col13.z

#############################################################################
##
#W  col13.z                GAP library of groups           Hans Ulrich Besche
##                                               Bettina Eick, Eamonn O'Brien
##

SMALL_GROUP_LIB[ 564 ] :=
[ 1299971237893, 58290463898753, 32876061759165803, 2296939114,
60872053089883, 2592984511276, 103303864923, 2435738135, 58290531058523, 91 ]
; 

PROPERTIES_SMALL_GROUPS[ 564 ] := rec(
isNilpotent := [ 4, 10 ], 
isSupersolvable := [ 1, -5, 7, -10 ], 
isAbelian := [ 4, 10 ], 
lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 5, -10 ], [ 1, -4 ] ] ),
frattFacs := rec( frattFacs := [ 3, 5, 7, 9 ], pos := [ 1, 2, 3, 4 ] ) );

SMALL_GROUP_LIB[ 567 ] :=
[ 23511610116016823, 41176193930323, 41466671393879, 23510593448301143,
23511099106775639, 41466671386103, 23510593448293367, 41466671370551,
23511602981599031, 23510593448277815, 23511099106752311, 23511602981840087,
23798311336879319, 13493642528118096695, 41466671487191, 325169750821280375,
162605103980955671, 286783270517783, 92197666361584375607,
92197380664546526423, 162606113514043607, 41466671479415, 41466671720471,
72619155907, 216838310659, 123091847628739, 72619202563, 41030955761155,
72619754659, 41175175250275, 41175302652259, 23346396369379267, 73129766807,
41464887999383, 41465779813271, 41464887983831, 286781486773367, 505788864023
, 286781486796695, 162605102197219031, 73129743479, 41464887976055,
73129984535, 127411339, 127527979, 72364460683, 72364484011, 128398871, 1559
]; 

PROPERTIES_SMALL_GROUPS[ 567 ] := rec(
isNilpotent := [ 2, 24, -32, 44, -47, 49 ], 
isAbelian := [ 2, 24, 27, 44, 49 ], 
lgLength := rec( lgLength := [ 2, 3, 4, 5 ], pos := [ [ 48, -49 ], [ 8, -11,
15, 22, 24, -26, 33, -47 ], [ 3, -7, 12, -14, 16, -21, 23, 27, -32 ], [ 1, -2
] ] ),
frattFacs := rec( frattFacs := [ 5, 9, 14, 18, 51, 55 ], pos := [ 1, 2, 23,
32, 43, 47 ] ) );

SMALL_GROUP_LIB[ 568 ] :=
[ 274155336141470069, 7007198788100, 155719735567936750069, 482665586900069,
274154463498020069, 482665562890069, 482665730960069, 12317134830,
12485204830, 3973050596274830, 848993600069, 69 ]; 

PROPERTIES_SMALL_GROUPS[ 568 ] := rec(
isNilpotent := [ 2, 8, -10, 12 ], 
isAbelian := [ 2, 8, 12 ], 
lgLength := rec( lgLength := [ 2, 3, 4 ], pos := [ [ 11, -12 ], [ 3, -10 ], [
1, -2 ] ] ),
frattFacs := rec( frattFacs := [ 4, 7, 11, 14 ], pos := [ 1, 2, 7, 10 ] ) );

SMALL_GROUP_LIB[ 570 ] :=
[ 184747682699, 186895911563, 105299687197835, 335923595, 917070731,
164603001, 523883988107, 57108223, 521841575663, 92182370457, 298616112764171
, 395 ]; 

PROPERTIES_SMALL_GROUPS[ 570 ] := rec(
isNilpotent := [ 12 ], 
isAbelian := [ 12 ], 
lgLength := rec( lgLength := [ 4 ], pos := [ [ 1, -12 ] ] ),
frattFacs := rec( frattFacs := [ ], pos := [ ] ) );

SMALL_GROUP_LIB[ 572 ] :=
[ 54772922169, 66939811355, 38922273259895, 10638996, 38234668496411,
21881281020035447, 710639640695, 117448823, 96215181, 68044271735, 119 ]; 

PROPERTIES_SMALL_GROUPS[ 572 ] := 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[ 580 ] :=
[ 549178561459, 4937409333835, 2874317948162415, 315321636, 2861322084584011,
317783427044275, 966906896205806981487, 966906901499126108527,
5344886687677141359, 1659048006495113583, 15888513392751, 8516673647,
963781367, 4955671375983, 111 ]; 

