prop1944.z

#############################################################################
##
#W  prop1944.z             GAP library of groups           Hans Ulrich Besche
##                                               Bettina Eick, Eamonn O'Brien
##

PROPERTIES_SMALL_GROUPS[ 1944 ] := rec(
isNilpotent := [ 2, 9, -11, 71, -99, 103, 586, -672, 772, -801, 1087, -1115,
2163, -2252, 2283, -2288, 2946, -2975, 3416, -3433, 3439, 3776, -3781, 3871,
-3873, 3973 ], 
isSupersolvable := [ 1, -2, 4, -99, 102, -103, 109, -219, 291, -801, 940,
-956, 1028, -1115, 1130, -1558, 1668, -2288, 2339, -2346, 2673, -2737, 2847,
-2975, 2997, -3250, 3266, -3439, 3562, -3579, 3689, -3730, 3746, -3781, 3789,
-3844, 3846, -3873, 3932, -3941, 3957, -3966, 3968, -3973 ], 
isAbelian := [ 2, 9, 79, 92, 103, 594, 607, 772, 789, 1095, 1108, 2163, 2180,
2283, 2946, 2963, 3416, 3439, 3776, 3871, 3973 ], 
lgLength := rec( lgLength := [ 2, 3, 4, 5, 6, 7, 8 ], pos := [ [ 3936, -3941,
3963, -3966, 3972, -3973 ], [ 940, 1067, 1087, 2339, -2342, 2682, 2693, 2703,
-2711, 2725, -2732, 2859, 2872, 2883, 2902, 2923, 2936, -2939, 2946, -2962,
3564, 3567, -3579, 3691, 3699, -3700, 3710, 3715, -3730, 3748, 3755, 3762,
3768, 3773, -3781, 3821, -3845, 3866, -3873, 3898, -3902, 3904, -3906, 3914,
-3919, 3921, -3922, 3927, -3929, 3931, -3935, 3946, 3954, 3956, -3962, 3967,
-3971 ], [ 109, -113, 277, 486, -488, 546, -547, 586, 615, 644, 804, 807, 883
, 935, 941, -954, 1014, 1029, -1037, 1043, -1044, 1046, 1048, 1050, 1060,
1062, 1068, -1084, 1088, -1107, 1189, 1192, 1194, 1197, 1199, 1258, -1264,
1328, -1390, 1482, -1527, 1559, -1593, 1617, -1623, 1628, -1633, 1635, 1640,
1643, -1646, 1648, 1657, -1658, 1660, 1664, -1665, 1667, 1702, 1705, -1706,
1741, 1745, -1746, 1774, 1777, -1778, 1817, 1819, 1843, 1846, 1865, 1867,
1915, 1918, -1919, 1976, 1981, -1982, 2044, 2046, 2085, 2088, 2113, -2124,
2143, -2150, 2163, -2179, 2193, -2209, 2223, -2239, 2295, 2308, -2310, 2314,
2317, -2320, 2322, -2325, 2330, 2334, -2337, 2343, -2346, 2374, -2375, 2388,
2422, 2463, -2464, 2489, -2491, 2506, -2509, 2512, 2518, 2520, 2546, -2547,
2586, 2592, 2608, 2657, -2658, 2661, 2667, -2671, 2673, 2675, -2677, 2679,
2681, 2683, -2687, 2692, 2695, -2696, 2698, -2699, 2712, -2724, 2733, -2772,
2796, -2802, 2807, -2812, 2814, 2819, 2822, -2825, 2827, 2836, -2837, 2839,
2843, -2844, 2846, 2848, -2851, 2853, -2854, 2858, 2860, -2861, 2863, 2871,
2874, -2875, 2877, -2878, 2881, -2882, 2884, -2888, 2890, -2893, 2896, -2898,
2900, -2901, 2903, -2915, 2922, 2925, -2926, 2928, -2929, 2931, 2940, -2945,
2963, -2975, 3009, 3011, -3012, 3014, 3016, 3018, 3020, 3059, -3060, 3062,
3064, 3066, -3067, 3069, -3072, 3074, -3077, 3123, 3125, 3128, 3130, -3131,
3153, -3265, 3272, 3274, -3275, 3291, 3293, 3307, 3310, -3311, 3328, 3330,
