col2.z

#############################################################################
##
#W  col2.z                 GAP library of groups           Hans Ulrich Besche
##                                               Bettina Eick, Eamonn O'Brien
##

SMALL_GROUP_LIB[ 81 ] :=
[ 3488263, 43011, 124937, 10202635, 43013, 3402253, 43032, 3484186, 3484698,
282258971, 513, 520, 41993, 41996, 0 ]; 

PROPERTIES_SMALL_GROUPS[ 81 ] := rec(
isAbelian := [ 1, -2, 5, 11, 15 ], 
lgLength := rec( lgLength := [ 1, 2, 3, 4 ], pos := [ [ 15 ], [ 2, -4, 11,
-14 ], [ 5, -10 ], [ 1 ] ] ),
frattFacs := rec( frattFacs := [ 5, 10, 23 ], pos := [ 1, 10, 14 ] ) );

SMALL_GROUP_LIB[ 84 ] :=
[ 14329614137, 60550457, 57771973, 283379513, 23814281243, 664914, 170906123,
393610763, 995339, 113529996, 5476367453, 3359243, 705055, 283398923, 11 ]; 

PROPERTIES_SMALL_GROUPS[ 84 ] := 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[ 88 ] :=
[ 361912670009, 460850900, 31843384750009, 4111700009, 361856420009,
4111690009, 4111760009, 5130090, 5200090, 40105070090, 46400009, 9 ]; 

PROPERTIES_SMALL_GROUPS[ 88 ] := 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[ 90 ] :=
[ 1109144629, 36053527, 105295657501, 131613, 401431, 139293, 36057111,
12202037, 3246012439, 23 ]; 

PROPERTIES_SMALL_GROUPS[ 90 ] := rec(
isNilpotent := [ 4, 10 ], 
isAbelian := [ 4, 10 ], 
lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 5, 8, -10 ], [ 1, -4, 6, -7
] ] ),
frattFacs := rec( frattFacs := [ 3, 5, 7, 9 ], pos := [ 1, 2, 3, 4 ] ) );

SMALL_GROUP_LIB[ 100 ] :=
[ 414243239183, 13763379, 4181335752766735, 4142412815, 132111, 39985459,
4132057359, 131388, 3945996595, 396037370127, 41289059594511, 41289125130511,
197025807, 401423, 41299983, 15 ]; 

PROPERTIES_SMALL_GROUPS[ 100 ] := rec(
isNilpotent := [ 2, 5, 8, 16 ], 
isAbelian := [ 2, 5, 8, 16 ], 
lgLength := rec( lgLength := [ 2, 3, 4 ], pos := [ [ 13, 15, -16 ], [ 4, -5,
7, -8, 10, -12, 14 ], [ 1, -3, 6, 9 ] ] ),
frattFacs := rec( frattFacs := [ 5, 9, 14, 18, 22, 15, 19, 23 ], pos := [ 1,
2, 3, 4, 5, 6, 7, 8 ] ) );

SMALL_GROUP_LIB[ 104 ] :=
[ 1277778924299, 1125489456, 132185868178187, 132874717600523, 12284379659,
1277641050635, 12284358923, 12284504075, 10637700, 10782852, 115946650500,
1271021269259, 117448715, 11 ]; 

PROPERTIES_SMALL_GROUPS[ 104 ] := rec(
isNilpotent := [ 2, 9, -11, 14 ], 
isAbelian := [ 2, 9, 14 ], 
lgLength := rec( lgLength := [ 2, 3, 4 ], pos := [ [ 13, -14 ], [ 4, -12 ], [
1, -3 ] ] ),
frattFacs := rec( frattFacs := [ 4, 7, 11, 14, 17 ], pos := [ 1, 2, 3, 8, 11
] ) );

SMALL_GROUP_LIB[ 108 ] :=
[ 7996764065373607, 6289883499, 1339482445948, 74044111592839, 58196359,
685031037227, 6289887339, 666741790763, 72013834639659, 73371439602855,
679321603111, 58196077, 58204205, 6173499501, 7994904959085607, 721775798407,
72044351436807, 12402563164, 1339478252124, 12402563132, 1339478252092,
12402563612, 6342842631, 58200199, 6173562887, 666794793223, 679365057671,
6289951751, 524423, 589831, 57213063, 58200109, 6289889323, 679321541671,
524334, 73353084475435, 23753207777360935, 170414087, 18856046599,
2036454683655, 114825244, 528391, 58202119, 6289890311, 7 ]; 

