prop1600.z

#############################################################################
##
#W  prop1600.z             GAP library of groups           Hans Ulrich Besche
##                                               Bettina Eick, Eamonn O'Brien
##

PROPERTIES_SMALL_GROUPS[ 1600 ] := rec(
isNilpotent := [ 2, 126, -178, 875, -1011, 1014, 1516, -1583, 1954, -2006,
2054, -2060, 5463, -5599, 5605, 9721, -9788, 10247, -10253, 10281 ], 
isSupersolvable := [ 1, -1014, 1016, -2006, 2013, -2060, 2062, -2295, 2383,
-5599, 5603, -5642, 5773, -6489, 6787, -9788, 9796, -9820, 9891, -10005,
10068, -10253, 10262, 10269, -10270, 10274, -10281 ], 
isAbelian := [ 2, 126, 150, 174, 875, 903, 1003, 1014, 1516, 1570, 1954, 1978
, 2002, 2054, 5463, 5491, 5591, 5605, 9721, 9775, 10247, 10281 ], 
lgLength := rec( lgLength := [ 2, 3, 4, 5, 6, 7, 8 ], pos := [ [ 10278,
-10279, 10281 ], [ 3584, -3595, 3688, -3836, 3887, -3930, 3932, 4224, -4226,
4229, -4257, 4861, -4892, 5142, -5151, 5153, -5169, 5171, -5176, 5182, -5198,
5204, -5209, 5423, -5428, 5434, -5436, 5438, 5443, -5444, 5446, 5462, -5490,
5604, -5605, 5704, -5740, 5823, -5827, 5954, -5972, 5975, -5988, 6061, -6066,
6115, -6116, 6145, -6150, 6153, -6158, 6187, 6231, -6235, 6325, -6343, 6345,
-6358, 6397, -6402, 6439, -6440, 6462, -6467, 6469, -6474, 6489, 6521, -6524,
6604, -6623, 6668, -6671, 6700, -6701, 6722, -6728, 6745, 6753, 6763, -6771,
6778, 6781, -6786, 6923, -6928, 6936, -6938, 6948, -6950, 7000, -7003, 7017,
-7018, 7028, 7038, 7049, -7054, 7062, -7064, 7074, -7076, 7126, -7129, 7143,
-7144, 7154, 7164, 7175, -7180, 7188, -7190, 7200, -7202, 7252, -7255, 7269,
-7270, 7280, 7290, -8106, 8215, -8252, 8281, -8632, 8639, -8647, 8653, -8702,
8707, 8710, -8730, 8738, -8804, 8811, -8816, 8822, -8846, 8853, -8858, 8866,
-8882, 8917, -8972, 9347, -9615, 9662, -9677, 9681, -9689, 9693, -9697, 9700,
-9702, 9707, -9714, 9719, -9774, 9796, 9806, -9809, 9819, -9820, 9833, -9868,
9891, -9895, 9907, -9916, 9919, -9923, 9926, -9932, 9939, -9947, 9963, -9972,
9977, -9981, 9986, -9992, 10002, -10009, 10021, -10027, 10031, -10033, 10037,
-10042, 10050, -10064, 10092, -10094, 10097, -10098, 10101, -10102, 10105,
-10106, 10109, 10113, -10115, 10118, -10119, 10122, -10123, 10126, -10127,
10130, 10134, -10136, 10139, -10140, 10143, -10144, 10147, -10148, 10151,
-10206, 10227, -10253, 10261, -10262, 10264, 10266, 10269, -10273, 10275,
-10277, 10280 ], [ 273, -304, 555, -581, 583, -588, 599, -621, 835, -840, 847
, -850, 856, -858, 874, -902, 1015, 1026, -1031, 1039, -1041, 1051, -1053,
1103, -1106, 1120, -1121, 1131, 1141, -1410, 1457, -1466, 1470, -1481, 1485,
-1492, 1499, -1509, 1514, -1569, 1599, -1622, 1667, -1693, 1708, -1709, 1837,
-1843, 1848, -1849, 1851, -1856, 1865, -1872, 1909, -1921, 1923, -1924, 1926,
1929, 1931, 1933, -1934, 1936, -1938, 1940, -1946, 1954, -1977, 2016, -2018,
2021, -2022, 2025, -2026, 2029, -2030, 2033, -2060, 2098, -2153, 2180, -2190,
2226, -2269, 2283, -2291, 2311, -2340, 2355, -2361, 2372, -2382, 2498, -2499,
2502, -2511, 2514, -2520, 2528, -2533, 2535, -2538, 2547, -2549, 2553, -2557,
2560, -2563, 2566, -2567, 2569, 2592, -2593, 2596, -2605, 2608, -2614, 2622,
-2627, 2629, -2632, 2641, -2643, 2647, -2651, 2654, -2657, 2660, -2661, 2663,
2684, -2685, 2688, -2697, 2700, -2706, 2714, -2719, 2721, -2724, 2733, -2735,