-3331, 3344, 3347, 3358, 3360, 3372, 3374, -3375, 3391, 3393, 3401, -3433,
3438, -3439, 3482, 3486, -3499, 3507, 3511, 3517, -3537, 3547, 3551, -3563,
3565, -3566, 3586, 3595, -3596, 3605, 3612, 3620, -3625, 3632, 3639, 3648,
-3649, 3660, 3668, 3678, 3682, -3690, 3692, -3698, 3701, -3709, 3711, -3714,
3731, -3747, 3749, -3754, 3756, -3761, 3763, -3767, 3769, -3772, 3782, 3786,
3788, -3820, 3846, -3865, 3874, -3875, 3877, 3879, -3880, 3883, 3887, 3890,
-3891, 3893, -3897, 3903, 3907, -3913, 3920, 3923, -3926, 3930, 3942, -3945,
3947, -3953, 3955 ], [ 51, 71, 104, 114, -205, 222, -224, 228, -246, 252,
-262, 273, -276, 278, -290, 294, -320, 336, -341, 343, 345, 347, 349, 351,
353, 355, 358, -359, 387, -389, 391, 394, -395, 410, -427, 438, -441, 443,
445, 447, 449, 451, 453, 472, -473, 475, 477, 489, -539, 548, -581, 587, -606
, 616, -635, 645, -664, 685, 698, 709, 728, 749, 762, -765, 772, -788, 802,
805, -806, 808, 814, -817, 820, -822, 834, -837, 841, -844, 847, 850, -868,
870, -876, 878, -882, 884, -895, 900, -910, 927, -929, 931, 934, 936, -939,
955, -956, 959, -961, 965, -983, 989, -999, 1010, -1013, 1015, -1028, 1041,
-1042, 1045, 1047, 1049, 1051, -1054, 1061, 1063, -1066, 1085, -1086, 1108,
-1115, 1118, 1124, -1128, 1130, -1134, 1142, -1162, 1170, -1176, 1182, -1188,
1190, -1191, 1193, 1195, -1196, 1198, 1200, -1224, 1251, -1257, 1272, -1285,
1293, -1306, 1391, -1481, 1528, -1558, 1594, -1616, 1624, -1627, 1634, 1636,
-1639, 1641, -1642, 1647, 1649, -1656, 1659, 1661, -1663, 1666, 1669, 1672,
-1682, 1684, 1687, -1689, 1691, 1693, 1701, 1703, -1704, 1707, -1712, 1714,
1716, 1718, 1740, 1743, -1744, 1749, -1750, 1752, -1755, 1758, -1759, 1761,
-1764, 1770, -1773, 1775, -1776, 1779, -1793, 1795, 1797, -1803, 1805, 1807,
-1808, 1810, 1816, 1818, 1820, -1823, 1825, 1827, 1842, 1845, 1848, -1849,
1851, -1852, 1854, -1855, 1857, -1858, 1862, -1864, 1866, 1868, -1877, 1879,
1882, -1892, 1897, -1898, 1900, 1902, -1905, 1907, -1908, 1911, -1914, 1916,
-1917, 1920, -1958, 1975, 1978, 1980, 1984, -1985, 1987, 1989, -1991, 1993,
-1994, 1996, 1998, -2000, 2004, -2006, 2020, 2022, -2028, 2032, -2033, 2035,
-2037, 2039, 2041, -2043, 2045, 2047, -2072, 2084, 2087, 2090, -2091, 2093,
-2094, 2096, -2097, 2099, -2100, 2103, -2104, 2125, -2142, 2151, -2162, 2180,
-2192, 2210, -2222, 2240, -2252, 2255, 2262, 2269, 2275, 2280, -2290, 2298,
2303, -2305, 2311, -2312, 2315, 2321, 2326, -2328, 2331, 2338, 2347, -2349,
2361, -2365, 2368, -2373, 2380, -2387, 2391, -2393, 2395, -2408, 2411, -2413,
2420, -2421, 2423, -2428, 2433, -2434, 2438, -2442, 2444, -2449, 2455, -2460,
2474, -2480, 2482, -2484, 2486, -2488, 2492, -2505, 2510, -2511, 2513, -2517,
2519, 2526, -2531, 2542, -2545, 2548, -2559, 2566, -2570, 2574, 2577, -2585,