PROPERTIES_SMALL_GROUPS[ 108 ] := rec(
isNilpotent := [ 2, 5, 12, -14, 29, -31, 35, 45 ], 
isSupersolvable := [ 1, -2, 4, -14, 16, -17, 23, -35, 38, -40, 42, -45 ], 
isAbelian := [ 2, 5, 12, 29, 35, 45 ], 
lgLength := rec( lgLength := [ 2, 3, 4, 5 ], pos := [ [ 39, -41, 44, -45 ], [
16, -22, 25, 27, -31, 34, -35, 37, -38, 42, -43 ], [ 3, -5, 8, 10, -15, 23,
-24, 26, 32, -33, 36 ], [ 1, -2, 6, -7, 9 ] ] ),
frattFacs := rec( frattFacs := [ 7, 13, 20, 26, 32, 21, 27, 33, 58, 64, 70,
76, 82, 88, 77, 83, 89, 95 ], pos := [ 1, 2, 3, 4, 5, 9, 11, 14, 15, 17, 22,
26, 28, 31, 32, 33, 34, 35 ] ) );

SMALL_GROUP_LIB[ 112 ] :=
[ 906343320913061, 1627178241816, 8092320261701, 906241654246469,
101510153960265797, 101510154852079685, 11369137344167655077, 8092320253925,
906241654238693, 8092320238373, 906340645564709, 906241654223141,
8092320355013, 141234982476299141, 15818318037860997605, 15818318037861005381
, 1771651620240946370213, 8092320347237, 14523849684, 28665578772,
3224926568916, 14523896340, 1612654508052, 180617415176628, 20229150109290516
, 2265664811849190612, 906240762549221, 72237951365, 8091428681093,
8091428665541, 100523151365, 1261025732696261, 1261025732478533,
141234882593034821, 72237928037, 72238169093, 127409790, 127526430,
1612527059262, 14396579742, 6436107363384, 638005253, 5 ]; 

PROPERTIES_SMALL_GROUPS[ 112 ] := rec(
isNilpotent := [ 2, 19, -26, 37, -40, 43 ], 
isSupersolvable := [ 1, -40, 42, -43 ], 
isAbelian := [ 2, 19, 22, 37, 43 ], 
lgLength := rec( lgLength := [ 2, 3, 4, 5 ], pos := [ [ 42, -43 ], [ 10, -13,
18, -21, 27, -41 ], [ 3, -9, 14, -17, 22, -26 ], [ 1, -2 ] ] ),
frattFacs := rec( frattFacs := [ 5, 9, 14, 18, 51, 55 ], pos := [ 1, 2, 18,
26, 36, 40 ] ) );

SMALL_GROUP_LIB[ 120 ] :=
[ 247732507841, 735009969219, 88211749800967, 2046829680,
[ (1,2,4,8)(3,6,9,5)(7,12,13,17)(10,14,11,15)(16,20,21,24)(18,22,19,23), (1,
3,7)(2,5,10)(4,9,13)(6,11,8)(12,16,20)(14,18,22)(15,19,23)(17,21,24) ],
87224918086723, 10495991250881543, 1214251665415, 1214251664391,
145710373276679, 1214251679751, 145710373292039, 145710373291015,
17485244966521863, 3625571831624128, 88191197662227, 6123816979, 734926096403
, 6123815955, 6123831315, 29721895259185, 2063730737, 247682189361,
2063729713, 2063745073, 10585380005039111, 735093917703, 88211498158087,
735093916679, 735093932039, 16778268, 16793628, 243621973020,
[ (1,2,3,4,5), (1,2) ], [ (1,2,3,5,4), (1,3)(2,4)(6,7) ], 88183317070855,
7045550996422864, 845466135231709296, 3633996234819, 726881403923,
87466593944583, 10117316615, 4078436464, 50462727, 16908301, 6123880455, 7 ];


