prop960.z

#############################################################################
##
#W  prop960.z              GAP library of groups           Hans Ulrich Besche
##                                               Bettina Eick, Eamonn O'Brien
##

PROPERTIES_SMALL_GROUPS[ 960 ] := rec(
isNilpotent := [ 4, 584, -636, 5544, -5680, 10795, -10862, 11348, -11354,
11394 ], 
isSupersolvable := [ 1, -215, 218, -636, 643, -779, 813, -3720, 3738, -5680,
5836, -6250, 6403, -9638, 9673, -10862, 11004, -11066, 11152, -11273, 11288,
-11354, 11377, 11385, -11387, 11391, -11394 ], 
isSolvable := [ 1, -636, 643, -5680, 5748, -10862, 10893, -11354, 11359,
-11394 ], 
isAbelian := [ 4, 584, 608, 632, 5544, 5572, 5672, 10795, 10849, 11348, 11394
], 
lgLength := rec( lgLength := [ 3, 4, 5, 6, 7, 8, false ], pos := [ [ 11366,
-11367, 11387, 11390, -11394 ], [ 2762, -2818, 2822, -3133, 3135, 3664, -3668
, 3672, -3719, 3738, -3769, 4020, -4045, 4047, -4053, 4064, -4086, 4300,
-4305, 4312, -4315, 4321, -4323, 4339, -4371, 4622, -4647, 4649, -4655, 4666,
-4688, 4902, -4907, 4914, -4917, 4923, -4925, 4941, -4973, 5224, -5249, 5251,
-5257, 5268, -5290, 5504, -5509, 5516, -5519, 5525, -5527, 5543, -5571, 5748,
5835, 5940, -5947, 6025, -6045, 6048, -6056, 6124, -6129, 6178, -6179, 6211,
-6217, 6220, -6224, 6250, 6262, 6310, 6360, -6361, 6401, -6402, 6413, -6418,
6426, -6428, 6438, -6440, 6490, -6493, 6507, -6508, 6518, 6528, 6539, -6544,
6552, -6554, 6564, -6566, 6616, -6619, 6633, -6634, 6644, 6654, -8138, 8359,
-8881, 8924, -9275, 9318, -9489, 9550, -9638, 9647, 9656, 9667, -9941, 9988,
-9997, 10001, -10012, 10016, -10023, 10030, -10040, 10045, -10315, 10362,
-10371, 10375, -10386, 10390, -10397, 10404, -10414, 10419, -10689, 10736,
-10745, 10749, -10760, 10764, -10771, 10778, -10788, 10793, -10848, 11004,
-11008, 11024, -11033, 11038, -11042, 11047, -11053, 11063, -11066, 11155,
-11157, 11160, -11161, 11164, -11165, 11168, -11169, 11172, 11176, -11178,
11181, -11182, 11185, -11186, 11189, -11190, 11193, -11273, 11288, -11354,
11360, 11364, -11365, 11372, -11386, 11388, -11389 ], [ 25, -64, 143, -188,
213, -217, 223, -231, 236, -237, 239, -242, 251, -258, 295, -307, 309, -310,
312, 315, -316, 318, -319, 322, -324, 326, -332, 345, -353, 358, -359, 361,
-364, 373, -380, 417, -429, 431, -432, 434, 437, -438, 440, -441, 444, -446,
448, -454, 467, -475, 480, -481, 483, -486, 495, -502, 539, -551, 553, -554,
556, 559, -560, 562, -563, 566, -568, 570, -576, 584, -607, 679, -734, 761,
-771, 780, -781, 784, 788, -789, 792, 796, -801, 808, -812, 834, -835, 838,
-847, 850, -856, 864, -869, 871, -874, 885, -887, 889, -893, 896, -899, 902,
-903, 905, 928, -929, 932, -941, 944, -950, 958, -963, 965, -968, 979, -981,
983, -987, 990, -993, 996, -997, 999, 1039, -1716, 1759, -2458, 2507, -2761,
2819, -2821, 3134, 3136, -3663, 3669, -3671, 3720, 3722, -3724, 3727, -3732,
3734, -3735, 3770, -3990, 4012, -4019, 4046, 4054, -4063, 4087, -4187, 4190,
-4231, 4233, -4237, 4241, -4269, 4273, -4284, 4288, -4299, 4306, -4311, 4316,
-4320, 4324, -4338, 4372, -4592, 4614, -4621, 4648, 4656, -4665, 4689, -4789,
4792, -4833, 4835, -4839, 4843, -4871, 4875, -4886, 4890, -4901, 4908, -4913,
4918, -4922, 4926, -4940, 4974, -5194, 5216, -5223, 5250, 5258, -5267, 5291,
-5391, 5394, -5435, 5437, -5441, 5445, -5473, 5477, -5488, 5492, -5503, 5510,
-5515, 5520, -5524, 5528, -5542, 5572, -5671, 5754, 5761, -5763, 5828, -5834,
5842, -5929, 5948, -6024, 6046, -6047, 6057, -6123, 6130, -6177, 6180, -6210,