PROPERTIES_SMALL_GROUPS[ 580 ] := rec(
isNilpotent := [ 4, 15 ], 
isAbelian := [ 4, 15 ], 
lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 11, -15 ], [ 1, -10 ] ] ),
frattFacs := rec( frattFacs := [ 3, 5, 7, 9 ], pos := [ 1, 2, 3, 4 ] ) );

SMALL_GROUP_LIB[ 584 ] :=
[ 333772487534850119, 8063151500736, 194701989245640781895,
194922546585294385223, 571525704327239, 333771483285725255, 571525677453383,
571525865570375, 13786293240, 13974410232, 4700780346917880,
113705660797554012991559, 333393821520629831, 977778376775, 71 ]; 

PROPERTIES_SMALL_GROUPS[ 584 ] := rec(
isNilpotent := [ 2, 9, -11, 15 ], 
isAbelian := [ 2, 9, 15 ], 
lgLength := rec( lgLength := [ 2, 3, 4 ], pos := [ [ 14, -15 ], [ 4, -11, 13
], [ 1, -3, 12 ] ] ),
frattFacs := rec( frattFacs := [ 4, 7, 11, 14, 17 ], pos := [ 1, 2, 3, 8, 11
] ) );

SMALL_GROUP_LIB[ 585 ] :=
[ 12560398727, 10639861, 21899135, 1919 ]; 

PROPERTIES_SMALL_GROUPS[ 585 ] := 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[ 588 ] :=
[ 27215238426272435935835, 26385115629179483, 44275885117303,
131308574865349211, 77211552769477158311, 75804219761, 46284419092338752327,
1269347876369996615, 44872682828615, 132220838153916, 15518728026175402547,
223313893768007, 75295599187, 131312164543891271, 127464263,
27063952765012607218343, 132520877281265, 46676655552347, 26123371817756507,
78010223943323483, 78626902545108827, 46232617646393993051,
45870010628544210779, 75812151281, 44579112771419, 45627885903707,
375454650353, 222870534809435, 75295576909, 220769421290147,
131047892315189927, 127410186, 9356850238980535469208629927,
26640970577755580531615579, 15859616314441628681791559, 134768021336135,
26211463198470215, 26828141800255559, 45870363615651664967, 75582222407,
79403784263, 44427525802055, 44573543903303, 45622317035591,
26209219646048327, 26825898247833671, 77055314401589454683,
45308318060550410531495, 2622574817351, 525028552895, 2158754130634823,
1542077314219079, 131046831067604039, 159252551, 75851956295, 77635584071,
150208434684, 45099921874253, 26219858938330931, 26836537540116275, 638005319
, 379022395463, 128397523, 375455140031, 222870535050311, 71 ]; 

PROPERTIES_SMALL_GROUPS[ 588 ] := rec(
isNilpotent := [ 6, 15, 32, 66 ], 
isSupersolvable := [ 1, -9, 12, -15, 17, -32, 36, -38, 40, -46, 49, -56, 61,
-66 ], 
isAbelian := [ 6, 15, 32, 66 ], 
lgLength := rec( lgLength := [ 3, 4, 5 ], pos := [ [ 35, -39, 41, -46, 49, 51
, -53, 55, -57, 59, -60, 62, -63, 65, -66 ], [ 7, -16, 18, -23, 25, -26, 28,
-29, 31, -34, 40, 47, -48, 50, 54, 58, 61, 64 ], [ 1, -6, 17, 24, 27, 30 ]
] ),
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, 71, 75, 79, 83, 87, 91,
95 ], 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, 31, 32 ] ) );

SMALL_GROUP_LIB[ 592 ] :=
[ 7206809893594695760931, 348373840213262016, 4264979783452173847526435,
12173665121221072931, 7206788120478308112419, 4266431391977127191549987,
4266431392013782271170595, 2525727384072189255810235427, 12173665121160606755
, 7206788120478247646243, 12173665121039674403, 7206809783630182493219,
7206788120478126713891, 12173665121946667043, 4509367524860923134038051,
2669545574717687569808225315, 2669545574717687569868691491,
1580370980232871062365252041763, 12173665121886200867, 588462811028784,
1173954253657392, 695567782707387696, 588463173825840, 347785378307683632,
205888944090180030768, 121886254880935983691056, 72156662889493616075537712,
4264979761679242304977955, 2524868018892333751595351075,
7204357742325663919139, 4264979761679243030572067, 7204357742325784851491,
4264979761679243151504419, 7204357742326510445603, 7206788083824135484451,
20563507648696355, 12173628467955437603, 12173628467834505251,
21734504078376995, 7617174836384117016611, 7617174836382423963683,
4509367503161115152111651, 20563507467297827, 20563509341749283, 990738295020
, 991645287660, 347784387267014892, 587473161082092, 12169523592260527139,
34681463636003, 35 ]; 