PROPERTIES_SMALL_GROUPS[ 120 ] := rec(
isNilpotent := [ 4, 31, -33, 47 ], 
isSupersolvable := [ 1, -4, 6, -14, 16, -33, 36, 40, -42, 44, -47 ], 
isSolvable := [ 1, -4, 6, -33, 36, -47 ], 
isAbelian := [ 4, 31, 47 ], 
lgLength := rec( lgLength := [ 3, 4, 5, false ], pos := [ [ 42, 44, -47 ], [
8, -33, 36, -41, 43 ], [ 1, -4, 6, -7 ], [ 5, 34, -35 ] ] ),
frattFacs := rec( frattFacs := [ 4, 7, 10, 13, 17, 20, 23, 26, 29, 32, 35, 38
, 41 ], pos := [ 1, 2, 3, 4, 5, 6, 7, 14, 15, 20, 25, 30, 33 ] ) );

SMALL_GROUP_LIB[ 126 ] :=
[ 32026547279, 88420943, 10870376443, 422726735, 1487212537315, 666211,
254347823, 88439087, 10957462319, 829487, 3359279, 705091, 422744879,
85660603, 53272017839, 47 ]; 

PROPERTIES_SMALL_GROUPS[ 126 ] := 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[ 132 ] :=
[ 691530901, 6139210109, 810501610019, 5130190, 7481280019, 1367521900,
46400019, 5440091, 6139360019, 19 ]; 

PROPERTIES_SMALL_GROUPS[ 132 ] := 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[ 135 ] :=
[ 18089333, 131421, 133213, 17828189, 87 ]; 

PROPERTIES_SMALL_GROUPS[ 135 ] := rec(
isAbelian := [ 1, -2, 5 ], 
lgLength := rec( lgLength := [ 2, 3, 4 ], pos := [ [ 5 ], [ 2, -4 ], [ 1 ]
] ),
frattFacs := rec( frattFacs := [ 4, 8 ], pos := [ 1, 4 ] ) );

SMALL_GROUP_LIB[ 136 ] :=
[ 9388062605327, 4630843136, 1273596662185999, 1276699197767695, 69023694863,
9387492638735, 69023629327, 69024088079, 33620208, 34078960, 625220452592,
173203482589986831, 9364691812367, 505413647, 15 ]; 

PROPERTIES_SMALL_GROUPS[ 136 ] := 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[ 140 ] :=
[ 282052551, 469174145, 67002226727, 664986, 39113447367, 38302872476711,
1954285079, 3359255, 2032161, 478483223, 23 ]; 

