prop1296.z

#############################################################################
##
#W  prop1296.z             GAP library of groups           Hans Ulrich Besche
##                                               Bettina Eick, Eamonn O'Brien
##

PROPERTIES_SMALL_GROUPS[ 1296 ] := rec(
isNilpotent := [ 2, 20, -27, 48, -56, 73, -76, 558, -629, 634, 650, -653,
1201, -1236, 1747, -1778, 1921, -1929, 1934, 2689, -2704, 2881, -2888, 3077,
-3080, 3483, -3486, 3609 ], 
isSupersolvable := [ 1, -2, 4, -56, 63, -76, 78, -218, 238, -629, 633, -653,
791, -943, 1001, -1236, 1242, -1496, 1507, -1778, 1857, -1862, 1901, -1934,
2000, -2077, 2230, -2508, 2539, -2704, 2710, -2815, 2817, -2888, 2984, -2985,
3030, -3041, 3062, -3080, 3186, -3272, 3322, -3439, 3443, -3486, 3538, 3582,
-3585, 3597, -3602, 3605, -3609 ], 
isAbelian := [ 2, 20, 23, 48, 51, 73, 558, 561, 585, 588, 634, 650, 1201,
1204, 1747, 1759, 1921, 1924, 1934, 2689, 2881, 2884, 3077, 3483, 3609 ], 
lgLength := rec( lgLength := [ 2, 3, 4, 5, 6, 7, 8 ], pos := [ [ 3538, 3557,
3583, -3585, 3600, -3602, 3604, 3608, -3609 ], [ 1795, -1799, 1857, -1858,
1886, -1888, 1892, 1899, 1909, 1914, -1915, 1921, -1923, 2777, -2783, 2795,
-2799, 2811, -2816, 2872, -2875, 2880, -2883, 2946, -2964, 2984, -2985, 3032,
3035, -3041, 3052, -3061, 3064, 3070, 3075, -3080, 3106, -3108, 3113, -3115,
3120, -3122, 3127, -3129, 3149, -3151, 3156, -3157, 3161, -3163, 3168, -3169,
3173, -3174, 3181, -3185, 3205, -3272, 3310, -3311, 3314, 3317, -3318, 3321,
3377, -3439, 3473, -3486, 3496, -3501, 3524, 3526, -3531, 3533, -3537, 3544,
3549, -3553, 3565, -3568, 3572, -3576, 3579, -3582, 3589, 3595, -3599, 3603,
3605, -3607 ], [ 179, -190, 223, -225, 229, 236, 352, -354, 356, 441, 483,
-486, 489, -492, 551, -552, 558, -560, 567, -569, 576, -578, 655, -656, 660,
786, -787, 790, -813, 870, -891, 1030, 1034, -1036, 1069, -1070, 1095, -1096,
1120, 1122, 1131, -1138, 1159, -1162, 1173, -1176, 1187, -1190, 1201, -1203,
1210, -1212, 1219, -1221, 1228, -1230, 1330, 1332, -1333, 1335, 1337, -1338,
1340, 1421, -1448, 1482, -1506, 1553, -1555, 1559, 1599, 1654, -1656, 1660,
1710, 1727, -1730, 1733, -1736, 1745, -1758, 1782, 1785, 1789, 1791, -1794,
1800, -1811, 1813, -1814, 1825, 1833, -1834, 1841, 1855, -1856, 1859, -1862,
1867, -1869, 1873, 1880, 1882, -1885, 1889, -1891, 1893, -1898, 1900, 1902,
-1903, 1908, 1910, -1913, 1916, -1920, 1924, -1929, 1944, -1949, 1964, -1965,
1970, 1975, -1977, 1981, -1982, 1986, -1987, 1991, -1992, 1996, -2077, 2218,
-2219, 2222, -2223, 2226, 2229, 2253, 2255, -2256, 2258, 2261, -2264, 2267,
-2269, 2271, -2272, 2274, 2312, 2314, -2315, 2317, 2319, 2321, 2323, 2325,
-2326, 2328, -2330, 2332, 2347, -2508, 2547, 2549, -2551, 2567, -2568, 2579,
-2580, 2591, 2593, 2607, 2609, -2611, 2631, -2632, 2645, -2646, 2659, 2661,
2669, -2705, 2721, -2725, 2744, -2750, 2756, -2776, 2784, -2794, 2800, -2810,
2824, -2827, 2832, 2840, -2843, 2848, 2856, -2859, 2864, -2871, 2876, -2879,
2884, -2888, 2908, -2911, 2919, 2924, -2940, 2945, 2970, -2971, 2974, -2978,
2982, -2983, 2991, 2997, 3003, -3007, 3012, 3016, 3024, 3028, -3031, 3033,
-3034, 3042, -3051, 3062, -3063, 3065, -3069, 3071, -3074, 3099, -3101, 3109,
-3112, 3116, -3119, 3123, -3126, 3130, -3133, 3137, -3139, 3144, -3145, 3152,
-3155, 3158, -3160, 3164, -3167, 3170, -3172, 3175, -3180, 3186, -3204, 3282,
-3284, 3296, -3297, 3300, 3303, -3304, 3307, -3309, 3312, -3313, 3315, -3316,
3319, -3320, 3322, -3376, 3440, -3472, 3490, 3492, -3494, 3503, -3509, 3514,
-3523, 3525, 3532, 3540, 3543, 3545, -3548, 3554, -3556, 3560, -3564, 3569,
-3571, 3577, -3578, 3586, -3588, 3590, -3594 ], [ 78, -106, 191, -222, 226,