2739, -2743, 2746, -2749, 2752, -2753, 2755, 2780, -3151, 3176, -3555, 3596,
-3687, 3837, -3886, 3931, 3933, -4223, 4227, -4228, 4258, -4290, 4540, -4549,
4551, -4567, 4569, -4574, 4580, -4596, 4602, -4607, 4821, -4826, 4832, -4834,
4836, 4841, -4842, 4844, 4860, 4893, -5113, 5135, -5141, 5152, 5170, 5177,
-5181, 5199, -5203, 5210, -5310, 5313, -5354, 5356, -5367, 5371, -5399, 5403,
-5409, 5413, -5422, 5429, -5433, 5437, 5439, -5442, 5445, 5447, -5461, 5491,
-5590, 5601, -5603, 5606, -5615, 5631, -5647, 5652, -5654, 5658, -5703, 5741,
-5745, 5748, -5751, 5758, 5765, -5766, 5768, 5770, 5779, -5822, 5828, -5943,
5973, -5974, 5989, -6060, 6067, -6114, 6117, -6144, 6151, -6152, 6159, -6186,
6193, -6230, 6236, -6319, 6344, 6359, -6396, 6403, -6438, 6441, -6461, 6468,
6475, -6488, 6496, -6520, 6525, -6597, 6624, -6667, 6672, -6699, 6702, -6721,
6729, -6744, 6746, -6752, 6754, -6762, 6772, -6777, 6779, -6780, 6797, -6802,
6810, -6812, 6822, -6824, 6874, -6877, 6891, -6892, 6902, 6912, -6922, 6929,
-6935, 6939, -6947, 6954, -6962, 6964, -6979, 6982, -6999, 7004, -7016, 7019,
-7027, 7030, -7037, 7039, -7048, 7055, -7061, 7065, -7073, 7080, -7088, 7090,
-7105, 7108, -7125, 7130, -7142, 7145, -7153, 7156, -7163, 7165, -7174, 7181,
-7187, 7191, -7199, 7206, -7214, 7216, -7231, 7234, -7251, 7256, -7268, 7271,
-7279, 7282, -7289, 8107, -8214, 8253, -8280, 8633, -8638, 8648, -8652, 8703,
-8706, 8708, -8709, 8731, -8737, 8805, -8810, 8817, -8821, 8847, -8852, 8859,
-8865, 8883, -8916, 8973, -9241, 9288, -9303, 9307, -9315, 9319, -9323, 9326,
-9328, 9333, -9340, 9345, -9346, 9616, -9661, 9678, -9680, 9690, -9692, 9698,
-9699, 9703, -9706, 9715, -9718, 9775, -9795, 9797, -9805, 9810, -9818, 9821,
-9832, 9872, -9874, 9881, -9883, 9885, 9887, 9890, 9896, -9906, 9917, -9918,
9924, -9925, 9933, -9938, 9948, -9962, 9973, -9976, 9982, -9985, 9993, -10001
, 10010, -10020, 10028, -10030, 10034, -10036, 10043, -10049, 10065, -10067,
10071, -10073, 10076, -10077, 10080, -10081, 10084, -10085, 10088, -10091,
10095, -10096, 10099, -10100, 10103, -10104, 10107, -10108, 10110, -10112,
10116, -10117, 10120, -10121, 10124, -10125, 10128, -10129, 10131, -10133,
10137, -10138, 10141, -10142, 10145, -10146, 10149, -10150, 10207, -10226,
10254, -10255, 10258, -10260, 10263, 10265, 10267, -10268, 10274 ], [ 9, -15,
20, -21, 23, -28, 37, -44, 81, -93, 95, -96, 98, 101, -102, 104, -105, 108,
-110, 112, -118, 126, -149, 200, -201, 204, -213, 223, -235, 237, -240, 252,
-257, 259, -261, 263, 265, -267, 269, 272, 305, -525, 547, -554, 582, 589,
-598, 622, -722, 725, -766, 768, -772, 776, -804, 808, -819, 823, -834, 841,
-846, 851, -855, 859, -873, 903, -1002, 1016, -1025, 1032, -1038, 1042, -1050
, 1057, -1065, 1067, -1082, 1085, -1102, 1107, -1119, 1122, -1130, 1133,
-1140, 1411, -1456, 1467, -1469, 1482, -1484, 1493, -1498, 1510, -1513, 1570,
-1583, 1623, -1666, 1694, -1707, 1715, -1721, 1726, -1727, 1729, -1734, 1743,
-1750, 1787, -1799, 1801, -1802, 1804, 1807, 1809, 1811, -1812, 1814, -1816,
1818, -1824, 1844, -1847, 1850, 1857, -1864, 1873, -1883, 1886, -1904, 1922,
1925, 1927, -1928, 1930, 1932, 1935, 1939, 1947, -1953, 1978, -2001, 2007,
-2015, 2019, -2020, 2023, -2024, 2027, -2028, 2031, -2032, 2062, -2093, 2154,
-2179, 2191, -2223, 2270, -2282, 2292, -2307, 2341, -2354, 2362, -2371, 2404,
-2405, 2408, -2417, 2420, -2426, 2434, -2439, 2441, -2444, 2453, -2455, 2459,
