col22.z

#############################################################################
##
#W  col22.z                GAP library of groups           Hans Ulrich Besche
##                                               Bettina Eick, Eamonn O'Brien
##

SMALL_GROUP_LIB[ 891 ] :=
[ 1305088820519111, 1464729911911, 4381083311911, 3906464974711911,
1464730511911, 1302159362511911, 1464737611911, 1305075720211911,
1305077358611911, 1162823920853111911, 1638511191, 1640011191, 1461454511191,
1461454811191, 11119 ]; 

PROPERTIES_SMALL_GROUPS[ 891 ] := rec(
isAbelian := [ 1, -2, 5, 11, 15 ], 
lgLength := rec( lgLength := [ 2, 3, 4, 5 ], pos := [ [ 15 ], [ 2, -4, 11,
-14 ], [ 5, -10 ], [ 1 ] ] ),
frattFacs := rec( frattFacs := [ 5, 10, 23 ], pos := [ 1, 10, 14 ] ) );

SMALL_GROUP_LIB[ 900 ] :=
[ 2833586712605541610293, 8513277296616095691039,
6860384165068933288274219127, 3498315287130567, 6895754550512099501106344223,
5647191552289071229174332148994167, 12906120000072284774121591,
9396587947646531440, 9459196995885416543, 3148429680461299957,
7622649054904217621020791, 3886945452151, 9459196995885404495,
3490584348086733, 8513360698009036853535, 3141502911825064757,
7662024885363391074209887, 3886945440115, 22617538122101930603925458407519,
50759347282232860738597151, 15696999834974171423, 10456162308731335,
9445374287888265503, 3148429680461288389, 2846166469093069722397,
2561637755285277773680765, 3878355481073, 7661949500569000701137231,
6895757390440761911135506719, 6206181651396942874917524541535,
2544601550382298360197941, 51527935372820613954124398792799,
5027054527286304068112166271649124447, 78286289188376608863,
70683038919767580803167, 10440674673443061, 211354062507584104497247,
63614735028076857640943711, 10440653182879216, 10510218768220255,
3878357598333, 9459289664100302943, 3490558579327221, 8513360983736031445087,
4295032927, 19969355000301911694937278373728899167,
6197076891999790186121275650335, 20994197423568506851002846381180450521183,
25130597913446493029859606623, 56399274758036559773791, 9396591792714953159,
8460098471846172700959, 7650677785011439625318687, 7650677802406057174118687,
22828053920910976851940125, 20545240162968851844190457981,
18591141919804556409179238846589, 18591141919757590941797478846589,
52195556451172447, 3190207652023009501, 3059048926394065633405,
126809924569867912233085, 22952027197346474279846013, 17441110972448863,
10440653182867408, 14127473604762904827151, 11617888649335, 10494859965120607
, 3498255160770805, 3162407187670139101, 2846264172538127728765, 4294983805,
27922886570495997367554335, 25130597913446397144714711135,
56399274758036207440207, 43893674881579487519, 50759347282232860739113247,
17441110620115279, 11617888637299, 10494859965108559, 3878357570033,
10456162309771719, 9445374287888781599, 3490558579315653, 9410546269236499223
, 8500836860062968057951, 4294971772,
[ ( 1, 3, 2)( 4, 5, 6, 7, 8)(10,11,12), 
  ( 1, 2, 3)( 4, 6, 8, 5, 7)( 9,11,13,12,10) ],
10298745627645770753752824287519, 20355763789956333839939169981042783,
6885669176653369359452868943, 6197097214896835621308476166431,
11443107087269278987037704287, 55803507319887255877976159,
9268914415249328906761234168938591, 10298745627711501534544669704287,
14127299573182402396255, 156812531392050103567, 68893211278587723871,
62003890149599568724063, 15696914537279127647, 17441110972956767,
14127223083293776281695, 10440659624268147, 8500753094458410537295,
8500753113785763369295, 46975942914909147471, 9400070716225753543,
7650680933437215958634783, 7650680916042598409834783, 42278331228636925399327
, 8460063643827520934679, 6885612840093494963498389599,
6885612824438339169578389599, 38050498105774075144835167,
2827345496617729921989, 6860288092627159114078229271,
12722954559073615888257815, 5577399063256110881716653694652511,
5577399063256126536872447614652511, 30871296410669912958258781098079,
57253261513180586224245280863, 57994962272351, 19340256608375,
86984748591743071, 52195556451680351, 9445335418482983007, 17452612519461079,
78536709893683937375, 46976001111195648095, 8500801876910145273951,
11600725541109, 52195470544470231, 15707351307430396119,
234837831768769822815, 70683038904623526314079, 47226398348801474655,
42503758514222239842399, 85053640015967, 7743829181936, 68893315859432080655,
12886999135, 11660839354463, 4297064573, 11617889681527, 10494859965628511,
3878358614261, 10456162310291671, 9445374287889039455, 95 ]; 

