prop864.z

#############################################################################
##
#W  prop864.z              GAP library of groups           Hans Ulrich Besche
##                                               Bettina Eick, Eamonn O'Brien
##

PROPERTIES_SMALL_GROUPS[ 864 ] := rec(
isNilpotent := [ 2, 45, -63, 70, -72, 170, -193, 554, -610, 646, -651, 655,
1844, -1915, 1921, 2175, -2193, 2648, -2665, 3962, -3985, 4050, -4052, 4655,
-4660, 4725 ], 
isSupersolvable := [ 1, -2, 4, -72, 84, -193, 195, -302, 308, -610, 631, -655
, 762, -1291, 1328, -1915, 1920, -1921, 1924, -2050, 2052, -2193, 2423, -2512
, 2558, -2665, 2779, -3004, 3081, -3696, 3704, -3985, 4032, -4033, 4044,
-4052, 4337, -4407, 4489, -4600, 4610, -4660, 4704, 4717, -4719, 4722, -4725
], 
isAbelian := [ 2, 46, 59, 70, 170, 185, 557, 596, 646, 655, 1844, 1889, 1921,
2176, 2189, 2648, 3962, 3977, 4050, 4655, 4725 ], 
lgLength := rec( lgLength := [ 2, 3, 4, 5, 6, 7, 8 ], pos := [ [ 4704, 4718,
-4719, 4724, -4725 ], [ 2028, 2049, 2051, 2168, 2175, 2689, 2736, 2758, 2776,
2865, -3004, 3073, 3356, -3509, 3558, -3610, 3632, -3668, 3681, -3696, 3699,
3876, -3906, 3930, -3938, 3942, -3948, 3952, -3955, 3960, -3976, 4032, -4033,
4046, 4048, -4052, 4074, -4092, 4113, -4121, 4195, -4196, 4211, -4214, 4223,
-4230, 4239, -4241, 4265, -4269, 4279, -4287, 4297, -4302, 4309, -4314, 4321,
-4322, 4328, -4407, 4479, -4481, 4483, 4485, 4488, 4526, -4600, 4608, -4609,
4640, -4660, 4673, 4679, 4686, -4687, 4691, -4693, 4695, 4698, 4700, -4701,
4703, 4707, 4710, 4716, -4717, 4720, -4723 ], [ 298, 301, 303, -307, 445, 539
, 541, 554, -556, 674, 678, 736, 754, 865, -1018, 1043, -1130, 1207, -1291,
1296, -1297, 1313, -1315, 1346, -1354, 1384, -1393, 1428, -1439, 1560, -1568,
1603, -1609, 1637, -1640, 1668, -1669, 1672, -1733, 1778, -1786, 1789, -1797,
1801, -1807, 1811, -1817, 1821, -1824, 1828, -1831, 1840, -1888, 1920, -1921,
1962, 1983, -2027, 2029, -2031, 2037, -2048, 2050, 2086, 2127, 2139, -2147,
2150, -2162, 2167, 2169, -2174, 2176, -2188, 2242, -2253, 2267, -2272, 2279,
-2288, 2413, -2415, 2417, 2419, 2422, -2512, 2548, -2557, 2566, -2569, 2580,
-2582, 2592, -2594, 2604, -2606, 2614, -2615, 2618, -2666, 2669, -2684, 2690,
-2699, 2711, 2718, -2731, 2737, -2754, 2759, -2764, 2768, 2770, -2775, 2777,
-2864, 3013, 3023, 3030, 3048, 3058, -3063, 3066, -3072, 3074, -3080, 3128,
-3215, 3244, -3355, 3510, -3557, 3611, -3631, 3669, -3680, 3697, 3700, -3701,
3704, -3734, 3758, -3766, 3770, -3776, 3780, -3783, 3788, -3820, 3844, -3852,
3856, -3862, 3866, -3869, 3874, -3875, 3907, -3929, 3939, -3941, 3949, -3951,
3956, -3959, 3977, -3985, 3992, 3994, -3996, 3998, -4005, 4007, -4008, 4012,
-4015, 4019, -4022, 4026, 4030, -4031, 4034, -4045, 4047, 4055, -4057, 4065,
