prop576.z

#############################################################################
##
#W  prop576.z              GAP library of groups           Hans Ulrich Besche
##                                               Bettina Eick, Eamonn O'Brien
##

PROPERTIES_SMALL_GROUPS[ 576 ] := rec(
isNilpotent := [ 2, 127, -179, 182, 810, -946, 1316, -1368, 1825, -1892, 4829
, -4965, 5028, -5034, 8194, -8261, 8268, 8645, -8651, 8681 ], 
isSupersolvable := [ 1, -2, 5, -182, 208, -946, 948, -1069, 1072, -1368, 1451
, -1892, 2106, -3607, 3625, -4965, 5008, -5034, 5730, -7411, 7446, -8261,
8267, -8268, 8536, -8590, 8605, -8651, 8675, 8679, -8681 ], 
isAbelian := [ 2, 127, 151, 175, 182, 810, 838, 938, 1316, 1340, 1364, 1825,
1879, 4829, 4857, 4957, 5028, 8194, 8248, 8268, 8645, 8681 ], 
lgLength := rec( lgLength := [ 2, 3, 4, 5, 6, 7, 8 ], pos := [ [ 8663, -8664,
8675, 8678, 8680, -8681 ], [ 3073, -3112, 3115, -3279, 3281, 3573, -3579,
3582, -3606, 4227, -4258, 4509, -4534, 4536, -4542, 4553, -4575, 4789, -4794,
4801, -4804, 4810, -4812, 4828, -4856, 5126, -5129, 5220, -5226, 5279, -5295,
5335, -5338, 5367, -5370, 5394, -5398, 5412, 5427, 5430, -5438, 5445, 5448,
-5452, 5512, 5614, -5619, 5627, -5629, 5639, -5641, 5691, -5694, 5708, -5709,
5719, 5729, -6545, 6682, -6973, 6998, -7195, 7220, -7321, 7356, -7411, 7420,
7429, 7440, -7445, 7820, -8088, 8135, -8144, 8148, -8159, 8163, -8170, 8177,
-8187, 8192, -8247, 8266, -8268, 8374, -8377, 8389, -8395, 8399, -8401, 8405,
-8410, 8418, -8432, 8518, -8520, 8523, -8524, 8527, -8528, 8531, -8532, 8535,
-8590, 8625, -8651, 8653, -8654, 8657, 8659, -8662, 8666, -8667, 8669, 8671,
8674, 8676, -8677, 8679 ], [ 208, -239, 490, -515, 517, -523, 534, -556, 770,
-775, 782, -785, 791, -793, 809, -837, 959, -982, 1027, -1053, 1068, -1071,
1199, -1207, 1212, -1213, 1215, -1218, 1227, -1234, 1271, -1283, 1285, -1286,
1288, 1291, -1292, 1294, -1295, 1298, -1300, 1302, -1308, 1316, -1339, 1380,
1425, 1434, 1445, -1719, 1766, -1775, 1779, -1790, 1794, -1801, 1808, -1818,
1823, -1878, 1909, -1938, 1953, -1959, 1970, -1980, 1989, -1990, 1993, 2033,
-2034, 2037, -2046, 2049, -2055, 2063, -2068, 2070, -2073, 2084, -2086, 2088,
-2092, 2095, -2098, 2101, -2102, 2104, 2129, -2500, 2525, -2904, 2933, -3072,
3113, -3114, 3280, 3282, -3572, 3580, -3581, 3607, 3609, -3611, 3614, -3619,
3621, -3622, 3625, -3656, 3907, -3932, 3934, -3940, 3951, -3973, 4187, -4192,
4199, -4202, 4208, -4210, 4226, 4259, -4479, 4501, -4508, 4535, 4543, -4552,
4576, -4676, 4679, -4720, 4722, -4726, 4730, -4758, 4762, -4773, 4777, -4788,
4795, -4800, 4805, -4809, 4813, -4827, 4857, -4956, 5008, -5041, 5046, -5048,
5053, -5054, 5119, -5125, 5132, -5135, 5142, 5149, -5150, 5152, 5154, 5163,
-5213, 5227, -5278, 5296, -5334, 5339, -5366, 5371, -5393, 5399, -5411, 5413,
-5426, 5428, -5429, 5439, -5444, 5446, -5447, 5464, 5501, 5513, 5526, -5529,
5548, 5562, -5563, 5603, -5613, 5620, -5626, 5630, -5638, 5645, -5653, 5655,
-5670, 5673, -5690, 5695, -5707, 5710, -5718, 5721, -5728, 6546, -6681, 6974,
-6997, 7196, -7219, 7322, -7355, 7412, -7415, 7421, -7422, 7428, 7446, -7714,
7761, -7770, 7774, -7785, 7789, -7796, 7803, -7813, 7818, -7819, 8089, -8134,
8145, -8147, 8160, -8162, 8171, -8176, 8188, -8191, 8248, -8265, 8279, -8360,
8364, -8366, 8368, 8370, 8373, 8378, -8388, 8396, -8398, 8402, -8404, 8411,
-8417, 8454, -8474, 8482, -8488, 8515, -8517, 8521, -8522, 8525, -8526, 8529,
-8530, 8533, -8534, 8591, -8624, 8652, 8656, 8658, 8665, 8668, 8670, 8672,
-8673 ], [ 3, -4, 10, -18, 23, -24, 26, -29, 38, -45, 82, -94, 96, -97, 99,
