col4.z

#############################################################################
##
#W  col4.z                 GAP library of groups           Hans Ulrich Besche
##                                               Bettina Eick, Eamonn O'Brien
##

SMALL_GROUP_LIB[ 1170 ] :=
[ 11214159376916615, 11347929405759359, 13120690418508406655, 38212696776839,
52522264666247, 14330207511807, 61575295041314687, 5604672206764669,
6713920141029131605, 6579866020413045493, 7855711637282900861173,
264996626303, 38204574402431, 38318710654847, 44699175963133823,
38212712204423, 44699069964683399, 44832839985563519, 52298035788152735615,
8408532863, 44877350783, 12262442967, 52628278544255, 4108716277,
52522280093831, 14330222939391, 61575295048779647, 4782208653949,
61451170863027431, 16766366146284255, 72043095936904152959, 1919 ]; 

PROPERTIES_SMALL_GROUPS[ 1170 ] := rec(
isNilpotent := [ 12, 32 ], 
isAbelian := [ 12, 32 ], 
lgLength := rec( lgLength := [ 4, 5 ], pos := [ [ 13, -15, 20, -23, 28, -32 ]
, [ 1, -12, 16, -19, 24, -27 ] ] ),
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[ 1180 ] :=
[ 20540266535959, 390049752897205, 461066740498792695, 1709254872567,
24209757965806615, 1685465374801608819959, 1210475784537831, 330622747367,
17744269037, 390733620057063, 231 ]; 

PROPERTIES_SMALL_GROUPS[ 1180 ] := 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[ 1188 ] :=
[ 2491789371315015648153090111, 15839426390262283010119,
2960379633081981336552405001911, 16320335708173001119,
2489852038250206606484001911, 5275853650920197191100, 13332850409996001119,
2097465800770192280009111, 2489813392103841989588001911, 13737394188001119,
13332850409989011019, 16290161886721011019, 19352684948620805011019,
1765523680396049019011, 1483648008707019011, 1759606566032129019011,
4179065576893715217019011, 2136171143293305737010191, 15839426390262531010119
, 22990989719063497601010119, 4964768634360711613321010191,
2097453961583788945090111, 1762573862175105090111,
2537771463141019878345001191, 2136168305777459649001191, 14014218245001119,
14014234625001119, 16292930142213001119, 2489686674063882371457090111,
3029893942958127729102273001191, 1808473203419400001191, 16290161889796001119
, 19355672131951104001119, 2090458499810093320001191,
2148572749698706696001191, 1807083019193600001191, 5275862359347848009111,
2090412590484304512009111, 68927249082849692484001191,
2148466286485580104001191, 2483462901205249846080001191,
2552504426762885672264001191, 2550415738169252138816001191,
4440954241794119100, 5275853642531618119100, 4440954241793119100,
5275853642531617119100, 4440954241824119100, 11222909448001119,
13712245248001119, 16290138833416001119, 1486131036944001911,
1248854532001911, 1481150333696001911, 3517731967107856001911,
1798122613244808001191, 13332850410244001119, 19352684948636544001119,
2090448149219918728001191, 1765533637673872009111, 1483648139648009111,
2136169785369560008001191, 1798121469264320001191, 11534340001119,
11550720001119, 13714341892001119, 11222909441011109, 1248854529011901,
13332850410241011019, 1483648008961019011, 15839426390262657010119,
1762573862044545090111, 18817238551942398913001119, 311427073001119,
2093930316222038785019011, 27363419886809552831361010119,
7462748320951088235393090111, 97523190668448627151605697001119,
13712232960001119, 16320033724928001119, 1248862464001911,
16290161889920001119, 19388200091916928001119, 19388312180497920001119,
1483648016768009111, 19352712423412416001119, 58164577760710400001119,
27363578066103029472960001119, 1771445777607040009111,
23149217821882324672001119, 3738174208111900, 9437696001119, 1049088001191,
11222909696001119, 1248854784001911, 13332850410368001119,
1483648009088009111, 15839426390262720001119, 1119 ]; 

