prop1440.z

#############################################################################
##
#W  prop1440.z             GAP library of groups           Hans Ulrich Besche
##                                               Bettina Eick, Eamonn O'Brien
##

PROPERTIES_SMALL_GROUPS[ 1440 ] := rec(
isNilpotent := [ 4, 198, -216, 222, 919, -942, 1438, -1456, 1676, -1681, 4540
, -4563, 4589, 5835, -5840, 5958 ], 
isSupersolvable := [ 1, -73, 75, -253, 269, -653, 661, -945, 949, -1231, 1233
, -1456, 1478, -1508, 1543, -1621, 1631, -1681, 1697, -1814, 1950, -2520,
2558, -2632, 2708, -4102, 4110, -4563, 4573, 4581, -4583, 4586, -4589, 4719,
-4757, 4946, -5063, 5215, -5361, 5440, -5478, 5518, -5750, 5760, -5840, 5889,
5913, -5916, 5924, 5940, -5942, 5946, -5950, 5953, -5958 ], 
isSolvable := [ 1, -1681, 1694, -4589, 4657, -5840, 5855, -5958 ], 
isAbelian := [ 4, 199, 212, 222, 919, 934, 1439, 1452, 1676, 4540, 4555, 4589
, 5835, 5958 ], 
lgLength := rec( lgLength := [ 3, 4, 5, 6, 7, 8, false ], pos := [ [ 5924,
5947, -5950, 5953, 5956, -5958 ], [ 1079, 1121, 1187, 1229, 1232, 1267, 1390,
1431, 1438, 1748, 1779, 1804, 1835, 1860, 1882, 1907, 1929, 1939, 1947, 2166,
-2520, 2543, 2575, 2625, 2650, 2675, 2700, 3081, -3131, 3174, -3276, 3325,
-3377, 3401, -3428, 3453, -3512, 3541, -3572, 3611, -3661, 3704, -3806, 3855,
-3907, 3931, -3958, 3983, -4042, 4071, -4102, 4105, 4110, -4140, 4164, -4177,
4181, -4184, 4188, -4189, 4194, -4195, 4368, -4398, 4422, -4435, 4439, -4442,
4446, -4447, 4452, -4484, 4508, -4521, 4525, -4528, 4532, -4533, 4538, -4554,
4583, 4586, -4589, 4657, 4664, 4679, 4686, 4719, -4737, 4758, -4776, 4797,
-4805, 4923, -4924, 4977, -4980, 4989, -4996, 5005, -5011, 5020, -5027, 5036,
-5041, 5048, -5054, 5062, -5066, 5073, -5079, 5087, -5092, 5101, -5108, 5117,
-5122, 5129, -5134, 5141, -5147, 5157, -5165, 5175, -5180, 5187, -5192, 5199,
-5361, 5439, 5443, -5445, 5447, 5449, 5452, 5469, -5471, 5473, 5475, 5478,
5482, -5484, 5486, 5488, 5491, 5495, -5497, 5499, 5501, 5504, 5508, -5510,
5512, 5514, 5517, 5571, -5750, 5758, -5774, 5805, -5840, 5859, -5860, 5862,
5871, 5876, -5882, 5889, -5892, 5898, -5902, 5904, 5906, 5908, -5909, 5914,
-5923, 5927, -5928, 5931, -5933, 5936, 5939, -5940, 5942, -5946, 5951, -5952,
5954, -5955 ], [ 72, 74, 109, 150, 191, 198, 253, 268, 286, 311, 381, -421,
440, -552, 601, -653, 656, 661, -691, 715, -728, 732, -735, 739, -740, 745,
-777, 801, -809, 813, -819, 823, -826, 831, -863, 887, -895, 899, -905, 909,
-912, 917, -933, 1012, 1034, -1078, 1080, -1082, 1094, -1120, 1122, -1123,
1142, -1186, 1188, -1190, 1202, -1228, 1230, -1231, 1238, -1246, 1249, -1261,
1266, 1268, -1273, 1308, 1349, 1361, -1369, 1372, -1384, 1389, 1391, -1396,
1402, -1410, 1413, -1425, 1430, 1432, -1437, 1439, -1451, 1486, -1493, 1502,
-1508, 1542, 1546, -1548, 1550, 1552, 1555, 1559, -1561, 1563, 1565, 1568,
-1621, 1629, -1681, 1717, 1728, -1743, 1749, -1774, 1780, -1799, 1805, -1830,
1836, -1855, 1861, -1878, 1883, -1902, 1908, -1925, 1930, -1938, 1940, -1946,
1948, -2165, 2529, 2533, 2537, -2539, 2550, 2557, 2560, -2565, 2568, -2574,