-4073, 4093, -4112, 4143, -4183, 4206, -4207, 4210, 4215, -4222, 4231, -4238,
4242, -4244, 4251, -4256, 4263, -4264, 4270, -4278, 4288, -4296, 4303, -4308,
4315, -4320, 4323, -4327, 4430, -4440, 4466, -4468, 4470, 4472, 4475, -4478,
4482, 4484, 4486, -4487, 4489, -4525, 4601, -4607, 4610, -4639, 4662, 4666,
-4670, 4676, -4678, 4680, -4681, 4683, -4685, 4688, 4690, 4694, 4697, 4699,
4702, 4705, -4706, 4708, -4709, 4711, -4715 ], [ 3, 38, 45, 79, 84, -114, 138
, -146, 150, -156, 160, -163, 168, -184, 224, -297, 299, -300, 302, 336, -339
, 346, 356, -359, 388, -396, 416, -419, 442, -444, 447, 454, -456, 464, -465,
470, 482, -499, 502, -510, 513, -529, 538, 540, 542, -553, 557, -595, 629,
-651, 660, -673, 675, -677, 679, 686, 696, 700, -701, 724, -728, 735, 739,
-744, 747, -753, 755, -864, 1019, -1042, 1131, -1206, 1292, -1293, 1298,
-1302, 1307, -1309, 1316, -1321, 1328, -1345, 1355, -1383, 1394, -1427, 1440,
-1451, 1466, -1472, 1488, -1491, 1502, -1504, 1516, -1519, 1530, -1532, 1540,
-1559, 1571, -1579, 1586, -1602, 1613, -1619, 1626, -1636, 1644, -1647, 1656,
-1659, 1664, -1667, 1670, -1671, 1734, -1777, 1787, -1788, 1798, -1800, 1808,
-1810, 1818, -1820, 1825, -1827, 1832, -1839, 1889, -1919, 1935, -1961, 1963,
-1982, 2032, -2036, 2057, -2065, 2068, -2080, 2085, 2087, -2092, 2098, -2106,
2109, -2121, 2126, 2128, -2138, 2148, -2149, 2163, -2166, 2189, -2241, 2256,
-2257, 2260, -2266, 2273, -2278, 2306, -2308, 2315, -2317, 2324, -2326, 2331,
-2365, 2391, -2393, 2397, -2399, 2403, -2405, 2408, -2412, 2416, 2418, 2420,
-2421, 2513, -2547, 2558, -2565, 2570, -2579, 2583, -2591, 2595, -2603, 2607,
-2613, 2616, -2617, 2685, -2688, 2700, -2707, 2712, -2717, 2732, -2735, 2755,
-2757, 2765, -2767, 2769, 3005, 3009, 3014, -3019, 3024, -3026, 3033, -3038,
3041, -3047, 3049, -3057, 3064, -3065, 3081, -3127, 3216, -3243, 3698, 3702,
-3703, 3735, -3757, 3767, -3769, 3777, -3779, 3784, -3787, 3821, -3843, 3853,
-3855, 3863, -3865, 3870, -3873, 3988, 3990, -3991, 3993, 3997, 4006, 4009,
-4011, 4016, -4018, 4023, -4025, 4027, -4029, 4058, -4064, 4122, -4124, 4128,
-4142, 4184, -4194, 4199, -4200, 4203, -4205, 4208, -4209, 4245, -4250, 4257,
-4262, 4408, -4429, 4441, -4465, 4469, 4471, 4473, -4474, 4661, 4663, 4665,
4671, -4672, 4674, -4675, 4682, 4689, 4696 ], [ 9, -17, 20, -32, 37, 39, -44,
46, -58, 73, 77, 80, -81, 115, -137, 147, -149, 157, -159, 164, -167, 185,
-193, 195, -223, 318, -322, 328, -335, 340, -345, 347, -355, 360, -363, 368,
-387, 399, -415, 420, -423, 428, -429, 436, -437, 440, -441, 446, 448, -453,
457, -463, 466, -469, 471, -481, 500, -501, 511, -512, 530, -537, 596, -628,
654, -655, 657, -659, 680, 684, -685, 689, 692, 695, 697, -699, 702, -714,
721, -723, 730, 732, 734, 737, -738, 745, -746, 1294, -1295, 1303, -1306,
