prop1344.z

#############################################################################
##
#W  prop1344.z             GAP library of groups           Hans Ulrich Besche
##                                               Bettina Eick, Eamonn O'Brien
##

PROPERTIES_SMALL_GROUPS[ 1344 ] := rec(
isNilpotent := [ 6, 761, -813, 6174, -6310, 11220, -11287, 11677, -11683,
11720 ], 
isSupersolvable := [ 1, -390, 395, -813, 835, -1436, 1474, -4330, 4368, -6310
, 6490, -6863, 6977, -10028, 10098, -11287, 11430, -11449, 11502, -11588,
11617, -11683, 11704, 11709, -11710, 11717, -11720 ], 
isSolvable := [ 1, -813, 815, -6310, 6317, -11287, 11306, -11683, 11687,
-11720 ], 
isAbelian := [ 6, 761, 785, 809, 6174, 6202, 6302, 11220, 11274, 11677, 11720
], 
lgLength := rec( lgLength := [ 3, 4, 5, 6, 7, 8, false ], pos := [ [ 11690,
-11691, 11693, 11698, -11699, 11704, 11709, -11710, 11715, -11720 ], [ 815,
-818, 835, -866, 1116, -1125, 1127, -1143, 1145, -1150, 1156, -1172, 1178,
-1183, 1397, -1402, 1408, -1410, 1412, 1417, -1418, 1420, 1436, 2980, -3000,
3166, -3438, 3532, -3606, 3608, 4137, -4140, 4144, -4192, 4194, -4221, 4368,
-4399, 4649, -4658, 4660, -4676, 4678, -4683, 4689, -4705, 4711, -4716, 4930,
-4935, 4941, -4943, 4945, 4950, -4951, 4953, 4969, -5001, 5251, -5260, 5262,
-5278, 5280, -5285, 5291, -5307, 5313, -5318, 5532, -5537, 5543, -5545, 5547,
5552, -5553, 5555, 5571, -5603, 5853, -5862, 5864, -5880, 5882, -5887, 5893,
-5909, 5915, -5920, 6134, -6139, 6145, -6147, 6149, 6154, -6155, 6157, 6173,
-6201, 6392, 6405, 6453, 6490, -6758, 6805, -6820, 6824, -6832, 6836, -6840,
6843, -6845, 6850, -6857, 6862, -6863, 6877, -6878, 6918, 6933, -6934, 6976,
-8460, 8633, -8701, 8750, -9383, 9390, -9398, 9405, -9411, 9418, -9504, 9509,
9513, 9516, -9552, 9568, -9682, 9689, -9694, 9701, -9704, 9711, -9753, 9763,
-9770, 9786, -9811, 9872, -10014, 10037, 10046, 10065, 10075, 10086, -10366,
10413, -10428, 10432, -10440, 10444, -10448, 10451, -10453, 10458, -10465,
10470, -10740, 10787, -10802, 10806, -10814, 10818, -10822, 10825, -10827,
10832, -10839, 10844, -11114, 11161, -11176, 11180, -11188, 11192, -11196,
11199, -11201, 11206, -11213, 11218, -11273, 11310, 11430, -11449, 11502,
-11588, 11617, -11683, 11688, 11692, 11694, -11697, 11700, -11703, 11705,
-11708, 11711, -11714 ], [ 12, -18, 23, -24, 26, -31, 40, -47, 84, -96, 98,
-99, 101, 104, 106, 108, -109, 111, -113, 115, -121, 147, -186, 265, -310,
335, -361, 391, -394, 400, -406, 411, -412, 414, -419, 428, -435, 472, -484,
486, -487, 489, 492, 494, 496, -497, 499, -501, 503, -509, 522, -528, 533,
-534, 536, -541, 550, -557, 594, -606, 608, -609, 611, 614, 616, 618, -619,
621, -623, 625, -631, 644, -650, 655, -656, 658, -663, 672, -679, 716, -728,
730, -731, 733, 736, 738, 740, -741, 743, -745, 747, -753, 761, -784, 819,
-820, 823, 827, -828, 831, 867, -1087, 1109, -1115, 1126, 1144, 1151, -1155,
1173, -1177, 1184, -1284, 1287, -1328, 1330, -1341, 1345, -1373, 1377, -1383,
1387, -1396, 1403, -1407, 1411, 1413, -1416, 1419, 1421, -1435, 1437, -1442,
1449, -1461, 1469, -1473, 1512, -2189, 2232, -2931, 3001, -3165, 3439, -3531,
3607, 3609, -4136, 4141, -4143, 4193, 4222, -4321, 4332, -4334, 4337, -4342,
4344, -4345, 4349, -4351, 4355, -4362, 4364, -4365, 4400, -4620, 4642, -4648,
4659, 4677, 4684, -4688, 4706, -4710, 4717, -4817, 4820, -4861, 4863, -4874,
4878, -4906, 4910, -4916, 4920, -4929, 4936, -4940, 4944, 4946, -4949, 4952,
4954, -4968, 5002, -5222, 5244, -5250, 5261, 5279, 5286, -5290, 5308, -5312,
5319, -5419, 5422, -5463, 5465, -5476, 5480, -5508, 5512, -5518, 5522, -5531,