2576, -2582, 2600, 2610, -2615, 2618, -2624, 2626, -2632, 2635, -2640, 2643,
-2649, 2651, -2657, 2660, -2665, 2668, -2674, 2676, -2682, 2685, -2690, 2693,
-2699, 2701, -2707, 2746, -2796, 2839, -2941, 2990, -3080, 3132, -3173, 3277,
-3324, 3378, -3400, 3429, -3452, 3513, -3540, 3573, -3610, 3662, -3703, 3807,
-3854, 3908, -3930, 3959, -3982, 4043, -4070, 4103, 4106, -4107, 4141, -4163,
4178, -4180, 4185, -4187, 4190, -4193, 4196, -4226, 4250, -4263, 4267, -4270,
4274, -4275, 4280, -4312, 4336, -4349, 4353, -4356, 4360, -4361, 4366, -4367,
4399, -4421, 4436, -4438, 4443, -4445, 4448, -4451, 4485, -4507, 4522, -4524,
4529, -4531, 4534, -4537, 4555, -4564, 4566, 4569, -4582, 4584, -4585, 4658,
-4663, 4665, -4678, 4680, -4685, 4687, -4695, 4700, -4702, 4707, -4718, 4738,
-4757, 4777, -4796, 4833, -4907, 4927, -4928, 4931, 4934, -4935, 4938, 4941,
-4942, 4945, -4949, 4958, -4965, 4974, -4976, 4981, -4988, 4997, -5004, 5012,
-5019, 5028, -5035, 5042, -5047, 5055, -5061, 5067, -5072, 5080, -5086, 5093,
-5100, 5109, -5116, 5123, -5128, 5135, -5140, 5148, -5156, 5166, -5174, 5181,
-5186, 5193, -5198, 5384, -5416, 5440, -5442, 5446, 5448, 5450, -5451, 5456,
-5458, 5460, 5462, 5465, -5468, 5472, 5474, 5476, -5477, 5479, -5481, 5485,
5487, 5489, -5490, 5492, -5494, 5498, 5500, 5502, -5503, 5505, -5507, 5511,
5513, 5515, -5516, 5518, -5570, 5751, -5757, 5775, -5804, 5855, -5858, 5861,
5863, -5864, 5866, -5869, 5874, -5875, 5883, -5888, 5894, -5895, 5897, 5903,
5905, 5907, 5910, -5913, 5925, -5926, 5929, -5930, 5934, -5935, 5937, -5938,
5941 ], [ 25, -71, 73, 80, -88, 91, -103, 108, 110, -115, 121, -129, 132,
-144, 149, 151, -156, 162, -170, 173, -185, 190, 192, -197, 199, -211, 227,
-252, 254, 258, 262, -264, 271, -276, 279, -285, 287, -293, 296, -301, 304,
-310, 312, -380, 422, -439, 553, -600, 654, 657, -658, 692, -714, 729, -731,
736, -738, 741, -744, 778, -800, 810, -812, 820, -822, 827, -830, 864, -886,
896, -898, 906, -908, 913, -916, 934, -942, 967, -1011, 1013, -1033, 1083,
-1093, 1124, -1141, 1191, -1201, 1233, -1237, 1247, -1248, 1262, -1265, 1279,
-1287, 1290, -1302, 1307, 1309, -1314, 1320, -1328, 1331, -1343, 1348, 1350,
-1360, 1370, -1371, 1385, -1388, 1397, -1401, 1411, -1412, 1426, -1429, 1452,
-1456, 1463, -1485, 1494, -1501, 1509, -1541, 1543, -1545, 1549, 1551, 1553,
-1554, 1556, -1558, 1562, 1564, 1566, -1567, 1622, -1628, 1697, -1712, 1718,
-1727, 1744, -1747, 1775, -1778, 1800, -1803, 1831, -1834, 1856, -1859, 1879,
-1881, 1903, -1906, 1926, -1928, 2521, 2525, 2530, -2532, 2534, -2536, 2540,
-2542, 2544, -2546, 2551, -2553, 2558, -2559, 2566, -2567, 2585, -2590, 2593,
-2599, 2601, -2609, 2616, -2617, 2633, -2634, 2641, -2642, 2658, -2659, 2666,
-2667, 2683, -2684, 2691, -2692, 2708, -2745, 2797, -2838, 2942, -2989, 4104,
4108, -4109, 4227, -4249, 4264, -4266, 4271, -4273, 4276, -4279, 4313, -4335,
4350, -4352, 4357, -4359, 4362, -4365, 4565, 4567, -4568, 4696, -4699, 4703,
-4706, 4809, -4814, 4818, -4832, 4908, -4922, 4925, -4926, 4929, -4930, 4932,
-4933, 4936, -4937, 4939, -4940, 4943, -4944, 4950, -4957, 4966, -4973, 5362,
