##
#W  col9.z                 GAP library of groups           Hans Ulrich Besche
##                                               Bettina Eick, Eamonn O'Brien
##

SMALL_GROUP_LIB[ 1395 ] :=
[ 809382612359759, 4062701639759, 2327020679759, 64282438019, 4059927388019,
1451548019, 1684828019, 28019 ]; 

PROPERTIES_SMALL_GROUPS[ 1395 ] := rec(
isNilpotent := [ 4, 8 ], 
isAbelian := [ 4, 8 ], 
lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 5, -8 ], [ 1, -4 ] ] ),
frattFacs := rec( frattFacs := [ 3, 5, 7, 9 ], pos := [ 1, 2, 3, 4 ] ) );

SMALL_GROUP_LIB[ 1400 ] :=
[ 566371149778311273630885, 671886981771866245985,
794061746508523172937446733, 683217906146202947,
1110087451010176977529428102309, 1587275076621786833692194343204173,
1133772442569292208820997512525, 578455315932495130044621,
809837442305501057796019533, 809837458978065857819537613,
578455315932495130091277, 578455327841469988649613,
809837458978065857819584269, 944399903776410943637087, 479920297641822239,
674571359839096115231, 479920297641775583, 481836684401845151,
792922829217679158999978765, 404550821268511757517, 566373449441198563810509,
404550821268511710861, 404552463885734834253, 1111686468453511184666949614925
, 567186961791790078033677, 794061763181079411547686669,
567186961791790077987021, 567186973700764936592013, 488000559933635,
11986321113119363, 23493201372595934371139, 1133767913348322685340680150797,
940180577016124222776, 792919607864412143438716557,
1133767911872704881200343566541, 412894705176639042189, 342799013786243,
288964871497589961, 405133338803767054989, 342456906371, 479919270272367101,
288006433494203307, 673230849698645302919, 404168914965977524389,
942529908934809632113475, 12003101481509699, 402825113585841273771,
3947414939846292445486727, 792167847188945276458395813,
7763244522799133880903179567939, 792167847668384422647195813,
7763244522802489954926501167939, 2819505389626819128748197,
27628143883180197963084464963, 2013988583023701791, 2013988583023655135,
2819584017644561540447, 2013988583025101471, 2819584017644562986783,
2819584017644562940127, 3947417624703797471833439, 2829170752678365752579,
2829170752678365705923, 3960839053757838887527235, 2829170752678367152259,
3960839053757838888973571, 3960839053757838888926915,
5545174675260982569308220227, 288692080765546701, 404168913743276697357,
288692080766946381, 404168913743278143693, 565836479241258823790349,
2819588818885160013059, 2819588818885159966403, 3947424346447476173947715,
2819588818885161412739, 3947424346447476175394051, 3947424346447476175347395,
5526394085026474895618640707, 3960839048963447431564547,
3960839048963447431517891, 3960839048963447432964227,
5545174668548834522670945539, 7763244535968368339855714192195,
671886499250612563385, 342799013506937, 479918927816996729, 342799013460281,
342799014906617, 403208664645951122943, 205718555586495, 288006188883556287,
205718555539839, 205718556986175, 942523187182569516674399,
480879175945957151, 673230847986363987743, 480879175945910495,
480879175947356831, 565836479241258465472269, 288692080407228621,
404168913742919825613, 288692080407181965, 288692080408628301,
1319541872496756009039481667, 673235649226961014019, 942529908926248220235011
, 673235649226960967363, 673235649226962413699, 8561413371587, 8561414817923,
16792364656677677891, 1552648980488853281195713840441509,
15215960008773275254146367154658083651, 2819773738569954357023,
5545174930310964821919788291, 5545174933667038845241388291,
792169726205475984362666637, 7763263316542484103436559226563,
7763244902435345961214844800259, 7763244907133849593865084800259,
19736537715735640486964483, 2013932421166774811277,
19736534841155502462490307, 19738414241649684176579843,
27631152802019356077967682819, 1552648981991836896471856687020237,
15215960017982339563093227059074045187,
15215980666552629426050235354108878531, 2173708574790073296821569081288666893
, 21302344025175295122045775018603107371843, 2020836247445864579,
671557560082394760, 287732248116803967, 2819582099893912828127,
565834176563548971563661, 5545174659142238476463675075,
565834176906005504555661, 5545174659144635672194619075,
2013932421166416493197, 19734388487985844263491267, 1438562265366659,
2020836246108143747, 1027516581052617, 10068565553998774403,
2829170749253806301315, 244635697283, 146790973581, 343483938422915,
206207791055049, 480882600517165187, 131 ]; 