1310, -1312, 1322, -1327, 1452, -1465, 1473, -1487, 1492, -1501, 1505, -1515,
1520, -1529, 1533, -1539, 1569, -1570, 1580, -1585, 1610, -1612, 1620, -1625,
1641, -1643, 1648, -1655, 1660, -1663, 1923, -1934, 2052, -2056, 2066, -2067,
2081, -2084, 2093, -2097, 2107, -2108, 2122, -2125, 2254, -2255, 2258, -2259,
2289, -2305, 2309, -2314, 2318, -2323, 2327, -2330, 2366, -2390, 2394, -2396,
2400, -2402, 2406, -2407, 2668, 2708, -2710, 3006, -3008, 3010, -3012, 3020,
-3022, 3027, -3029, 3031, -3032, 3039, -3040, 3986, -3987, 3989, 4053, -4054,
4125, -4127, 4197, -4198, 4201, -4202, 4664 ], [ 4, -8, 18, -19, 33, -36, 59,
-63, 66, 68, -72, 74, -76, 78, 82, -83, 194, 308, -317, 323, -327, 364, -367,
397, -398, 424, -427, 430, -435, 438, -439, 652, -653, 656, 681, -683, 687,
-688, 690, -691, 693, -694, 715, -720, 729, 731, 733, 1922, 2667 ], [ 1, -2,
64, -65, 67 ] ] ),
frattFacs := rec( frattFacs := [ 16, 31, 47, 62, 77, 48, 63, 78, 184, 199,
214, 229, 140, 155, 170, 185, 200, 215, 726, 741, 756, 771, 786, 187, 202,
217, 232, 593, 608, 623, 638, 653, 668, 683, 698, 713, 728, 743, 758, 3399,
3414, 3429, 3444, 3459, 3474, 550, 565, 580, 595, 610, 625, 640, 655, 670,
685, 2741, 2756, 2771, 2786, 2801, 2816, 2831, 2846, 2861, 2876, 2891, 2906,
2921, 2936, 2951, 2966, 2307, 2322, 2337, 2352, 2367, 2382, 2397, 2412, 2427,
2442, 2457, 2472, 2487, 2502, 2517, 2532, 2547, 2562, 2577, 2592, 2607, 2622,
2637, 2652, 2667, 15373, 15388, 15403, 15418, 15433, 15448, 15463, 15478,
15493, 15508, 15523, 15538, 15553, 15568, 15583, 15598, 15613, 15628, 15643,
15658, 15673, 15688, 11024, 11039, 11054, 11069, 11084, 11099, 11114, 11129,
11144, 11159, 11174, 11189, 11204, 11219, 11234, 11249, 11264, 11279, 11294,
11309, 11324, 11339, 11354, 11369, 11384, 11399, 11414, 11429, 11444, 11459,
11474, 11489, 11504, 11519, 11534, 11549, 11564, 11579, 11594, 11609, 11624,
11639 ], pos := [ 1, 2, 3, 44, 63, 67, 69, 72, 76, 83, 169, 193, 194, 302,
307, 471, 553, 610, 621, 628, 630, 645, 651, 652, 653, 654, 655, 656, 674,
679, 695, 707, 736, 761, 1291, 1327, 1671, 1843, 1915, 1916, 1917, 1918, 1919
, 1920, 1921, 1922, 1923, 1964, 2031, 2050, 2051, 2092, 2133, 2174, 2193,
2196, 2241, 2253, 2260, 2283, 2288, 2332, 2365, 2409, 2422, 2512, 2547, 2557,
2617, 2647, 2665, 2666, 2667, 2668, 2699, 2717, 2746, 2764, 2769, 2778, 3004,
3008, 3012, 3016, 3023, 3030, 3055, 3080, 3275, 3610, 3696, 3703, 3789, 3875,
3961, 3985, 3989, 3993, 3996, 3997, 4000, 4005, 4006, 4007, 4008, 4012, 4015,
4019, 4022, 4026, 4030, 4031, 4033, 4038, 4043, 4047, 4049, 4052, 4053, 4054,
4061, 4064, 4067, 4070, 4073, 4112, 4121, 4124, 4127, 4142, 4157, 4172, 4183,
4194, 4196, 4203, 4210, 4241, 4264, 4299, 4322, 4327, 4336, 4407, 4418, 4429,
4440, 4451, 4462, 4475, 4488, 4525, 4578, 4600, 4607, 4609, 4624, 4639, 4654,
4660 ] ) );