col20.z

#############################################################################
##
#W  col20.z                GAP library of groups           Hans Ulrich Besche
##                                               Bettina Eick, Eamonn O'Brien
##

SMALL_GROUP_LIB[ 1881 ] :=
[ 1012019142239, 11233383119, 1903198127623775, 540842687, 6335 ]; 

PROPERTIES_SMALL_GROUPS[ 1881 ] := rec(
isNilpotent := [ 2, 5 ], 
isAbelian := [ 2, 5 ], 
lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 4, -5 ], [ 1, -3 ] ] ),
frattFacs := rec( frattFacs := [ 3, 5 ], pos := [ 1, 2 ] ) );

SMALL_GROUP_LIB[ 1884 ] :=
[ 11927809215375859883, 81740766879137963, 572209535946673, 88596073698517163
, 166915108876255564343, 142820668793399, 314310672821442863489195,
81740254590738743, 166840747365201895595, 314327967856504274260535,
89738065167409463, 43513123111223, 1714172581096560, 154089294725711996507,
47019189215543, 322179071605, 88596082582106423, 311 ]; 

PROPERTIES_SMALL_GROUPS[ 1884 ] := rec(
isNilpotent := [ 6, 18 ], 
isSupersolvable := [ 1, -12, 15, -18 ], 
isAbelian := [ 6, 18 ], 
lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 8, 11, -18 ], [ 1, -7, 9,
-10 ] ] ),
frattFacs := rec( frattFacs := [ 3, 5, 7, 9, 11, 13 ], pos := [ 1, 2, 3, 4, 5
, 6 ] ) );

SMALL_GROUP_LIB[ 1890 ] :=
[ 991738501130138396231, 994537183311567162275, 1874388215012779128458147,
524914976957081159, 874426114170398279, 524729756536776693,
1655113233321599372195, 625898778322124458101139,
1182957951326220325435850179, 1182952002996169993776383899,
2234610745181994486302046621907, 3241351085050787, 524729365539807071,
992087826656316645215, 992087826998773178207, 524729365539713759,
992087826656316551903, 524914194270488159, 526210147576520483,
996982463364356251427, 996982465076638916387, 526210147576427171,
996982463364356158115, 527503948405753379, 991739796300757835555,
1884294058375924200939299, 1884294058377636483604259, 991739796300757742243,
1884294058375924200845987, 996980983267244361251, 2972769107319756773851,
5618860058270654926117339, 5618529770245649730853339, 524914976968651847,
992088012267799144391, 5618532216823612648692187,
10619645508735526902211123675, 10619021264368267083162163675,
991738501130149966919, 1875045992380608179333063, 5618540612857828527050611,
10619645517131561118041706355, 10619021272764301298992746355,
994537183311572947619, 1884296855762935018944035,
10619025896796558957349064563, 20069950189663024718047265640307,
20071130011517145776049800040307, 1874388215012779134243491,
3561315770330500996354831907, 277732630650719, 524914292091510623,
524914634548043615, 277732630557407, 524914292091417311, 277732678239839,
462658800148319, 647487530829407, 1223751640348647263, 277634427608997,
462463158290085, 874055478404472741, 875721284789837603, 6116908251276363299,
11560956596466671853347, 175217934064299091, 92610054976723,
174848179043747923, 660751267944645930067, 332911485241016949211,
874426114181968967, 2312890601150650247111, 1248821646004879210420699,
331862397048718596991, 524729756548347381, 1651964854782626097525,
1248820596916686912068479, 629209707036934348361587, 1655113233321605157539,
21850207967326988369425955, 1180451063828094936930537331,
331162635067464439699, 175033405012013971, 629202712838213645447755,
332911303348418707531, 627219934490431008619615, 331862214275517844063,
1189206346328746932889261939, 629209706959783808908915, 1712282759843,
1712330442275, 3237926567309987, 277634809628195, 278417555473955,
524730050464630307, 277732642408031, 524729365551564383, 526210147582305827,
991739796300763620899, 524914976974530503, 991738501130155845575,
994537183311575840291, 1874388215012779137136163, 49304569379, 244635698723,
146790975021, 463343724971555, 48946251379, 462658811905631, 277634439366309,
875721284795622947, 92610066827347, 874426114187847623, 524729756554226037,
1655113233321608050211, 175033398920606611, 1652665358818172698679,
991739242010024577621, 3128164010993165149552163, 1571 ]; 