PROPERTIES_SMALL_GROUPS[ 592 ] := rec(
isNilpotent := [ 2, 20, -27, 45, -48, 51 ], 
isAbelian := [ 2, 20, 23, 45, 51 ], 
lgLength := rec( lgLength := [ 2, 3, 4, 5 ], pos := [ [ 50, -51 ], [ 11, -14,
19, -22, 30, -31, 34, -49 ], [ 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 ] ) );

SMALL_GROUP_LIB[ 594 ] :=
[ 205696474521623609111, 5213537907801119, 122205743677533413801911,
978125801911, 8776922001119, 10720089601119, 6367728474001119,
582954208801911, 978137801911, 579064697601911, 343966336685601911,
359025781987601191, 5213537913801119, 3782430744624001119,
204328754942819601191, 345128348899609111, 581021091209111,
213260255636709001191, 359023996145601191, 1638601191, 1664001191,
974873801191, 14758401119, 1651201191, 8776928001119, 978144001911,
5213537916801119, 581020899209111, 3096841671499201119, 1119 ]; 

PROPERTIES_SMALL_GROUPS[ 594 ] := rec(
isNilpotent := [ 4, 20, -22, 30 ], 
isAbelian := [ 4, 20, 30 ], 
lgLength := rec( lgLength := [ 3, 4, 5 ], pos := [ [ 23, 28, -30 ], [ 5, -7,
10, 14, 16, -22, 24, -27 ], [ 1, -4, 8, -9, 11, -13, 15 ] ] ),
frattFacs := rec( frattFacs := [ 4, 7, 10, 13, 17, 20, 23, 26, 29, 32 ],
pos := [ 1, 2, 3, 4, 7, 11, 15, 17, 19, 22 ] ) );