PROPERTIES_SMALL_GROUPS[ 1400 ] := rec(
isNilpotent := [ 4, 29, -31, 40, 46, 111, -113, 153 ], 
isSupersolvable := [ 1, -32, 34, -113, 116, -127, 133, 135, -153 ], 
isAbelian := [ 4, 29, 40, 46, 111, 153 ], 
lgLength := rec( lgLength := [ 3, 4, 5, 6 ], pos := [ [ 133, -134, 144, -148,
151, -153 ], [ 33, 36, -40, 62, -90, 101, -113, 117, -132, 137, -143, 149,
-150 ], [ 7, -32, 34, -35, 41, 44, -46, 49, -61, 91, -100, 114, -116, 135,
-136 ], [ 1, -6, 42, -43, 47, -48 ] ] ),
frattFacs := rec( frattFacs := [ 7, 13, 19, 25, 32, 38, 44, 50, 56, 62, 68,
195, 201, 207, 213, 219, 225, 231, 237, 243, 34, 40, 46, 52, 58, 64, 113, 119
, 125, 131, 137, 143, 149, 155, 161, 167, 173, 179, 185, 191, 197, 203, 209,
215, 221 ], pos := [ 1, 2, 3, 4, 5, 6, 13, 18, 23, 28, 31, 32, 33, 34, 35, 36
, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 61,
68, 73, 80, 85, 90, 95, 100, 105, 110, 113 ] ) );

SMALL_GROUP_LIB[ 1410 ] :=
[ 103303867131, 7020655197, 145779878022139, 2435744483, 145564387023911,
9708772407077, 205549863951998075, 2299 ]; 

PROPERTIES_SMALL_GROUPS[ 1410 ] := rec(
isNilpotent := [ 8 ], 
isAbelian := [ 8 ], 
lgLength := rec( lgLength := [ 4 ], pos := [ [ 1, -8 ] ] ),
frattFacs := rec( frattFacs := [ ], pos := [ ] ) );

SMALL_GROUP_LIB[ 1416 ] :=
[ 21607616066991722249, 1229926243482599020161, 1741576462865935241697619,
2699040520493965651, 1273020162730349067187, 1273020162729692710419,
1802596551733334380360019, 1273020162739538061939, 1802596551733344225711539,
1802596551733343569354771, 2552476717255707723791534931,
43415988655289315282517880, 1741574662871086845384765, 868591168979552413,
1229925609019923538589, 868591168323195645, 868591178168547165,
30596338577664935114725, 15259655564699717, 21607583814265569861,
15259654908342949, 15259664753694469, 2466072268724652929850618707,
1229926877993844515763, 1741576460962531463265715, 1229926877993188158995,
1229926878003033510515, 1903414280140307, 1903424125491827,
3819148043966068882259, 61127915392589472521228, 86557131603563394280398124,
2546996451808880536161, 899024614203461747, 45693688884471596,
613047723020403, 10837762956523, 868591209673668723, 115 ]; 

PROPERTIES_SMALL_GROUPS[ 1416 ] := rec(
isNilpotent := [ 4, 28, -30, 39 ], 
isSupersolvable := [ 1, -11, 13, -30, 34, 36, -39 ], 
isAbelian := [ 4, 28, 39 ], 
lgLength := rec( lgLength := [ 3, 4, 5 ], pos := [ [ 34, 36, -39 ], [ 5, -33,
35 ], [ 1, -4 ] ] ),
frattFacs := rec( frattFacs := [ 4, 7, 10, 13, 17, 20, 23, 26, 29, 32 ],
pos := [ 1, 2, 3, 4, 11, 12, 17, 22, 27, 30 ] ) );

SMALL_GROUP_LIB[ 1420 ] :=
[ 1314961256478744769, 70700830424769, 52430949468103, 1205353501464769,
1714083996901290279, 4364081610279, 70680061760279, 657681920279,
74381066139228103, 7499043859647001130279, 3719027605440279, 848993600279,
37647684833, 1207099484640279, 279 ]; 