PROPERTIES_SMALL_GROUPS[ 1890 ] := rec(
isNilpotent := [ 12, 90, -92, 120 ], 
isAbelian := [ 12, 90, 120 ], 
lgLength := rec( lgLength := [ 4, 5, 6 ], pos := [ [ 93, -95, 104, -107, 116,
-120 ], [ 13, -30, 35, 40, 45, 50, -65, 68, 72, 76, 80, 82, -92, 96, -103,
108, -115 ], [ 1, -12, 31, -34, 36, -39, 41, -44, 46, -49, 66, -67, 69, -71,
73, -75, 77, -79, 81 ] ] ),
frattFacs := rec( frattFacs := [ 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37
, 41, 44, 47, 50, 53, 56, 59, 62, 65, 68, 71, 74, 77, 80, 83, 86, 89, 92, 95,
98 ], pos := [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 18, 24, 30, 35, 40, 45,
50, 56, 59, 62, 65, 69, 73, 77, 81, 83, 85, 87, 89, 92 ] ) );

SMALL_GROUP_LIB[ 1892 ] :=
[ 27146439088029, 123655416642365, 234993531158474675, 753581202611,
1166604503533475, 65420297123, 14438271171, 124203520095395, 419 ]; 

PROPERTIES_SMALL_GROUPS[ 1892 ] := rec(
isNilpotent := [ 4, 9 ], 
isAbelian := [ 4, 9 ], 
lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 5, -9 ], [ 1, -4 ] ] ),
frattFacs := rec( frattFacs := [ 3, 5, 7, 9 ], pos := [ 1, 2, 3, 4 ] ) );

SMALL_GROUP_LIB[ 1896 ] :=
[ 7106111718365432569207397, 3748132329286770928229, 170316598594225040569,
13100731202174943337061, 24838993466320222407033659, 21278328386168838971,
13473187810932973682360545457, 3747949226804650711505,
7106111714637365778884561, 3747949226801763537137, 3747949226845071152657,
13440650070442274177627, 13440650070439387003259, 25483472541256968431635259,
13440650070482694618779, 25483472541257011739250779,
25483472541257008852076411, 48316663938230905135083493691,
4846866750085769681, 4846866790506210833, 17423558699556545342406833,
613223380983286042409704680, 1225124605459871639200700193990,
24838979277030858428346545, 6909664788752243153, 13100727465238753355729,
6909664785865068785, 6909664829172684305, 322920001286755179593365,
89829655074383797, 170316456721327699381, 89829652187209429,
89829695494824949, 47094731590897379232819679547, 13100734939324783278683,
24838993455109344546310235, 13100734939321896104315, 13100734939365203719835,
11210924055513467, 11210967363128987, 40322465908194724604219,
645329412302379775032348, 1223544592971066643089950124, 4846784332806254747,
26888725411944558644741, 17450426165316056751656453, 7088946392974897307,
2578038834069659, 269113846205752236, 9203811271876425899525,
3642736351408283, 47673023170423, 6909664967757047963, 155 ]; 

PROPERTIES_SMALL_GROUPS[ 1896 ] := rec(
isNilpotent := [ 6, 39, -41, 54 ], 
isSupersolvable := [ 1, -21, 24, -41, 44, 47, -48, 51, -54 ], 
isAbelian := [ 6, 39, 54 ], 
lgLength := rec( lgLength := [ 3, 4, 5 ], pos := [ [ 44, 47, -48, 51, -54 ],
[ 7, -43, 45, -46, 49, -50 ], [ 1, -6 ] ] ),
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, 18, 21, 22, 23, 28, 33, 38, 41
] ) );

