col5.z

#############################################################################
##
#W  col5.z                 GAP library of groups           Hans Ulrich Besche
##                                               Bettina Eick, Eamonn O'Brien
##

SMALL_GROUP_LIB[ 1225 ] :=
[ 845372519, 669527, 32516135, 791 ]; 

PROPERTIES_SMALL_GROUPS[ 1225 ] := rec(
lgLength := rec( lgLength := [ 2, 3, 4 ], pos := [ [ 4 ], [ 2, -3 ], [ 1 ]
] ),
frattFacs := rec( frattFacs := [ 5, 10, 11 ], pos := [ 1, 2, 3 ] ) );

SMALL_GROUP_LIB[ 1230 ] :=
[ 58090536961759, 58092789764879, 71450507796484879, 22937601759, 51200001759
, 4014083163, 63036579841759, 1392646361, 62929100804879, 4843233342443,
77535110901761759, 1759 ]; 

PROPERTIES_SMALL_GROUPS[ 1230 ] := rec(
isNilpotent := [ 12 ], 
isAbelian := [ 12 ], 
lgLength := rec( lgLength := [ 4 ], pos := [ [ 1, -12 ] ] ),
frattFacs := rec( frattFacs := [ ], pos := [ ] ) );

SMALL_GROUP_LIB[ 1232 ] :=
[ 9815130514653709090005, 17664684299649549050009, 21849253684453573383000059
, 122748911222791000059, 107858110367928838000059, 107858110367928837000059,
132881191973444129287000059, 132881191873972015654000059,
132881191873972015653000059, 163709628388733679047207000059,
163873762558378431747684000059, 163709628511183931708006000059,
163873762680828684408357000059, 201892475471922227986830950000059,
201892475471922227986830949000059, 163709628511183850967654000059,
201690262325778504467092071000059, 163873762803378328442405000059,
201892475773762001323431463000059, 248731529781408184879849412199000059,
201690262325778603939205735000059, 201892475622780839873484327000059,
107858209759302147000059, 107858110367928866000059, 107858209759302177000059,
132881314622479536675000059, 132881191973363388963000059,
132881314423535309347000059, 132881314523007423011000059,
14338217738762005009, 17664670066278954005009, 21762891014559761066005009,
21762891014571295402005009, 26811881729951846630059005009,
14338217738761005009, 17664670066278953005009, 14352416506371005009,
17664684265046563005009, 17682191357051427005009, 14338217738786005009,
26590349099455744680005009, 32759310090529485621929005009,
32759310090529485621930005009, 40359470031532326294391467005009,
14352416506401005009, 7966826693130009005, 9815121457054250009005,
12092240766938645162009005, 12092240766945985194009005,
14897640624877460259499009005, 7966826693129009005, 9815121457054249009005,
7975862272515009005, 9815130492633635009005, 9826271369364003009005,
7966826693154009005, 16919705212886715048009005,
20845076822276436921001009005, 20845076822276436921002009005,
25681134645044570290653867009005, 7975862272545009005,
17734783834522374000059, 21849253584819979046000059,
26918280538948546593638000059, 26918280538948627333990000059,
33163321623984708955145063000059, 17734783834522373000059,
21849253584819979045000059, 17734883225895683000059,
21849253684211352355000059, 21849376233855386403000059,
17734783834522402000059, 229184679650288773105508000059,
282355525329155768544397157000059, 282355525329155768544397158000059,
347862007205519906846775707495000059, 17734883225895713000059,
99633594371000059, 199024967713000059, 245298313035811000059,
99633594373000059, 122649277628453000059, 151103910118949988000059,
186160017266625741925000059, 229349141272482993407079000059,
133014417660940654086000059, 132881191873891275334000059,
163873762558278959633990000059, 132881191873891275333000059,
163873762558278959633989000059, 163709628388634126193223000059,
201892475471799678342796871000059, 107858110287188516000059,
133014417660940654116000059, 163873762558278959633958000059,
87547167379972000059, 107966248101352964000059, 107858110287188548000059,
133014417660940654148000059, 87547167379970000059, 107858110287188546000059,
133014417660940654146000059, 87547167379969000059, 107966248101352961000059,
107858110287188483000059, 87547167380000000059, 107858110287188514000059,
107858110287188513000059, 132881191873891275299000059, 87634941580800000059,
87547167380032000059, 107966248101353024000059, 17664670054744645000509,
11638145540000509, 14338206204484000509, 14338206204482000509,
14219740672000509, 21583075556197954000509, 21583075556197894000509,
26590349085245441606000509, 11638145537000509, 11638145600000509,
9815121449714245000905, 6466568708000905, 7966819353156000905,
7966819353154000905, 9048163840000905, 13733526951167554000905,
13733526951167494000905, 16919705203843794502000905, 6466568705000905,
6466568768000905, 21849253584739238725000059, 14395116618500000059,
17734783753782084000059, 17734783753782082000059, 122561328318208000059,
186026525690088654658000059, 186026525690088654598000059,
229184679650189300991814000059, 14395116618497000059, 14395116618560000059,
80740353000059, 80740384000059, 122649196888099000059, 99552854052000059,
86327555947240960050009, 11147342264320059000, 71060951552000059,
9437696000059, 5243392000095, 11684283136000059, 59 ]; 