SMALL_GROUP_LIB[ 608 ] :=
[ 83003884016385711346370513, 8042232730035381718608,
136519546070683522583441, 83003632696621814926398353,
30683547779280989582952226030481, 30683640377548242045768532689809,
18655597049802841667097093029625809, 136519546070683284497873,
83003632696621814688312785, 83155932478964673217621457,
50466208678312776947497374353, 92734787210528741856317585,
56382902673292055213129522897, 56383054973074398071658831569,
56382750622768145161560916625, 34280712378643032879490708864721,
136519546070683488571217, 83003632696621814892386129,
136519546070683420546769, 83155933301599764975513041,
83003632696621814824361681, 50466665329225363055014575569,
50466360728014051909484871377, 50466360728426047078997884625,
30683547322381229203957714186193, 136769627138578737918353,
83004383765171086322368913, 34280804824610915672237415780305,
56382750622768145159248085393, 34280712378643032879488396033489,
34280712378641798926853174064017, 20880500537289139171294915082324753,
12695344326671796616147907128217241425,
12695344326671796616147907128251253649,
7718769350616452342617928132693635170257, 136769627138578703906129,
136519546070684236840145, 56382750622768145161526904401,
56382750622768145126562338129, 92734787210528709170570321,
34280712378641798926853072027345, 34280712378641798926818107461073,
34280712378641798926853140051793, 52757136983949967368, 13227355994978146824,
8029005374041252291080, 52757136984426138504, 8029048670768356534152,
4881661570126646217403272, 2968050234615300054822937608,
4881661570126576288270728, 2968050234615299984893805064,
2968050234615299985369976200, 32076382724760858379272,
4905669417696237877723656, 4905669439380194167882248,
2982646966451212067907814920, 13227355995454317960, 8029005374041728462216,
1807523074487568063634415882568, 1098974029288441382589459787156872,
668176209807372360614291264910525960, 83003882775656838185151953,
50558806945975202057959243217, 50558806695894134163560201681,
224950040195357632913, 136519544037814525065617, 136519544037813436674449,
83155932476931804458189201, 83155932065614258579243409,
83308231847957117108552081, 152524732383088681446737,
92735037702236522685365585, 92735288194621962895328465, 250863045620491710737
, 152524321065543856879889, 152524733060714458284305,
152524733060714390259857, 152525145055883903273105,
92735287783304418070761617, 92735037290918977860798737,
185333555859079946674267601, 56382902922549132734626362833,
56382902672467387216593253841, 56383055222331475593155671505,
152524732383088715458961, 92734787208495835173255569,
92734787208495834084864401, 92735037290241353206364561,
92735037701558899085310353, 92735287783304417118419345,
92735038113554068598323601, 56382902672056069671768686993,
224538722649682760465, 136519132720268850193169, 136519132720267761802001,
83003882776334467431236369, 83003882777012091065303825,
50466360728012019039773096849, 50466360728424014209252097873,
152524321065543040586513, 92734786797178288409991953,
56382750622766789880620679953, 34280712378642208889118044748689,
92751068802232532168040977, 56392649831757644771070472721,
34286731097708648284701353703953, 56392649831757644769029739281,
34286731097708648284700401361681, 34286731097708648284700333337233,
20846332507406858157361651952511761, 34286731097708648284698292603793,
20846332507406858157361650932145041, 12674570164503369759676147533377954705,
224538722649580723793, 136519132720268748156497, 224538722649444674897,
136519544037814491053393, 83155932064936634843139281,
136519132720268612107601, 136519132720268544083153, 224538722651587445009,
224538722650499053841, 136769625105709944473873, 136769625105709876449425,
92734787208496362022605329, 34286628768536962982857618000529,
56382750622766112779312336465, 250863045620389674065,
152524732383090722180177, 185333555859079948715001041, 250863045622532444177,
152524732383090756192401, 152524732383091776559121,
92735037289563730524639377, 56382750622766112779414373137,
20846270291270473493880919213767569, 34280712378641796894470925483857,
112682497363168562800336926161, 92734786797178287151539665,
92735037289563729572297105, 56382902672055392048134619537,
152524321065542938549841, 56392481527198951775212048913,
56382750622766112779346348689, 34286628768536962982857583988305,
224538722651485408337, 224950040198418733073, 21755285195786820,
43403578104519108, 26411094427005391428, 26411094427073415876,
26389410470783257284, 16071150975941929370436, 21755288358923652,
13227284669133530628, 8042189148138769719876, 13227284669201555076,
8042189112474469963524, 4889650980453700739240772, 8042189183803273549572,
8042167464182581597956, 4889637818292232612975428, 21755285671957956,
13205600711176773060, 13205600744916899268, 8029005267196238078340,
4881635202400137336233412, 2968034203059228304403109444,
4881635202400137438270084, 4881622040238671352738180,
2968026200465055685776550404, 136519132042647290871377, 369304898253120017,
224538045030266208785, 224538045030130159889, 412602039014031377,
152524320388445915746577, 250862368001075159057, 152524320388441834279697,
92734786796501190468858641, 92734786796500667837024657, 250862368031686160657
, 152524320387923624034833, 56382750372273049190965799825, 369304898015034449
, 369304902334586897, 35664435805554, 35665490184498, 13205565046298803698,
21719621916391986, 13205565085378849074, 4881622018554603706553010,
606312244740113, 17 ]; 

PROPERTIES_SMALL_GROUPS[ 608 ] := rec(
isNilpotent := [ 2, 44, -62, 149, -172, 188, -193, 195 ], 
isAbelian := [ 2, 45, 58, 149, 164, 188, 195 ], 
lgLength := rec( lgLength := [ 2, 3, 4, 5, 6 ], pos := [ [ 194, -195 ], [ 37,
44, 63, -93, 117, -125, 129, -135, 139, -142, 147, -163, 173, -193 ], [ 8,
-16, 19, -31, 36, 38, -43, 45, -57, 94, -116, 126, -128, 136, -138, 143, -146
, 164, -172 ], [ 3, -7, 17, -18, 32, -35, 58, -62 ], [ 1, -2 ] ] ),
frattFacs := rec( frattFacs := [ 6, 11, 17, 22, 58, 63, 209, 214 ], pos := [
1, 2, 43, 62, 148, 172, 187, 193 ] ) );