-5383, 5417, -5438, 5453, -5455, 5459, 5461, 5463, -5464, 5865, 5870, 5872,
-5873, 5893, 5896 ], [ 7, -24, 75, -79, 89, -90, 104, -107, 116, -120, 130,
-131, 145, -148, 157, -161, 171, -172, 186, -189, 212, -217, 220, -226, 255,
-257, 259, -261, 265, -267, 269, -270, 277, -278, 294, -295, 302, -303, 655,
659, -660, 943, 945, -966, 1274, -1278, 1288, -1289, 1303, -1306, 1315, -1319
, 1329, -1330, 1344, -1347, 1457, -1462, 1694, -1696, 1713, -1716, 2522,
-2524, 2526, -2528, 2547, -2549, 2554, -2556, 2583, -2584, 2591, -2592, 4806,
-4808, 4815, -4817 ], [ 1, -6, 218, -219, 944 ], [ 1682, -1693, 4590, -4656,
5841, -5854 ] ] ),
frattFacs := rec( frattFacs := [ 11, 21, 31, 41, 62, 72, 82, 92, 102, 112,
122, 132, 53, 63, 73, 83, 93, 103, 364, 374, 384, 394, 404, 414, 424, 434,
444, 454, 464, 474, 205, 215, 225, 235, 245, 255, 265, 275, 285, 295, 305,
315, 325, 335, 345, 355, 365, 375, 1926, 1936, 1946, 1956, 1966, 1976, 1986,
1996, 2006, 2016, 2026, 2036, 2046, 2056, 2066, 2076, 2086, 1197, 1207, 1217,
1227, 1237, 1247, 1257, 1267, 1277, 1287, 1297, 1307, 1317, 1327, 1337, 1347,
1357, 1367, 1377, 1387, 1397, 1407, 1417, 1427, 1437, 1447, 1457, 1467, 1477,
1487, 1497, 1507, 1517, 1527, 1537, 1547, 1557, 1567, 1577, 1587, 1597, 1607,
1617, 1627, 11888, 11898, 11908, 11918, 11928, 11938, 11948, 11958, 11968,
11978, 11988, 11998, 12008, 12018, 12028, 12038, 12048, 12058, 12068, 12078,
12088, 12098, 12108, 12118, 12128, 12138, 7639, 7649, 7659, 7669, 7679, 7689,
7699, 7709, 7719, 7729, 7739, 7749, 7759, 7769, 7779, 7789, 7799, 7809, 7819,
7829, 7839, 7849, 7859, 7879, 7889, 7899, 7909, 7919, 7929, 7939, 7949, 7959,
7969, 7979, 7989, 7999, 8009, 8019, 8029, 8039, 8049, 8059, 8069, 8079, 8089,
8099, 8109, 8119, 8129, 8139, 8149, 8159, 8169, 8179, 8189, 8199, 8209, 8219,
8229, 8239, 8249, 8259, 8269, 8279, 8289, 8299, 8309, 8319, 8329, 8339, 8349,
8359, 8369, 8379, 8389, 8399, 8409 ], pos := [ 1, 2, 3, 4, 5, 6, 73, 74, 115,
156, 197, 216, 217, 218, 219, 220, 221, 222, 253, 257, 261, 268, 293, 318,
653, 660, 746, 832, 918, 942, 943, 944, 945, 946, 947, 948, 1015, 1082, 1123,
1190, 1231, 1232, 1273, 1314, 1355, 1396, 1437, 1456, 1459, 1462, 1477, 1508,
1519, 1530, 1541, 1542, 1555, 1568, 1621, 1628, 1630, 1645, 1660, 1675, 1681,
1684, 1687, 1690, 1693, 1694, 1695, 1696, 1727, 1758, 1789, 1814, 1845, 1870,
1888, 1917, 1935, 1940, 1949, 2520, 2524, 2528, 2532, 2536, 2543, 2550, 2557,
2582, 2607, 2632, 2657, 2682, 2707, 3042, 3377, 3572, 3907, 4102, 4109, 4195,
4281, 4367, 4453, 4539, 4563, 4564, 4565, 4566, 4567, 4568, 4569, 4570, 4571,
4572, 4573, 4574, 4575, 4576, 4577, 4578, 4579, 4580, 4581, 4582, 4583, 4584,
4585, 4586, 4587, 4588, 4589, 4591, 4594, 4595, 4598, 4613, 4616, 4627, 4638,
4649, 4656, 4663, 4678, 4685, 4692, 4699, 4706, 4709, 4712, 4715, 4718, 4757,
4796, 4805, 4808, 4811, 4814, 4817, 4832, 4847, 4862, 4877, 4892, 4907, 4922,
4924, 4931, 4938, 4945, 4976, 5007, 5038, 5063, 5088, 5119, 5142, 5177, 5200,
5205, 5214, 5361, 5372, 5383, 5394, 5405, 5416, 5427, 5438, 5439, 5452, 5465,
5478, 5491, 5504, 5517, 5570, 5623, 5660, 5713, 5750, 5757, 5759, 5774, 5789,
5804, 5819, 5834, 5840 ] ) );