PROPERTIES_SMALL_GROUPS[ 1232 ] := rec(
isNilpotent := [ 4, 78, -85, 143, -146, 153 ], 
isSupersolvable := [ 1, -146, 149, -153 ], 
isAbelian := [ 4, 78, 81, 143, 153 ], 
lgLength := rec( lgLength := [ 3, 4, 5, 6 ], pos := [ [ 149, -153 ], [ 23,
-29, 37, -40, 45, 53, -56, 61, 69, -72, 77, -80, 86, -148 ], [ 5, -22, 30,
-36, 41, -44, 46, -52, 57, -60, 62, -68, 73, -76, 81, -85 ], [ 1, -4 ] ] ),
frattFacs := rec( frattFacs := [ 5, 9, 13, 17, 22, 26, 30, 34, 38, 127, 131,
135, 139, 143 ], pos := [ 1, 2, 3, 4, 29, 45, 61, 77, 85, 112, 122, 132, 142,
146 ] ) );

SMALL_GROUP_LIB[ 1236 ] :=
[ 3816881458261187609, 3088211966671385, 68669605524421, 6924188743914521,
8558310002687704283, 17125050960347, 3088118336279243, 7061084263909067,
2521633960139, 205559930916108, 3824085339466288445, 5600936968907,
58884319807, 6924190367552459, 203 ]; 

PROPERTIES_SMALL_GROUPS[ 1236 ] := rec(
isNilpotent := [ 6, 15 ], 
isSupersolvable := [ 1, -9, 12, -15 ], 
isAbelian := [ 6, 15 ], 
lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 7, -15 ], [ 1, -6 ] ] ),
frattFacs := rec( frattFacs := [ 3, 5, 7, 9, 11, 13 ], pos := [ 1, 2, 3, 4, 5
, 6 ] ) );

SMALL_GROUP_LIB[ 1240 ] :=
[ 11404065674368057581029, 9197826869267181029, 1838971997344683003,
17768158311174381029, 22070516662817410500119, 76644237384900119,
14141041420889810420102729, 9196827239511002729, 11404065662100955802729,
9196827239486702729, 9196827239851202729, 1493489712602729, 1493490052802729,
2296251982338509702729, 2277874142237037483003, 87559887865591792412100119,
56945866104048600119, 56945866104024300119, 70612874011401480900119,
56945866104388800119, 70612874011401845400119, 70612874011401821100119,
87559963774180187789700119, 22032501010030887302729, 14329143178202729,
17768145969423002729, 14329143153902729, 14329143518402729,
2280322806279668126103, 1483041879026103, 1838970007003826103,
1483041854726103, 1483042219226103, 27367440585428612103300119,
17798803665514200119, 22070516601107439000119, 17798803665489900119,
17798803665854400119, 61710360300119, 61710724800119, 94962395161037700119,
1492796044800119, 70614036140498775000119, 2985984000119, 1836995474904326103
, 70612812794787000300119, 45924051340800119, 11548915200119, 1197504000873,
14353828819200119, 119 ]; 

PROPERTIES_SMALL_GROUPS[ 1240 ] := rec(
isNilpotent := [ 6, 39, -41, 51 ], 
isAbelian := [ 6, 39, 51 ], 
lgLength := rec( lgLength := [ 3, 4, 5 ], pos := [ [ 42, 44, 47, -51 ], [ 7,
-14, 17, -41, 43, 45, -46 ], [ 1, -6, 15, -16 ] ] ),
frattFacs := rec( frattFacs := [ 4, 7, 10, 13, 16, 19, 23, 26, 29, 32, 35, 38
, 41, 44, 47 ], pos := [ 1, 2, 3, 4, 5, 6, 11, 14, 15, 16, 23, 28, 33, 38, 41
] ) );

SMALL_GROUP_LIB[ 1242 ] :=
[ 201729471902762212657139, 2737660319103037415, 250374937497584295948836131,
2417856580943847, 2204231350380839, 2413805547895719, 2997945976614275367,
130774080941454435, 105124867819555, 130354768867072355,
323670882429593105507, 169983122690698489547, 2737660319412255335,
3723448906300035596199, 201088390405566085533387, 162422246301823367795,
130565024684158835, 211119059879089990264011, 169983035130140362571,
1942063772263, 1943372794791, 2413973772751463, 1773838916519, 85096783179,
2204231659598759, 105125187344739, 2737660319566864295, 130565014789185395,
3400174132947967890855, 11175 ]; 

PROPERTIES_SMALL_GROUPS[ 1242 ] := 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[ 1254 ] :=
[ 674926816247, 683202284279, 846346373893367, 550914551, 917070839,
487089279, 1154989622519, 57110167, 1146819972743, 607192946847,
1448361906443639, 503 ]; 