PROPERTIES_SMALL_GROUPS[ 1188 ] := rec(
isNilpotent := [ 4, 10, 26, -28, 64, -66, 74, 99 ], 
isSupersolvable := [ 1, -5, 7, -28, 31, -43, 49, -74, 79, -90, 92, -99 ], 
isAbelian := [ 4, 10, 26, 64, 74, 99 ], 
lgLength := rec( lgLength := [ 3, 4, 5, 6 ], pos := [ [ 84, -92, 97, -99 ], [
33, 35, -51, 54, 58, 60, -67, 72, -74, 77, -83, 93, -96 ], [ 5, -13, 16, 20,
22, -32, 34, 52, -53, 55, -57, 59, 68, -71, 75, -76 ], [ 1, -4, 14, -15, 17,
-19, 21 ] ] ),
frattFacs := rec( frattFacs := [ 7, 13, 19, 25, 32, 38, 44, 50, 56, 62, 33,
39, 45, 51, 57, 63, 106, 112, 118, 124, 130, 136, 142, 148, 154, 160, 166,
172, 178, 184, 143, 149, 155, 161, 167, 173, 179, 185 ], pos := [ 1, 2, 3, 4,
5, 6, 7, 8, 9, 10, 13, 17, 21, 23, 25, 28, 29, 30, 34, 36, 38, 41, 43, 48, 51
, 55, 59, 61, 63, 66, 67, 68, 69, 70, 71, 72, 73, 74 ] ) );

SMALL_GROUP_LIB[ 1190 ] :=
[ 505414495, 169870325, 601801884511, 102761971, 600661034303, 200356663093,
716152480727903, 863 ]; 

PROPERTIES_SMALL_GROUPS[ 1190 ] := rec(
isNilpotent := [ 8 ], 
isAbelian := [ 8 ], 
lgLength := rec( lgLength := [ 4 ], pos := [ [ 1, -8 ] ] ),
frattFacs := rec( frattFacs := [ ], pos := [ ] ) );

SMALL_GROUP_LIB[ 1196 ] :=
[ 1579485379791, 3015156066801, 3639146117072663, 35862017047,
1888196200582351, 51916460675766602519, 36294665127687, 2526216967,
1326826457, 3042745562119, 263 ]; 

PROPERTIES_SMALL_GROUPS[ 1196 ] := 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[ 1197 ] :=
[ 64715720819, 644384790863, 773776361067911, 771331592639879, 7148556935,
462255292483919, 553319555946659207, 553322000715087239, 1222931775095,
540842615, 57113411, 644386364279, 646428777335, 6263 ]; 

PROPERTIES_SMALL_GROUPS[ 1197 ] := rec(
isNilpotent := [ 5, 14 ], 
isAbelian := [ 5, 14 ], 
lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 9, -14 ], [ 1, -8 ] ] ),
frattFacs := rec( frattFacs := [ 3, 5, 7, 9, 11 ], pos := [ 1, 2, 3, 4, 5
] ) );

SMALL_GROUP_LIB[ 1204 ] :=
[ 78602100244375469, 65287666894253, 9602248955801, 78714759602093,
95102856807952139, 479552805899, 65284975268603, 32660361467, 412478356244219
, 65420296955, 8065517759, 78988834665467, 251 ]; 

PROPERTIES_SMALL_GROUPS[ 1204 ] := rec(
isNilpotent := [ 6, 13 ], 
isAbelian := [ 6, 13 ], 
lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 7, -13 ], [ 1, -6 ] ] ),
frattFacs := rec( frattFacs := [ 3, 5, 7, 9, 11, 13 ], pos := [ 1, 2, 3, 4, 5
, 6 ] ) );

SMALL_GROUP_LIB[ 1206 ] :=
[ 509440059139247015, 422442630810023, 14188532576966023, 762215486669735,
19798412714531173735, 650947297703, 422423769922439, 422442896456327,
509440059404893319, 352171104647, 632086410119, 10322265031, 762215752316039,
11746424452423, 919233052668835079, 4487 ]; 

PROPERTIES_SMALL_GROUPS[ 1206 ] := 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[ 1210 ] :=
[ 44318005016532360399, 15128685480399, 18611540993, 68085299720399,
82385398989400399, 5160399, 22249830470520240399, 18633280399,
27458607562080399, 27376149450080399, 27870898122080399, 22693526560399,
22625379360399, 22761673760399, 23034262560399, 247430600800399, 204488640399
, 21760399, 25008000399, 25233280399, 24895360399, 46400399, 56264160399,
15680993, 55926240939, 68080911920399, 399 ]; 