SMALL_GROUP_LIB[ 1900 ] :=
[ 639160317420529047969, 1901054870960034815, 1228451598463901211208353,
1132313807695283, 2307368743763342017006393761,
4590973886847139078045336095393, 669005402705522475393, 1000553896601747,
336400167033804477, 646553296496816412033, 588222519443, 1000553890950485,
176619525226239, 1903290087925674431, 336165624044990625,
3616262357155885045043, 14705375893811, 335341519285501695,
12105600289428803023295, 1213555219520214565728417,
43809342991471950852969641267, 1213555219814322045792417,
43809342991477538895090857267, 3185519586506074697889,
114988758979442704126342451, 3353352779650067, 6387132672540537875,
176930924125629, 6371376808112650259, 12135552083435197339667, 526539461651,
93117912321, 1001730439896083, 176929231072701, 1903295970133835795, 1043 ];


PROPERTIES_SMALL_GROUPS[ 1900 ] := rec(
isNilpotent := [ 4, 11, 17, 36 ], 
isAbelian := [ 4, 11, 17, 36 ], 
lgLength := rec( lgLength := [ 3, 4, 5 ], pos := [ [ 27, -31, 34, -36 ], [ 7,
-12, 15, -17, 20, -26, 32, -33 ], [ 1, -6, 13, -14, 18, -19 ] ] ),
frattFacs := rec( frattFacs := [ 5, 9, 13, 17, 22, 26, 30, 34, 38, 42, 46, 23
, 27, 31, 35, 39, 43 ], pos := [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,
14, 15, 16, 17 ] ) );