PROPERTIES_SMALL_GROUPS[ 1254 ] := rec(
isNilpotent := [ 12 ], 
isAbelian := [ 12 ], 
lgLength := rec( lgLength := [ 4 ], pos := [ [ 1, -12 ] ] ),
frattFacs := rec( frattFacs := [ ], pos := [ ] ) );

SMALL_GROUP_LIB[ 1260 ] :=
[ 98251896751478188643, 99496333108792289291, 123798478142461946161163,
233439948031273571, 388778231038126691, 233316369786907665,
490948807188665395211, 98251526310984609199, 124777262568056792831923,
124189617841205747671495, 157223273589614922110533795, 2172886702067795,
2589556525005857634674699, 3262841023602095375816386571, 99494480421827336723
, 233315981465705039, 234303626094909971, 293978997469657537043,
293667333658825894929, 2589947977479937507780619,
1398430985101124756599759303, 12333228334242054016073197486243,
1631361898711833107, 99650433460808840395, 129481139655785919027811,
880846783788337944175, 7768473382812006534687331, 133682188819079647017571,
163146235970049851638889059, 185272042183247, 233069262949034028,
295220840400607429805, 308553360300623, 185171163699861, 389641906426321427,
77977401521219395, 99029573464307766475, 98563188761156621935,
124780375803168308480611, 1712282851859, 77977695424953497, 78965340054158399
, 98252760426866244671, 78101664677952995, 98251896751490039267,
99496333108798167947, 123798478142461952039819, 185269366602905,
308553360161945, 185171163561183, 389641906426182719, 61788966960781,
388778231049977315, 233316369798758289, 490948807188671273867,
77854508547541423, 489860574159912740255, 293978628102773714877,
618595497073083660642131, 15410544031571,
[ ( 1, 2, 3, 4, 5)( 7, 8,10)( 9,12,11), ( 3, 4, 5)( 6, 7, 8, 9,10,11,12) ],
[ ( 1, 2, 3, 4, 5)(13,14,15), ( 3, 4, 5)( 6, 7, 8, 9,10,11,12) ],
2055203591276921289791, 2589556367938173388160063, 2589556525005857640553355,
3262841023602095375822265227, 78963875261743379, 78100884798603599,
99496328219530002707, 78965342914683155, 99494480421833122067,
100581847720386674963, 125365373553394633457939, 1631483617643505149,
185174221160723, 185956967006483, 233316666390528275, 185272053940559,
233315981477462351, 234303626100695315, 293978997469663322387,
233069336320621791, 2055514267843293314111, 293667333658837745553,
2589947977479937513659275, 370020840396884411330493,
3263334451624734698939361107, 123601429429500661434799,
1090162358343910843246093727, 588067787865206821387462684605,
5186757888711509606588974578214739, 778687342895297162952748989,
6868020379786635921225437095763, 1294730521510163, 431740058370383,
1633209696414499091, 185171533775253, 1631361898717618451,
2718729197271171347, 2057844218118677250323, 544978722395161271,
2057850381553549148435, 233316370163000421, 2055515997242857697555,
3433364717317124899091, 2592891480758048185762067, 184975665169219,
1631360528801907383, 686673190854305096375, 233932302788346981,
2063281058721317560595, 3425598793533114962195, 3267043265755145384750960915,
294754577857065567333, 2599734133127243615625491, 4326039543824488662257939,
149824733459, 184975486019244, 234302253240813053, 244635697427, 146790973725
, 309238285123859, 48946250083, 308553372057935, 185171175457173,
389641906432106771, 61788978856771, 388778231055901367, 233316369804682341,
490948807188674212115, 275 ]; 

PROPERTIES_SMALL_GROUPS[ 1260 ] := rec(
isNilpotent := [ 12, 40, 60, 131 ], 
isSupersolvable := [ 1, -30, 33, -60, 63, -73, 75, -87, 94, -117, 120, -131 ]
, 
isSolvable := [ 1, -60, 63, -131 ], 
isAbelian := [ 12, 40, 60, 131 ], 
lgLength := rec( lgLength := [ 4, 5, 6, false ], pos := [ [ 67, 74, -77, 94,
101, -122, 127, -131 ], [ 15, -18, 23, -43, 48, -51, 56, -60, 63, -64, 68,
-73, 78, -83, 86, -93, 95, -100, 123, -126 ], [ 1, -14, 19, -22, 44, -47, 52,
-55, 65, -66, 84, -85 ], [ 61, -62 ] ] ),
frattFacs := rec( frattFacs := [ 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49
, 58, 62, 66, 70, 74, 78, 82, 86, 90, 94, 98, 102, 106, 110, 114, 118, 122,
126, 130, 134, 138, 142, 146, 150, 154, 158, 162, 166, 55, 59, 63, 67, 71, 75
, 79, 83, 87, 91, 95, 99, 103, 107, 111, 115, 119, 123, 127, 131 ], 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, 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, 59, 60
] ) );