PROPERTIES_SMALL_GROUPS[ 1210 ] := rec(
isNilpotent := [ 6, 27 ], 
isSupersolvable := [ 1, -6, 8, -27 ], 
isAbelian := [ 6, 27 ], 
lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 7, 9, -17, 19, -21, 23, -24
, 26, -27 ], [ 1, -6, 8, 18, 22, 25 ] ] ),
frattFacs := rec( frattFacs := [ 3, 5, 7, 9, 11, 13 ], pos := [ 1, 2, 3, 4, 5
, 6 ] ) );

SMALL_GROUP_LIB[ 1212 ] :=
[ 62211300990001, 6148560100010099, 7452066360100000199, 15513700000199,
7451373443300010099, 9031064593784100000199, 6272572800000199,
186219201990000, 5072000000199, 54400009901, 6148561600000199, 199 ]; 

PROPERTIES_SMALL_GROUPS[ 1212 ] := 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[ 1218 ] :=
[ 8441478980535, 8442019880839, 10281515020238727, 7710245815, 33356466512823
, 1151599814153, 40628150041867191, 393381385, 8516674487, 1593189897,
10395013100471, 334377541, 10358507454343, 1918779032273, 12661153939274679,
951 ]; 

PROPERTIES_SMALL_GROUPS[ 1218 ] := rec(
isNilpotent := [ 16 ], 
isAbelian := [ 16 ], 
lgLength := rec( lgLength := [ 4 ], pos := [ [ 1, -16 ] ] ),
frattFacs := rec( frattFacs := [ ], pos := [ ] ) );

SMALL_GROUP_LIB[ 1220 ] :=
[ 79488495326890859, 461840499370859, 24319608692403, 478029924010859,
584185640775840239, 2023846560239, 710976055081940650859, 461829288960239,
222289920239, 583099250009770859, 29637056161652403, 869499378946569267360239
, 869499379440384665760239, 2205567714946488480239, 711382070099394720239,
1481838935040239, 391910400239, 20321283543, 478839651840239, 239 ]; 

PROPERTIES_SMALL_GROUPS[ 1220 ] := rec(
isNilpotent := [ 6, 20 ], 
isAbelian := [ 6, 20 ], 
lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 8, -9, 16, -20 ], [ 1, -7,
10, -15 ] ] ),
frattFacs := rec( frattFacs := [ 3, 5, 7, 9, 11, 13 ], pos := [ 1, 2, 3, 4, 5
, 6 ] ) );