2589, -2591, 2597, -2598, 2602, 2604, -2607, 2609, 2611, -2626, 2642, -2651,
2653, -2654, 2656, 2659, 2662, -2664, 2672, 2674, 2678, 2680, 2688, -2691,
2694, 2697, 2700, -2702, 2773, -2795, 2803, -2806, 2813, 2815, -2818, 2820,
-2821, 2826, 2828, -2835, 2838, 2840, -2842, 2845, 2847, 2852, 2855, -2857,
2862, 2864, -2870, 2873, 2876, 2879, -2880, 2889, 2894, -2895, 2899, 2916,
-2921, 2924, 2927, 2930, 2932, -2935, 2976, 2986, 2990, -3008, 3010, 3013,
3015, 3017, 3019, 3021, -3058, 3061, 3063, 3065, 3068, 3073, 3078, -3122,
3124, 3126, -3127, 3129, 3132, -3152, 3266, -3271, 3273, 3276, -3290, 3292,
3294, -3306, 3308, -3309, 3312, -3327, 3329, 3332, -3343, 3345, -3346, 3348,
-3357, 3359, 3361, -3371, 3373, 3376, -3390, 3392, 3394, -3400, 3434, -3437,
3440, -3456, 3463, 3469, -3481, 3483, -3485, 3500, -3506, 3508, -3510, 3512,
-3516, 3538, -3546, 3548, -3550, 3580, -3585, 3587, -3594, 3597, -3604, 3606,
-3611, 3613, -3619, 3626, -3631, 3633, -3638, 3640, -3647, 3650, -3659, 3661,
-3667, 3669, -3677, 3679, -3681, 3783, -3785, 3787, 3876, 3878, 3881, -3882,
3884, -3886, 3888, -3889, 3892 ], [ 13, -21, 27, -28, 30, 32, 34, 44, 46, 52,
-68, 72, -91, 102, -103, 105, -108, 206, -221, 225, -227, 247, -251, 263,
-272, 291, -293, 330, -335, 342, 344, 346, 348, 350, 352, 354, 356, -357, 360
, -371, 390, 392, -393, 396, -409, 434, -437, 442, 444, 446, 448, 450, 452,
454, -461, 474, 476, 478, -485, 540, -545, 582, -585, 607, -614, 636, -643,
665, -672, 674, -677, 679, -680, 684, 686, -687, 689, 697, 700, -701, 703,
-704, 707, -708, 710, -714, 716, -719, 722, -724, 726, -727, 729, -741, 748,
751, -752, 754, -755, 757, 766, -771, 789, -801, 803, 812, -813, 818, -819,
824, -826, 831, -833, 838, -840, 845, -846, 848, -849, 869, 877, 914, -916,
918, -926, 930, 932, -933, 957, -958, 962, -964, 984, -988, 1000, -1009, 1038
, -1040, 1055, -1059, 1116, 1119, -1121, 1129, 1135, -1141, 1163, -1169, 1177
, -1181, 1225, -1250, 1265, -1271, 1286, -1292, 1307, -1327, 1668, 1670,
-1671, 1683, 1685, -1686, 1690, 1692, 1694, -1700, 1713, 1715, 1717, 1719,
-1739, 1742, 1747, -1748, 1751, 1756, -1757, 1760, 1765, -1769, 1794, 1796,
1804, 1806, 1809, 1811, -1815, 1824, 1826, 1828, -1841, 1844, 1847, 1850,
1853, 1856, 1859, -1861, 1878, 1880, -1881, 1893, -1896, 1899, 1901, 1906,
1909, -1910, 1959, -1974, 1977, 1979, 1983, 1986, 1988, 1992, 1995, 1997,
2001, -2003, 2007, -2019, 2021, 2029, -2031, 2034, 2038, 2040, 2073, -2083,
2086, 2089, 2092, 2095, 2098, 2101, -2102, 2105, -2112, 2253, -2254, 2256,
-2261, 2263, -2268, 2270, -2274, 2276, -2279, 2291, -2294, 2296, 2299, -2301,
2306, -2307, 2313, 2316, 2329, 2332, -2333, 2350, -2360, 2366, -2367, 2376,
-2379, 2389, -2390, 2394, 2409, -2410, 2414, -2419, 2429, -2432, 2435, -2437,