SMALL_GROUP_LIB[ 1904 ] :=
[ 607589413306966586884101, 1822512869777936562323471,
3478327068886677108390101087, 7597261752631111450719,
3469456276220903767429939215, 6605853012489428165747630145631,
10322383386734662021808223, 10322383386734662005031007,
19653817968346836118446014559, 19653817964360868973766508639,
19653817964360868973749731423, 37420869404143098564658690261087,
37444901562050872070808677646431, 37420869411728396135444724580447,
37444901569636169641592598036575, 71295092574144860424730186606444639,
71295092574144860424730186589667423, 37420869411728394041974585294943,
71249335359930862257862704189407327, 37444901577225451086052635705439,
71295092603037254885883019094130783, 135745856261171814248688185699167371359,
71249335359930866243829849389006943, 71295092588587263015631107372613727,
10322387370608337031790687, 10322383386734662491570271,
10322387370608337535107167, 19653825561612154254013759583,
19653817968344742648776491103, 19653825553640219963614560351,
19653825557626187108814159967, 957202136868872802319,
1822512299755924837388303, 3470064502349500955645464591,
3470064502349800022808219663, 6607002812474019520719748091919,
957202136868856025103, 1822512299755924820611087, 957771261679478263823,
1822512868880735442849807, 1823597051944229733945359, 957202136869275455503,
3932220301577400760286597135, 7486947454203371259555850768399,
7486947454203371259555867545615, 14255147952803218878406278122590223,
957771261679981580303, 319112086570930335749, 607589178592020867903493,
1156850242233287944297312261, 1156850242233411089599623173,
2202642861212414815968642002949, 319112086570913558533,
607589178592020851126277, 319346432081110560773, 607589412937531048128517,
608035841257793403285509, 319112086571332988933, 1619006678881151680449146885
, 3082588716589712835623407120389, 3082588716589712835623423897605,
5869248916386813239062983478407173, 319346432081613877253,
1826852452141978959741023, 3478327064896523023432024159,
6622734739148279475137568309343, 6622734739148281568607707594847,
12609686943338328108694768889888863, 1826852452141978942963807,
3478327064896523023415246943, 1826856436015653969723487,
3478327068880396698442006623, 3478334658161841158479675487,
1826852452141979429503071, 52387820054976034800147888078943,
99746409384674370261514643094634591, 99746409384674370261514643111411807,
189917163468420000977925913484466323551, 1826856436015654473039967,
3990154085528502367, 7974027761092132959, 15186536916681201025119,
3990154085562056799, 7593271598546136596575, 14457589125724151155261535,
27527249695380841383778582623, 52411883420005124052266671669343,
6605843655982749951224866734095, 12577526329253720726151926242082911,
3478320240920771605066416223, 3478320240920771605569732703,
6622721738709165116255853609055, 3478320240920771605099970655,
6622721738709165116255383847007, 6622721738709165116255887163487,
12609662190502246397330332533653599, 3469456275650885053719793679,
6605844748838707930359071264783, 1822193422388706261618703,
3469456275650885054122446863, 1822193422388706362281999,
3469456275650885054223110159, 1822193422388706764935183,
6605853012485438012624224649311, 12577544135772269992139205262704735,
3469460615803267809777025119, 6605853012485438012624694411359,
3469460615803267809810579551, 6605853012485438012624727965791,
3469460615803267810280341599, 19666439896033027410817450079,
19653817964358775504164094047, 37444901562046886103662974730335,
19653817964358775504147316831, 37444901562046886103662957953119,
37420869404139110504043888246879, 71295092574137271143285726048682079,
10322383384641192385839199, 19666439896033027411320766559,
37444901562046886103662437859423, 5421419843852399804511,
10329012550436509391519839, 10322383384641192922710111,
19666439896033027411857637471, 5421419843852366250079,
10322383384641192889155679, 19666439896033027411824083039,
5421419843852349472863, 10329012550436509341188191,
10322383384641191832191071, 5421419843852869566559,
10322383384641192352284767, 10322383384641192335507551,
19653817964358775503576891487, 5424901548593935024223, 5421419843853406437471
, 10329012550436510398152799, 1822512299456858127598863, 502731909248320783,
957201837802683106575, 957201837802649552143, 569687786446128399,
2065241754730950075352335, 2065241754730949068719375,
3932220301007976863576884495, 502731909197989135, 502731910254953743,
607589178468876018519813, 167600765102198533, 319111963426601045765,
319111963426567491333, 234556642300006149, 850318633742967966273285,
850318633742966959640325, 1619006678646683006025076485, 167600765051866885,
167600766108831493, 3478327064894429553812832351, 959481327720423489631,
1826852450048509860642911, 1826852450048509827088479, 7589785372659344736351,
27514611373409688444775432287, 27514611373409688443768799327,
52387820054972048833002185162847, 959481327720373157983,
959481327721430122591, 2093470156062815, 2093470676156511,
7593269505075963756639, 3988060615942864991,
12577526319168643029276936443854863, 23947610111705358892545563406012252255,
6605853005406360367212173197407, 8260394177570282810966031,
3469455701671624941036916751, 6605843660322332315267247374431,
1826848866032092750807135, 446595903667132821504, 957034368986509214991,
1822195701579557879414879, 2847383349528363103, 263891380600927,
87969520156917, 503928182127198303, 95 ]; 

PROPERTIES_SMALL_GROUPS[ 1904 ] := rec(
isNilpotent := [ 4, 80, -87, 168, -171, 186 ], 
isSupersolvable := [ 1, -174, 176, -178, 180, -186 ], 
isAbelian := [ 4, 80, 83, 168, 186 ], 
lgLength := rec( lgLength := [ 3, 4, 5, 6 ], pos := [ [ 182, -186 ], [ 25,
-31, 39, -42, 47, 55, -58, 63, 71, -74, 79, -82, 90, -92, 99, -100, 103, 106,
-107, 110, -171, 175, 178, -181 ], [ 7, -24, 32, -38, 43, -46, 48, -54, 59,
-62, 64, -70, 75, -78, 83, -87, 93, -98, 101, -102, 104, -105, 108, -109, 174
, 176, -177 ], [ 1, -6, 88, -89, 172, -173 ] ] ),
frattFacs := rec( frattFacs := [ 5, 9, 13, 17, 22, 26, 30, 34, 38, 42, 46,
131, 135, 139, 147, 151, 155, 159, 163, 167, 171 ], pos := [ 1, 2, 3, 4, 5, 6
, 31, 47, 63, 79, 87, 88, 89, 96, 103, 110, 137, 147, 157, 167, 171 ] ) );