SMALL_GROUP_LIB[ 1224 ] :=
[ 39647539125410813675765777, 484348454434416019702031,
50109713707872507214516191729, 451355152701766762783,
592680758821605617422106895, 2662128082351486481832729110381041,
61720627582869617989696282952177, 41197177556813163266048497,
50425345329541787894929162737, 50425349332409816596646724081,
41197177556813163282825713, 41197180827130180698898929,
50425349332409816596663501297, 48568106150951744027936886784,
593938898316488225809502239, 395709819206575853599, 485244197970263324758047,
395709819206559076383, 396441337487178076191, 48528845758281136783113646097,
32391780330972452548625, 39647749802517152971943953, 32391780330972435771409,
32391952452921214431249, 61334294477943124109983834178033,
40939308584858776630198769, 50109717710737844311785734641,
40939308584858776613421553, 40939311855175794046271985, 368749811827999007,
3294822932743717151, 4936227938296311958208799, 395709520139463495695,
26420894988291403777, 484348820492627493322783, 32339240370149098717201,
592842957386518023599292703, 3299907073889796383,
725440958008327078337914667279, 3260513585431641936362361935267627505,
2174941791722779844999039156721, 96780739660890056067178762496,
118459625349150896045737333879040, 1645707241379615245144079,
484216306528808937197599, 2174941243751214442108596257265,
33631468625967911535089, 79090176168491610368, 323291611662385439,
26463872703210196753, 33447126019221925921265, 299067296973087,
484216306229741841616911, 592680759187663828895727647,
725441249246802722875349401887, 48449712033019507347985203217,
1087136097227983488651004655278489887, 1008139516855468611017769186492703,
448379135442349461535, 448379135442332684319, 548816062584046793789471,
448379135442852778015, 548816062584047313883167, 548816062584047297105951,
671750860603675866652741663, 549764112069492295598367,
549764112069492278821151, 672911273175613561886474527,
549764112069492798914847, 672911273175613562406568223,
672911273175613562389791007, 823643398366953554721120452895,
26420947897876017169, 32339240211948238860305, 26420947898379333649,
32339240211948758954001, 39583230019409572360417297, 548816064378451901022495
, 548816064378451884245279, 671750862801819514513129759,
548816064378452404338975, 671750862801819515033223455,
671750862801819515016446239, 822223056069429680131733979423,
672911270979264320743932191, 672911270979264320727154975,
672911270979264321247248671, 823643395678622080956794667295,
1008139516310633429642825781215519, 39679825286727370154307584,
484348086880873463419151, 323291611561726223, 395709221072720105743,
323291611544949007, 323291612065042703, 32339110909248205233921,
21585620899995393, 26420842212152581889, 21585620883218177, 21585621403311873
, 592842955185682771274108959, 395709819210803712031,
484348819595426491535391, 395709819210786934815, 395709819211307028511,
39583230019409443511398417, 26420947769026998289, 32339240211819909935121,
26420947769010221073, 26420947769530314769, 725639779837806210179462594847,
484348821389831078674719, 592842957383826419654590751,
484348821389831061897503, 484348821389831581991199, 2691604481573151,
2691605001666847, 4035794426119646609695, 592680521248644962709475343,
725440958008693132151341776927, 887939732602641490567439895757087,
1330290530888919836527640493546543251743, 72586147562082738097832955460124689
, 1993554760554190660699105768072641438141120799,
1993554760550169607817769088092797059387621663,
1848693407874495414103741747739752935719199,
1510376579519921115696696529930724311327, 484347979819295392665631,
592842954347697778959843615, 592841927296032487883407647,
725639776119386942515577880863, 1330654583248035982589262929367572414751,
823646750265274565359568945439, 48449744424648796814847307793,
1008140936651138000419217718903071, 1233966154494791825890451833650938143,
88845681148511799622750286874222325777,
1848698477476391919768780806547825869455647, 449153684724875526431,
64599045552960767652096, 79069232955778006159269632,
79069231748954043513245952, 96780741137873840655852183296,
1344532059084900339727, 237270334484521283585, 3294550544392459793793055,
395601565689667653903, 484216306528813165056031, 592680759188561032464302367,
39583098066198757868892177, 888183085970574745627446703292703,
823643396123748861652135575839, 366322167312285983, 449153684243839189279,
64616176650555153, 1344489028533411119391, 549764110275091432997151,
64616305499643648, 263891380601119, 17600775979505, 323291615823135007,
21585625161404177, 395709819212917637407, 287 ]; 

PROPERTIES_SMALL_GROUPS[ 1224 ] := rec(
isNilpotent := [ 4, 30, -32, 38, 52, 116, -118, 164 ], 
isSupersolvable := [ 1, -13, 15, -41, 45, -47, 49, -55, 59, -89, 91, -121,
128, -131, 139, 147, -149, 153, -157, 159, -164 ], 
isAbelian := [ 4, 30, 38, 52, 116, 164 ], 
lgLength := rec( lgLength := [ 3, 4, 5, 6 ], pos := [ [ 139, 154, -157, 159,
162, -164 ], [ 47, 49, -52, 66, -95, 106, -118, 129, -138, 142, -144, 147,
149, -153, 158, 160, -161 ], [ 7, -33, 36, -38, 41, -46, 48, 53, 55, -65, 96,
-105, 119, 121, -128, 140, -141, 145, -146, 148 ], [ 1, -6, 34, -35, 39, -40,
54, 120 ] ] ),
frattFacs := rec( frattFacs := [ 7, 13, 19, 25, 32, 38, 44, 50, 56, 62, 68,
74, 33, 39, 45, 51, 57, 63, 202, 208, 214, 220, 226, 232, 238, 244, 250, 256,
262, 268, 274, 280, 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, 14, 19,
24, 29, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48,
49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 65, 72, 77, 84, 89, 90, 95, 100, 105,
110, 115, 118 ] ) );