2443, 2450, -2454, 2461, -2462, 2465, -2473, 2481, 2485, 2521, -2525, 2532,
-2541, 2560, -2565, 2571, -2573, 2575, -2576, 2587, -2588, 2593, -2596, 2599,
-2601, 2603, 2610, 2627, -2641, 2652, 2655, 2660, 2665, -2666, 2977, -2985,
2987, -2989, 3457, -3462, 3464, -3468 ], [ 3, -12, 25, -26, 29, 31, 33, 35,
-38, 45, 47, -50, 69, -70, 92, -101, 321, -329, 372, -386, 428, -433, 462,
-471, 673, 678, 681, -683, 688, 690, -696, 699, 702, 705, -706, 715, 720,
-721, 725, 742, -747, 750, 753, 756, 758, -761, 809, -811, 823, 827, -830,
896, -899, 911, -913, 917, 1117, 1122, -1123, 2297, 2302 ], [ 1, -2, 22, -24,
39, -43 ] ] ),
frattFacs := rec( frattFacs := [ 16, 31, 47, 62, 77, 48, 63, 78, 184, 199,
214, 229, 140, 155, 170, 185, 200, 215, 186, 201, 216, 231, 592, 607, 622,
637, 652, 667, 682, 697, 712, 727, 742, 757, 548, 563, 578, 593, 608, 623,
638, 653, 668, 683, 774, 789, 804, 819, 834, 2305, 2320, 2335, 2350, 2365,
2380, 2395, 2410, 2425, 2440, 2455, 2470, 2485, 2500, 2515, 2530, 2545, 2560,
2575, 2590, 2605, 2620, 2635, 2650, 2665, 2411, 2426, 2441, 2456, 2471, 2486,
2501, 2516, 2531, 2546, 2561, 2576, 2591, 2606, 2621, 2636, 2651, 3852, 3867,
3882, 3897, 3912, 3927, 10543, 10558, 10573, 10588, 10603, 10618, 10633,
10648, 10663, 10678, 10693, 10708, 10723, 10738, 10753, 10768, 10783, 10798,
10813, 10828, 10843, 10858, 10873, 10888, 10903, 10918, 10933, 10948, 10963,
10978, 10993, 11008, 11023, 11038, 11053, 11068, 11083, 11098, 11113, 11128,
11143, 11158, 11173, 11188, 11203, 11218, 11233, 11248, 11263, 11278, 11293,
11308, 11323, 11338, 11353, 11368, 13169, 13184, 13199, 13214, 13229, 13244,
13259, 13274, 13289, 13304, 13319, 13334, 13349, 13364, 13379, 13394, 13409,
13424, 13439, 13454, 13469, 13484, 13499, 13514 ], pos := [ 1, 2, 3, 8, 11,
50, 70, 99, 100, 101, 102, 103, 108, 219, 290, 485, 585, 672, 714, 761, 771,
801, 803, 806, 808, 847, 895, 934, 939, 956, 1027, 1066, 1086, 1115, 1123,
1129, 1327, 1481, 1558, 1667, 1877, 2112, 2162, 2252, 2259, 2272, 2279, 2282,
2288, 2295, 2302, 2307, 2311, 2316, 2321, 2327, 2333, 2338, 2346, 2388, 2488,
2520, 2611, 2658, 2666, 2672, 2702, 2724, 2737, 2846, 2888, 2935, 2945, 2975,
2976, 2983, 2989, 2993, 2996, 3037, 3114, 3152, 3180, 3209, 3250, 3265, 3300,
3365, 3400, 3415, 3433, 3434, 3435, 3436, 3437, 3438, 3439, 3452, 3453, 3454,
3455, 3456, 3460, 3468, 3472, 3474, 3476, 3479, 3485, 3489, 3493, 3496, 3499,
3503, 3508, 3516, 3519, 3523, 3528, 3532, 3537, 3544, 3550, 3554, 3557, 3561,
3566, 3571, 3576, 3579, 3586, 3605, 3620, 3625, 3640, 3661, 3668, 3675, 3681,
3685, 3688, 3695, 3706, 3714, 3718, 3723, 3730, 3745, 3752, 3765, 3772, 3775,
3781, 3782, 3783, 3784, 3785, 3786, 3787, 3788, 3793, 3800, 3803, 3810, 3815,
3820, 3827, 3834, 3839, 3844, 3845, 3850, 3855, 3860, 3865, 3870, 3873 ] ) );