5538, -5542, 5546, 5548, -5551, 5554, 5556, -5570, 5604, -5824, 5846, -5852,
5863, 5881, 5888, -5892, 5910, -5914, 5921, -6021, 6024, -6065, 6067, -6078,
6082, -6110, 6114, -6120, 6124, -6133, 6140, -6144, 6148, 6150, -6153, 6156,
6158, -6172, 6202, -6301, 6319, -6320, 6385, -6391, 6394, 6406, 6419, -6422,
6441, -6442, 6454, 6467, -6470, 6489, 6759, -6804, 6821, -6823, 6833, -6835,
6841, -6842, 6846, -6849, 6858, -6861, 6864, -6866, 6879, -6882, 6895, -6898,
6917, 6919, -6922, 6935, -6940, 6953, -6956, 6975, 8461, -8632, 8702, -8749,
9384, -9389, 9399, -9404, 9412, -9417, 9505, -9508, 9510, -9512, 9514, -9515,
9553, -9567, 9683, -9688, 9695, -9700, 9705, -9710, 9754, -9762, 9771, -9785,
9812, -9871, 10015, -10032, 10038, -10039, 10045, 10057, -10060, 10066,
-10068, 10074, 10367, -10412, 10429, -10431, 10441, -10443, 10449, -10450,
10454, -10457, 10466, -10469, 10741, -10786, 10803, -10805, 10815, -10817,
10823, -10824, 10828, -10831, 10840, -10843, 11115, -11160, 11177, -11179,
11189, -11191, 11197, -11198, 11202, -11205, 11214, -11217, 11274, -11287,
11306, -11309, 11311, -11429, 11450, -11501, 11589, -11616, 11687, 11689 ], [
19, -22, 25, 32, -39, 48, -58, 61, -79, 97, 100, 102, -103, 105, 107, 110,
114, 122, -128, 187, -264, 311, -334, 362, -385, 407, -410, 413, 420, -427,
436, -446, 449, -467, 485, 488, 490, -491, 493, 495, 498, 502, 510, -516, 529
, -532, 535, 542, -549, 558, -568, 571, -589, 607, 610, 612, -613, 615, 617,
620, 624, 632, -638, 651, -654, 657, 664, -671, 680, -690, 693, -711, 729,
732, 734, -735, 737, 739, 742, 746, 754, -760, 785, -808, 821, 824, 829, 832,
1088, -1108, 1285, -1286, 1329, 1342, -1344, 1374, -1376, 1384, -1386, 1443,
-1445, 1462, -1465, 1474, -1511, 2190, -2231, 2932, -2979, 4322, -4331, 4335,
-4336, 4348, 4352, -4354, 4621, -4641, 4818, -4819, 4862, 4875, -4877, 4907,
-4909, 4917, -4919, 5223, -5243, 5420, -5421, 5464, 5477, -5479, 5509, -5511,
5519, -5521, 5825, -5845, 6022, -6023, 6066, 6079, -6081, 6111, -6113, 6121,
-6123, 6302, -6310, 6317, -6318, 6321, -6384, 6393, 6395, -6404, 6407, -6418,
6423, -6440, 6443, -6452, 6455, -6466, 6471, -6488, 6867, -6876, 6883, -6894,
6899, -6916, 6923, -6932, 6941, -6952, 6957, -6974, 10033, -10036, 10040,
-10044, 10047, -10056, 10061, -10064, 10069, -10073, 10076, -10085 ], [ 7,
-11, 59, -60, 80, -83, 129, -146, 386, -390, 395, -399, 447, -448, 468, -471,
517, -521, 569, -570, 590, -593, 639, -643, 691, -692, 712, -715, 809, -813,
822, 825, -826, 830, 833, -834, 1446, -1448, 1466, -1468, 4343, 4346, -4347,
4363, 4366, -4367 ], [ 1, -6 ], [ 814, 6311, -6316, 11288, -11305, 11684,
-11686 ] ] ),
frattFacs := rec( frattFacs := [ 7, 13, 19, 25, 31, 37, 44, 50, 56, 62, 68,
74, 80, 86, 92, 255, 261, 267, 273, 279, 285, 291, 297, 303, 309, 315, 321,
327, 333, 339, 345, 1252, 1258, 1264, 1270, 1276, 1282, 1288, 1294, 1300,
1306, 1312, 1318, 1324, 1330, 1336, 1342, 1348, 1354, 1360, 1366, 1372, 7529,
7535, 7541, 7547, 7553, 7559, 7565, 7571, 7577, 7583, 7589, 7595, 7601, 7607,
7613, 7619, 7625, 7631, 7637, 7643, 7649, 7655, 7661, 7667, 7673, 7679, 7685
], pos := [ 1, 2, 3, 4, 5, 6, 128, 337, 390, 392, 394, 516, 638, 760, 813,
814, 816, 818, 826, 834, 1436, 1453, 1473, 4193, 4330, 4347, 4367, 4969, 5571
, 6173, 6310, 6313, 6316, 6317, 6318, 6392, 6393, 6441, 6489, 6863, 6918,
6976, 9960, 10028, 10056, 10085, 10091, 10097, 10471, 10845, 11219, 11287,
11298, 11305, 11308, 11309, 11310, 11315, 11370, 11373, 11394, 11415, 11422,
11429, 11449, 11470, 11491, 11496, 11501, 11581, 11588, 11597, 11606, 11611,
11616, 11636, 11656, 11676, 11683 ] ) );