102, -103, 105, -106, 109, -111, 113, -119, 127, -150, 183, -184, 187, 192,
-194, 197, -202, 204, -205, 240, -460, 482, -489, 516, 524, -533, 557, -657,
660, -701, 703, -707, 711, -739, 743, -754, 758, -769, 776, -781, 786, -790,
794, -808, 838, -937, 983, -1026, 1054, -1067, 1077, -1085, 1090, -1091, 1093
, -1096, 1105, -1112, 1149, -1161, 1163, -1164, 1166, 1169, -1170, 1172,
-1173, 1176, -1178, 1180, -1186, 1208, -1211, 1214, 1219, -1226, 1235, -1245,
1248, -1266, 1284, 1287, 1289, -1290, 1293, 1296, -1297, 1301, 1309, -1315,
1340, -1363, 1369, 1381, 1394, -1397, 1416, -1420, 1426, -1427, 1433, 1720,
-1765, 1776, -1778, 1791, -1793, 1802, -1807, 1819, -1822, 1879, -1892, 1894,
-1905, 1939, -1952, 1960, -1969, 1981, -1982, 1985, 1991, 1994, 1997, -2002,
2009, -2013, 2016, -2032, 2035, -2036, 2056, -2062, 2069, 2074, -2083, 2087,
2093, -2094, 2099, -2100, 2103, 2105, -2128, 2501, -2524, 2905, -2932, 3608,
3612, -3613, 3657, -3877, 3899, -3906, 3933, 3941, -3950, 3974, -4074, 4077,
-4118, 4120, -4124, 4128, -4156, 4160, -4171, 4175, -4186, 4193, -4198, 4203,
-4207, 4211, -4225, 4480, -4500, 4677, -4678, 4721, 4727, -4729, 4759, -4761,
4774, -4776, 4957, -5007, 5042, -5045, 5049, -5052, 5055, -5118, 5136, -5139,
5143, -5148, 5151, 5153, 5155, -5162, 5214, -5219, 5453, 5465, 5478, -5481,
5500, 5502, -5511, 5514, -5525, 5530, -5547, 5549, -5551, 5564, -5567, 5580,
-5583, 5602, 5642, -5644, 5654, 5671, -5672, 5720, 7416, -7419, 7423, -7427,
7430, -7439, 7715, -7760, 7771, -7773, 7786, -7788, 7797, -7802, 7814, -7817,
8276, -8278, 8361, -8363, 8367, 8369, 8371, -8372, 8433, -8453, 8475, -8481,
8489, -8514, 8655 ], [ 19, -22, 25, 30, -37, 46, -56, 59, -77, 95, 98, 100,
-101, 104, 107, -108, 112, 120, -126, 151, -174, 185, 188, 191, 195, -196,
461, -481, 658, -659, 702, 708, -710, 740, -742, 755, -757, 938, -946, 948,
-958, 1086, -1089, 1092, 1097, -1104, 1113, -1123, 1126, -1144, 1162, 1165,
1167, -1168, 1171, 1174, -1175, 1179, 1187, -1198, 1246, -1247, 1267, -1270,
1364, -1368, 1370, -1379, 1382, -1393, 1398, -1415, 1421, -1424, 1428, -1432,
1435, -1444, 1906, -1908, 1983, 1986, 1992, 1995, -1996, 2003, -2005, 2014,
-2015, 2047, -2048, 3620, 3623, -3624, 3878, -3898, 4075, -4076, 4119, 4125,
-4127, 4157, -4159, 4172, -4174, 5130, -5131, 5140, -5141, 5454, -5463, 5466,
-5477, 5482, -5499, 5552, -5561, 5568, -5579, 5584, -5601, 8269, -8275 ], [ 5
, -9, 57, -58, 78, -81, 175, -179, 181, -182, 186, 189, -190, 203, 206, -207,
947, 1072, -1076, 1124, -1125, 1145, -1148, 1893, 1984, 1987, -1988, 2006,
-2008 ], [ 1, -2, 180 ] ] ),
frattFacs := rec( frattFacs := [ 13, 25, 38, 50, 62, 39, 51, 63, 148, 160,
172, 184, 113, 125, 137, 149, 161, 173, 582, 594, 606, 618, 630, 475, 487,
499, 511, 523, 535, 547, 559, 571, 583, 595, 607, 2720, 2732, 2744, 2756,
2768, 2780, 2193, 2205, 2217, 2229, 2241, 2253, 2265, 2277, 2289, 2301, 2313,
2325, 2337, 2349, 2361, 2373, 18454, 18466, 18478, 18490, 18502, 18514, 18526
, 12299, 12311, 12323, 12335, 12347, 12359, 12371, 12383, 12395, 12407, 12419
, 12431, 12443, 12455, 12467, 12479, 12491, 12503, 12515, 12527, 12539, 12551
], pos := [ 1, 2, 4, 126, 179, 180, 181, 182, 190, 207, 809, 946, 947, 1069,
1071, 1193, 1315, 1368, 1416, 1444, 1450, 1824, 1892, 1893, 1963, 1980, 1988,
1996, 2013, 2105, 3607, 3624, 4226, 4828, 4965, 4986, 4993, 5002, 5007, 5027,
5034, 5052, 5126, 5129, 5156, 5412, 5452, 5500, 5548, 5603, 5729, 7411, 7439,
7445, 7819, 8193, 8261, 8262, 8263, 8264, 8265, 8266, 8267, 8268, 8275, 8278,
8283, 8300, 8355, 8360, 8373, 8420, 8432, 8453, 8474, 8481, 8488, 8509, 8514,
8535, 8590, 8599, 8604, 8624, 8644, 8651 ] ) );