PROPERTIES_SMALL_GROUPS[ 1420 ] := rec(
isNilpotent := [ 6, 15 ], 
isAbelian := [ 6, 15 ], 
lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 7, -8, 11, -15 ], [ 1, -6,
9, -10 ] ] ),
frattFacs := rec( frattFacs := [ 3, 5, 7, 9, 11, 13 ], pos := [ 1, 2, 3, 4, 5
, 6 ] ) );

SMALL_GROUP_LIB[ 1422 ] :=
[ 845159432893636223, 594387251043455, 38456714403930499, 2076596832835199,
63352592170376896219, 1497259021439, 594350458077791, 594387769254239,
845159433411847007, 1028130201695, 1460466055775, 20136202555,
2076597351045983, 27007962048835, 2952923400306658271, 6239 ]; 

PROPERTIES_SMALL_GROUPS[ 1422 ] := 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[ 1425 ] :=
[ 766929678587, 1021423355, 540843227, 383602470789, 1123432370957915, 6875 ]
; 

PROPERTIES_SMALL_GROUPS[ 1425 ] := rec(
isNilpotent := [ 2, 6 ], 
isSupersolvable := [ 1, -3, 6 ], 
isAbelian := [ 2, 6 ], 
lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 3, -6 ], [ 1, -2 ] ] ),
frattFacs := rec( frattFacs := [ 3, 5 ], pos := [ 1, 2 ] ) );

SMALL_GROUP_LIB[ 1428 ] :=
[ 1787048670341894239, 105221528820391685, 2551904668216542105695,
73719893466885, 368284990969103, 122784660332293, 527581052559954015,
24584528092929, 525911650311622687, 175336662762582037, 753385748900065837407
, 6133214347615, 752192000712384712799, 1074130176178124768677983,
1788764185505562975, 1251435492671839, 73688888115701, 1787048087903011167,
525788410452907279, 750827507950076039263, 750825838547827707935,
1072181681352420896014687, 2085550890680671, 417316873438495,
2980717388946735455, 122785665912597, 2978167758685995359,
4169286262647161183, 4256464431535592833375, 21474836981, 73615940869888,
35548224773287941, 257832255839, 86033564149, 369453288128863, 17314088433,
368285057025311, 122784726388501, 527581052592456031, 351 ]; 

PROPERTIES_SMALL_GROUPS[ 1428 ] := rec(
isNilpotent := [ 12, 40 ], 
isSupersolvable := [ 1, -30, 33, -40 ], 
isAbelian := [ 12, 40 ], 
lgLength := rec( lgLength := [ 4, 5 ], pos := [ [ 15, -18, 23, -40 ], [ 1,
-14, 19, -22 ] ] ),
frattFacs := rec( frattFacs := [ 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25 ]
, pos := [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 ] ) );

SMALL_GROUP_LIB[ 1430 ] :=
[ 592219496999, 45645079101, 846872277774887, 87589437, 117449255, 96215613,
168245932583, 32515479, 167417820479, 136989980253, 240594815269415, 551 ]; 

PROPERTIES_SMALL_GROUPS[ 1430 ] := rec(
isNilpotent := [ 12 ], 
isAbelian := [ 12 ], 
lgLength := rec( lgLength := [ 4 ], pos := [ [ 1, -12 ] ] ),
frattFacs := rec( frattFacs := [ ], pos := [ ] ) );

SMALL_GROUP_LIB[ 1444 ] :=
[ 2789342414138803859, 97015145363, 1930359079013507, 54167939, 1320423510437
, 1930299902467667, 19403029331, 4024927849377225288275, 25069501638467,
1336764384323, 917070659, 323 ]; 

PROPERTIES_SMALL_GROUPS[ 1444 ] := rec(
isNilpotent := [ 2, 4, 7, 12 ], 
isSupersolvable := [ 1, -7, 9, -12 ], 
isAbelian := [ 2, 4, 7, 12 ], 
lgLength := rec( lgLength := [ 2, 3, 4 ], pos := [ [ 9, -10, 12 ], [ 3, -4, 6
, -8, 11 ], [ 1, -2, 5 ] ] ),
frattFacs := rec( frattFacs := [ 5, 9, 14, 18, 15, 19, 23 ], pos := [ 1, 2, 3
, 4, 5, 6, 7 ] ) );