PROPERTIES_SMALL_GROUPS[ 900 ] := rec(
isNilpotent := [ 4, 12, 18, 27, 45, 72, 87, 150 ], 
isSupersolvable := [ 1, -7, 9, -18, 22, -30, 34, -38, 40, -45, 51, -63, 67,
-72, 79, -87, 104, -115, 123, -138, 142, -150 ], 
isSolvable := [ 1, -87, 89, -150 ], 
isAbelian := [ 4, 12, 18, 27, 45, 72, 87, 150 ], 
lgLength := rec( lgLength := [ 3, 4, 5, 6, false ], pos := [ [ 94, -96, 98,
100, -101, 123, 129, -132, 135, -141, 143, 147, 149, -150 ], [ 35, -40, 43,
-45, 48, -50, 59, 61, -66, 68, -69, 71, -72, 74, -75, 78, 80, 84, 86, -87, 90
, -91, 93, 97, 99, 102, -103, 105, -107, 113, -116, 119, -122, 125, -128, 133
, -134, 142, 144, 146, 148 ], [ 7, -13, 16, -21, 23, -24, 26, -28, 30, -34,
41, -42, 46, -47, 52, -54, 56, -58, 60, 67, 70, 73, 76, -77, 79, 81, 83, 85,
89, 92, 104, 109, -112, 117, -118, 124, 145 ], [ 1, -6, 14, -15, 22, 25, 29,
51, 55, 82, 108 ], [ 88 ] ] ),
frattFacs := rec( frattFacs := [ 9, 17, 25, 33, 50, 58, 66, 74, 82, 90, 98,
106, 43, 51, 59, 67, 75, 83, 44, 52, 60, 68, 76, 84, 92, 100, 108, 165, 173,
181, 189, 197, 205, 213, 221, 229, 237, 245, 253, 261, 269, 277, 285, 293,
301, 190, 198, 206, 214, 222, 230, 238, 246, 254, 262, 270, 278, 286, 294,
302, 310, 318, 326, 334, 342, 350, 358, 366, 374, 382, 390, 398, 167, 175,
183, 191, 199, 207, 215, 223, 231, 239, 247, 255, 263, 271, 279 ], 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,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79,
80, 81, 82, 83, 84, 85, 86, 87 ] ) );

SMALL_GROUP_LIB[ 904 ] :=
[ 7316304423582629999, 72991945408256, 6612877568842345414767,
6613930973257339175023, 8093242308558959, 7316295320930484335,
8093242151207023, 8093243252670575, 80721555600, 81823019152,
65911258425798800, 5973096722529833160212591, 7309085186937913455,
8947660488815, 111 ]; 

PROPERTIES_SMALL_GROUPS[ 904 ] := 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[ 910 ] :=
[ 117449207, 53748281, 106965578231, 32514903, 106689540863, 48530536025,
97340669540855, 503 ]; 

PROPERTIES_SMALL_GROUPS[ 910 ] := rec(
isNilpotent := [ 8 ], 
isAbelian := [ 8 ], 
lgLength := rec( lgLength := [ 4 ], pos := [ [ 1, -8 ] ] ),
frattFacs := rec( frattFacs := [ ], pos := [ ] ) );