6218, -6219, 6225, -6249, 6251, 6263, 6276, -6279, 6298, -6299, 6311, 6324,
-6327, 6346, -6349, 6362, -6365, 6378, -6381, 6400, 6403, -6412, 6419, -6425,
6429, -6437, 6444, -6452, 6454, -6469, 6472, -6489, 6494, -6506, 6509, -6517,
6520, -6527, 6529, -6538, 6545, -6551, 6555, -6563, 6570, -6578, 6580, -6595,
6598, -6615, 6620, -6632, 6635, -6643, 6646, -6653, 8139, -8358, 8882, -8923,
9276, -9317, 9490, -9549, 9639, -9642, 9648, -9649, 9655, 9942, -9987, 9998,
-10000, 10013, -10015, 10024, -10029, 10041, -10044, 10316, -10361, 10372,
-10374, 10387, -10389, 10398, -10403, 10415, -10418, 10690, -10735, 10746,
-10748, 10761, -10763, 10772, -10777, 10789, -10792, 10849, -10862, 10893,
10906, -10909, 10912, -10913, 10924, 10927, -10928, 10939, -11003, 11009,
-11023, 11034, -11037, 11043, -11046, 11054, -11062, 11067, -11154, 11158,
-11159, 11162, -11163, 11166, -11167, 11170, -11171, 11173, -11175, 11179,
-11180, 11183, -11184, 11187, -11188, 11191, -11192, 11274, -11287, 11359,
11361, -11363, 11368, -11371 ], [ 65, -142, 189, -212, 232, -235, 238, 243,
-250, 259, -269, 272, -290, 308, 311, 313, -314, 317, 320, -321, 325, 333,
-339, 354, -357, 360, 365, -372, 381, -391, 394, -412, 430, 433, 435, -436,
439, 442, -443, 447, 455, -461, 476, -479, 482, 487, -494, 503, -513, 516,
-534, 552, 555, 557, -558, 561, 564, -565, 569, 577, -583, 608, -631, 643,
-674, 735, -760, 772, -779, 782, 785, 790, 793, 802, -804, 815, -833, 836,
-837, 857, -863, 870, 875, -884, 888, 894, -895, 900, -901, 904, 906, 909,
-927, 930, -931, 951, -957, 964, 969, -978, 982, 988, -989, 994, -995, 998,
1000, -1038, 1717, -1758, 2459, -2506, 3721, 3725, -3726, 3991, -4011, 4188,
-4189, 4232, 4238, -4240, 4270, -4272, 4285, -4287, 4593, -4613, 4790, -4791,
4834, 4840, -4842, 4872, -4874, 4887, -4889, 5195, -5215, 5392, -5393, 5436,
5442, -5444, 5474, -5476, 5489, -5491, 5672, -5680, 5749, -5750, 5755, -5757,
5764, -5827, 5836, -5841, 5930, -5939, 6252, -6261, 6264, -6275, 6280, -6297,
6300, -6309, 6312, -6323, 6328, -6345, 6350, -6359, 6366, -6377, 6382, -6399,
6441, -6443, 6453, 6470, -6471, 6519, 6567, -6569, 6579, 6596, -6597, 6645,
9643, -9646, 9650, -9654, 9657, -9666, 10894, -10905, 10910, -10911, 10914,
-10923, 10925, -10926, 10929, -10938 ], [ 7, -24, 218, -222, 270, -271, 291,
-294, 340, -344, 392, -393, 413, -416, 462, -466, 514, -515, 535, -538, 632,
-636, 675, -678, 783, 786, -787, 791, 794, -795, 805, -807, 813, -814, 848,
-849, 907, -908, 942, -943, 3733, 3736, -3737, 5751, -5753, 5758, -5760 ], [
1, -6 ], [ 637, -642, 5681, -5747, 10863, -10892, 11355, -11358 ] ] ),
frattFacs := rec( frattFacs := [ 7, 13, 19, 25, 38, 44, 50, 56, 62, 68, 74,
80, 207, 213, 219, 225, 231, 237, 243, 249, 255, 261, 267, 273, 279, 285,
1138, 1144, 1150, 1156, 1162, 1168, 1174, 1180, 1186, 1192, 1198, 1204, 1210,
1216, 1222, 1228, 1234, 1240, 1246, 1252, 7121, 7127, 7133, 7139, 7145, 7151,
7157, 7163, 7169, 7175, 7181, 7187, 7193, 7199, 7205, 7211, 7217, 7223, 7229,
7235, 7241, 7247, 7253, 7259, 7265, 7271, 7277, 7283 ], pos := [ 1, 2, 3, 4,
5, 6, 215, 217, 339, 461, 583, 636, 639, 642, 779, 787, 795, 812, 906, 1000,
3720, 3737, 4339, 4941, 5543, 5680, 5725, 5747, 5748, 5754, 5761, 5835, 6250,
6298, 6346, 6401, 6402, 6528, 6654, 9638, 9666, 9672, 10046, 10420, 10794,
10862, 10883, 10892, 10893, 10908, 10909, 10924, 10939, 10994, 10997, 11000,
11003, 11066, 11087, 11108, 11115, 11122, 11143, 11148, 11151, 11172, 11193,
11273, 11282, 11287, 11307, 11327, 11347, 11354 ] ) );