-2463, 2466, -2469, 2472, -2473, 2475, 2479, -2497, 2500, -2501, 2521, -2527,
2534, 2539, -2546, 2550, -2552, 2558, -2559, 2564, -2565, 2568, 2570, 2573,
-2591, 2594, -2595, 2615, -2621, 2628, 2633, -2640, 2644, -2646, 2652, -2653,
2658, -2659, 2662, 2664, 2667, -2683, 2686, -2687, 2707, -2713, 2720, 2725,
-2732, 2736, -2738, 2744, -2745, 2750, -2751, 2754, 2756, -2779, 3152, -3175,
3556, -3583, 4291, -4511, 4533, -4539, 4550, 4568, 4575, -4579, 4597, -4601,
4608, -4708, 4711, -4752, 4754, -4765, 4769, -4797, 4801, -4807, 4811, -4820,
4827, -4831, 4835, 4837, -4840, 4843, 4845, -4859, 5114, -5134, 5311, -5312,
5355, 5368, -5370, 5400, -5402, 5410, -5412, 5591, -5600, 5616, -5630, 5648,
-5651, 5655, -5657, 5752, -5755, 5759, -5764, 5767, 5769, 5771, -5778, 5944,
-5953, 6188, -6192, 6320, -6324, 6490, -6495, 6598, -6603, 6787, -6796, 6803,
-6809, 6813, -6821, 6828, -6836, 6838, -6853, 6856, -6873, 6878, -6890, 6893,
-6901, 6904, -6911, 6951, -6953, 6963, 6980, -6981, 7029, 7077, -7079, 7089,
7106, -7107, 7155, 7203, -7205, 7215, 7232, -7233, 7281, 9242, -9287, 9304,
-9306, 9316, -9318, 9324, -9325, 9329, -9332, 9341, -9344, 9869, -9871, 9875,
-9880, 9884, 9886, 9888, -9889, 10068, -10070, 10074, -10075, 10078, -10079,
10082, -10083, 10086, -10087, 10256, -10257 ], [ 16, -19, 22, 29, -36, 45,
-55, 58, -76, 94, 97, 99, -100, 103, 106, -107, 111, 119, -125, 150, -173,
181, -199, 202, -203, 216, -222, 236, 241, -251, 258, 262, 264, 268, 270,
-271, 526, -546, 723, -724, 767, 773, -775, 805, -807, 820, -822, 1003, -1011
, 1054, -1056, 1066, 1083, -1084, 1132, 1588, -1598, 1722, -1725, 1728, 1735,
-1742, 1751, -1761, 1764, -1782, 1800, 1803, 1805, -1806, 1808, 1810, 1813,
1817, 1825, -1836, 1884, -1885, 1905, -1908, 2002, -2006, 2094, -2097, 2224,
-2225, 2308, -2310, 2385, -2403, 2406, -2407, 2427, -2433, 2440, 2445, -2452,
2456, -2458, 2464, -2465, 2470, -2471, 2474, 2476, -2478, 2512, -2513, 2571,
-2572, 2606, -2607, 2665, -2666, 2698, -2699, 4512, -4532, 4709, -4710, 4753,
4766, -4768, 4798, -4800, 4808, -4810, 5746, -5747, 5756, -5757, 6825, -6827,
6837, 6854, -6855, 6903 ], [ 4, -8, 56, -57, 77, -80, 174, -180, 214, -215,
1013, -1014, 1585, -1587, 1710, -1714, 1762, -1763, 1783, -1786, 2061, 2383,
-2384, 2418, -2419 ], [ 1, -3, 1012, 1584 ] ] ),
frattFacs := rec( frattFacs := [ 13, 25, 38, 50, 62, 147, 159, 171, 40, 52,
64, 593, 605, 617, 629, 114, 126, 138, 150, 162, 174, 186, 198, 2815, 2827,
2839, 2851, 2863, 488, 500, 512, 524, 536, 548, 560, 572, 584, 596, 608, 620,
632, 19629, 19641, 19653, 19665, 19677, 19689, 2470, 2482, 2494, 2506, 2518,
2530, 2542, 2554, 2566, 2578, 2590, 2602, 2614, 2626, 2638, 2650, 2662, 14303
, 14315, 14327, 14339, 14351, 14363, 14375, 14387, 14399, 14411, 14423, 14435
, 14447, 14459, 14471, 14483, 14495, 14507, 14519, 14531, 14543 ], pos := [ 1
, 2, 3, 125, 178, 272, 874, 1011, 1012, 1013, 1014, 1015, 1141, 1515, 1583,
1584, 1585, 1586, 1587, 1709, 1831, 1953, 2006, 2009, 2012, 2033, 2053, 2060,
2061, 2198, 2295, 2365, 2382, 2476, 2570, 2664, 2756, 4258, 4860, 5462, 5599,
5600, 5601, 5602, 5603, 5604, 5605, 5642, 5657, 5745, 5772, 6187, 6489, 6745,
6785, 6786, 6912, 7038, 7164, 7290, 8972, 9346, 9720, 9788, 9795, 9820, 9832,
9868, 9871, 9874, 9877, 9890, 9942, 10005, 10052, 10064, 10067, 10088, 10109,
10130, 10151, 10206, 10226, 10246, 10253 ] ) );