SMALL_GROUP_LIB[ 918 ] :=
[ 12267563399026778894609, 217437306525585695, 11263193819485142675103505,
15822670012177, 236858994856223, 268367139180831, 246360956592984351,
14556761067364113, 15822795841297, 14493711475941137, 13305258017407639313,
13943042106097406449, 217437306588500255, 226159358655546265887,
12214806794933890978289, 13334308419776082193, 14525358304981265,
12799686126171687227889, 13943013175344501233, 17181970929, 17448309233,
15788570317297, 257832259871, 17314091505, 236859057770783, 15822860853009,
217437306619957535, 14525356291715345, 199607449890267861279, 4383 ]; 

PROPERTIES_SMALL_GROUPS[ 918 ] := 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[ 920 ] :=
[ 214791957049657947, 1502609483085077949, 1385693611383349211767,
77851058791132, 197322342041953520219, 4175204316646938708357751,
4932903168427013911, 4932903168421860279, 4538270921622492568183,
4932903168499164759, 4538270921622569872663, 4538270921622564719031,
4175209247899358143615095, 1382398939061277414881, 1633267624639617,
1502607541098590849, 1633267619485985, 1633267696790465,
197608211867133540311, 233469269974647, 214791534930908279, 233469264821015,
233469342125495, 1274838113548022180259959, 1506188687914815255,
1385693601673159247127, 1506188687909661623, 1506188687986966103, 84442262234
, 84519566714, 71545333773903770, 4538406554646257121047, 214480848509238039,
4538265561563195517879, 5361844010119255, 1773838905431, 253970985425,
1637152051071063, 87 ]; 

PROPERTIES_SMALL_GROUPS[ 920 ] := rec(
isNilpotent := [ 4, 29, -31, 39 ], 
isAbelian := [ 4, 29, 39 ], 
lgLength := rec( lgLength := [ 3, 4, 5 ], pos := [ [ 35, -39 ], [ 7, -34 ], [
1, -6 ] ] ),
frattFacs := rec( frattFacs := [ 4, 7, 10, 13, 17, 20, 23, 26, 29, 32, 35 ],
pos := [ 1, 2, 3, 4, 5, 6, 13, 18, 23, 28, 31 ] ) );

SMALL_GROUP_LIB[ 924 ] :=
[ 15400843737701059, 4204060787301905, 14230346375238501059, 1525452901905,
13642969701509, 7580889701905, 12672829049701059, 1518809705901,
12606146169705019, 7004764588909015, 11709694402582500159, 1638501590,
46244556249600159, 16667660800159, 1522496000195, 15400807852800159,
83278297600159, 16667507200519, 77052046630400159, 10605427200915,
76949214070400159, 107723363168000159, 71196091129948800159, 2048000195,
3032697615900, 1420055369619005, 14758400159, 8204800195, 13715065600159,
1651200591, 13642976000519, 7580896000915, 12672829052800159, 159 ]; 

PROPERTIES_SMALL_GROUPS[ 924 ] := rec(
isNilpotent := [ 12, 34 ], 
isSupersolvable := [ 1, -24, 27, -34 ], 
isAbelian := [ 12, 34 ], 
lgLength := rec( lgLength := [ 4, 5 ], pos := [ [ 13, -34 ], [ 1, -12 ] ] ),
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[ 930 ] :=
[ 5381925042241019, 5787313921019, 5797604161019, 5798316962759,
5391567917282759, 1554914881019, 9295236001019, 8619815581921019, 6428161019,
1762561019, 12052801019, 1270081773, 11223606241019, 440643571,
11197893602759, 1159181306133, 10437981971761019, 1019 ]; 

PROPERTIES_SMALL_GROUPS[ 930 ] := rec(
isNilpotent := [ 18 ], 
isAbelian := [ 18 ], 
lgLength := rec( lgLength := [ 4 ], pos := [ [ 1, -18 ] ] ),
frattFacs := rec( frattFacs := [ ], pos := [ ] ) );