PROPERTIES_SMALL_GROUPS[ 140 ] := 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[ 144 ] :=
[ 4271039780059399619, 203208592983508, 1209427065561092780912,
88593623763896965848515, 29659998455907715, 4272432652851662211,
615233498359787478403, 615233498360391458179, 29659998455907651,
4272432652851662147, 29659998455907523, 4272432739220769987,
4272432652851662019, 29669671796001923, 776076020118846003338563,
5389416806380870950147, 111754946897113825067261379, 776076020118846003338627
, 29669671796001859, 1420963086793, 8359281428809, 1203765717764553,
1411299410762, 201797293574986, 29064328367975178, 4185263285035215690,
602677913045117840330, 204619489772369, 29469441628619203, 1411165193816,
266287551635650776146595184344, 1849219108580908167692975768,
174132220368737261384012, 404986157334740, 4300885994481518232,
619327583204149692120, 4272432652247684419, 205972203160835,
29669671192024323, 29669671192024195, 1804904305902595, 37426505445714023555,
37426495772373927299, 5389416784183406220675, 205972203160643,
206039379137539, 9865003589, 29058140677, 602578744249029, 4184573217541,
611017386871782949315, 602637733233027, 86779834751287747, 86779747778201987,
12496283681226525123, 12725525257944144131, 12496296118982056323,
1832475637144508275075, 12496296118378076547, 1799466641047003896259,
263876491748809743112643, 1799466641133976984003, 602724102340803,
602637733234819, 86779921724377283, 86779834147309763, 86779834751289539,
8398799066389082928, 1420963119753, 204590096091785, 29465119951989385,
29465120153315977, 4242977302272584393, 1420963119689, 204590096091721,
1420963119305, 204618885793993, 204590096091337, 1420963121289,
86771368363993609, 12495077044591438409, 12495077044591438473,
1799291094421343480521, 1420963121225, 204648883470723, 29469353447573891,
4243599334802774403, 4243599335406754179, 611078304299168618947,
204648883470659, 29469353447573827, 204648883470531, 29469439816681667,
29469353447573699, 204648883472515, 37426305214338685187,
5389387950865357330755, 5389387950865357330819, 776071864924612042283459,
204648883472451, 9797894348, 19394463820, 2802533271756, 9797895244,
1401367301196, 201796958309388, 29058762023390284, 4184461731395030220,
1209251530338442735884, 2812404564236, 58323573894344816, 1430358377475,
67109891, 12670056387653716163740099, 610960669284212951171,
87978336376926254155971, 12668880608405176204482819,
1824318807610345373024737667, 262701908295889733715141417411,
12670675598623412646103235, 12841799365102056961504856,
89179162257653184362008, 8397580071547756628, 1849219108579305078733045336,
12841799365134063055044120, 1209251530301667078220, 673316579613640704850,
4675809580651070226, 1807659125080145, 611017386783607407043,
87986503696752794716611, 4243176297710272707, 611017386783607408835,
4243176297710272835, 611017386783607408963, 4243176297710274627,
88371702572351875, 86779747174224259, 12725525170971054467,
1832475624620383637955, 602637129255171, 12725525170971052419, 4184976163075,
613692375138563, 88371702572355843, 4184976162947, 602637129257091,
88371702572355715, 602637129253059, 4184976164867, 602637129255043,
86779747174222019, 4261748768771, 613692375142403, 2812399059032,
29867263855560216, 4300885994011756120, 204589894766917, 9865036037,
1420761796869, 1420761796741, 29058236421, 602578744348805, 602578744344965,
86771339372892549, 9865035845, 9865039877, 29469352843596099, 1421164462339,
204648279494915, 204648279494787, 12533989752835, 259904896713740419,
259904896713736579, 37426305127365595523, 1421164462147, 1421164466179,
67108934, 67110918, 1401300191430, 9730787590,
37832585391152708497031906052419, 8397580148302225420, 2410227265945648,
87986502692039710261571, 4242782425002559491, 12670675598610713990187203,
58316528294092812, 8397580071528886284, 12553185951753, 29466502084214851,
29058433027, 19534970892, 405024811315248, 67141635, 9865052163, 3 ]; 

PROPERTIES_SMALL_GROUPS[ 144 ] := rec(
isNilpotent := [ 2, 20, -27, 30, 47, -50, 101, -108, 113, 178, -181, 197 ], 
isSupersolvable := [ 1, -2, 4, -30, 37, -50, 52, -67, 69, -108, 112, -113,
137, -154, 158, -181, 192, 195, -197 ], 
isAbelian := [ 2, 20, 23, 30, 47, 101, 104, 113, 178, 197 ], 
lgLength := rec( lgLength := [ 2, 3, 4, 5, 6 ], pos := [ [ 184, 192, 194, 196
, -197 ], [ 63, -68, 92, -95, 100, -103, 111, -113, 115, -116, 120, 132, -133
, 136, -154, 168, -181, 183, 186, -187, 189, 191, 193, 195 ], [ 3, 11, -14,
19, -22, 37, -50, 52, -62, 76, -79, 84, -91, 96, -99, 104, -110, 117, -119,
124, -126, 130, -131, 134, -135, 155, -167, 182, 185, 188, 190 ], [ 4, -10,
15, -18, 23, -27, 29, -36, 51, 69, -75, 80, -83, 114, 121, -123, 127, -129 ],
[ 1, -2, 28 ] ] ),
frattFacs := rec( frattFacs := [ 9, 17, 26, 34, 42, 27, 35, 43, 100, 108, 116
, 124, 77, 85, 93, 101, 109, 117, 390, 398, 406, 414, 422, 319, 327, 335, 343
, 351, 359, 367, 375, 383, 391, 399, 407 ], pos := [ 1, 2, 3, 19, 27, 28, 29,
30, 33, 36, 46, 50, 51, 67, 68, 84, 100, 108, 109, 110, 111, 112, 113, 114,
119, 120, 123, 126, 129, 136, 154, 157, 167, 177, 181 ] ) );