-228, 230, -235, 237, 278, -282, 313, -320, 347, -351, 355, 361, -368, 373,
-380, 397, -398, 423, -424, 434, -435, 440, 442, -455, 481, -482, 487, -488,
495, -498, 501, -504, 507, -510, 513, -516, 519, -526, 537, -540, 553, -557,
561, -566, 570, -575, 579, -587, 594, -596, 603, -605, 612, -614, 621, -623,
632, -634, 657, -659, 682, -683, 693, 708, 712, -714, 731, -732, 739, 741,
743, 779, 781, 783, -785, 788, -789, 814, -869, 892, -943, 952, -954, 958,
967, -969, 973, 982, -984, 988, 995, 997, 999, 1005, -1012, 1029, 1031, -1033
, 1037, -1052, 1055, -1058, 1067, -1068, 1071, -1078, 1081, -1084, 1093,
-1094, 1097, -1104, 1107, -1110, 1119, 1121, 1123, -1130, 1139, -1158, 1163,
-1172, 1177, -1186, 1191, -1200, 1204, -1209, 1213, -1218, 1222, -1227, 1231,
-1236, 1271, -1272, 1274, -1275, 1278, -1279, 1281, 1283, -1284, 1286, 1288,
-1289, 1291, -1292, 1294, -1295, 1297, -1298, 1318, -1329, 1331, 1334, 1336,
1339, 1341, -1420, 1449, -1481, 1517, -1521, 1541, -1550, 1556, -1558, 1560,
1565, -1572, 1577, -1578, 1589, -1590, 1597, -1598, 1600, -1602, 1613, -1617,
1642, -1651, 1657, -1659, 1661, 1664, -1667, 1672, -1679, 1684, -1685, 1698,
-1699, 1708, -1709, 1711, -1726, 1731, -1732, 1737, -1744, 1759, -1781, 1783,
-1784, 1786, -1788, 1790, 1812, 1820, -1824, 1826, -1832, 1835, -1840, 1842,
1848, -1854, 1863, -1866, 1870, -1872, 1874, -1879, 1881, 1901, 1904, -1907,
1933, -1934, 1940, -1943, 1950, -1955, 1962, -1963, 1966, -1969, 1971, -1974,
1978, -1980, 1983, -1985, 1988, -1990, 1993, -1995, 2091, -2092, 2095, 2106,
-2107, 2117, 2125, 2127, 2131, -2143, 2152, -2153, 2160, 2166, 2168, 2172,
2191, -2192, 2194, 2197, -2198, 2201, -2202, 2205, -2206, 2209, 2212, 2215,
-2217, 2220, -2221, 2224, -2225, 2227, -2228, 2230, -2252, 2254, 2257, 2259,
-2260, 2265, -2266, 2270, 2273, 2275, -2311, 2313, 2316, 2318, 2320, 2322,
2324, 2327, 2331, 2333, -2346, 2509, -2546, 2548, 2552, -2566, 2569, -2578,
2581, -2590, 2592, 2594, -2606, 2608, 2612, -2630, 2633, -2644, 2647, -2658,
2660, 2662, -2668, 2708, -2720, 2726, -2743, 2751, -2755, 2817, -2823, 2828,
-2831, 2833, -2839, 2844, -2847, 2849, -2855, 2860, -2863, 2897, -2898, 2901,
-2907, 2912, -2913, 2917, -2918, 2920, -2923, 2941, -2944, 2967, -2969, 2972,
-2973, 2979, -2981, 2986, -2990, 2992, -2996, 2998, -3002, 3008, -3011, 3013,
-3015, 3017, -3023, 3025, -3027, 3081, -3092, 3095, -3098, 3102, -3105, 3134,
-3136, 3140, -3143, 3146, -3148, 3273, -3281, 3285, -3295, 3298, -3299, 3301,
-3302, 3305, -3306, 3488, 3491, 3495, 3502, 3510, -3513, 3539, 3541, -3542,
3558, -3559 ], [ 3, 11, -14, 19, -22, 36, 41, -42, 48, -50, 63, -77, 107,
-178, 243, -252, 273, -277, 283, -302, 305, -312, 323, -326, 331, -338, 341,
-346, 357, -360, 369, -372, 383, -386, 395, -396, 399, -406, 409, -412, 421,
-422, 425, -433, 436, -439, 456, -480, 493, -494, 499, -500, 505, -506, 511,
-512, 517, -518, 527, -536, 541, -550, 588, -593, 597, -602, 606, -611, 615,
-620, 624, -631, 637, 643, 648, -654, 670, -671, 674, -681, 688, -692, 694,
-707, 709, -711, 715, -730, 733, -738, 740, 742, 744, 755, -756, 759, -768,
772, -778, 780, 782, 944, -951, 955, -957, 959, -966, 970, -972, 974, -981,
985, -987, 989, -994, 996, 998, 1000, -1004, 1013, -1028, 1053, -1054, 1059,
-1066, 1079, -1080, 1085, -1092, 1105, -1106, 1111, -1118, 1240, -1270, 1273,
1276, -1277, 1280, 1282, 1285, 1287, 1290, 1293, 1296, 1299, -1317, 1507,
-1516, 1522, -1540, 1551, -1552, 1561, -1564, 1573, -1576, 1579, -1588, 1591,
-1596, 1603, -1612, 1618, -1641, 1652, -1653, 1662, -1663, 1668, -1671, 1680,
-1683, 1686, -1697, 1700, -1707, 1815, -1819, 1843, -1847, 1930, -1932, 1937,
-1939, 1956, -1961, 2078, -2090, 2093, -2094, 2096, -2105, 2108, -2116, 2118,
-2124, 2126, 2128, -2130, 2144, -2151, 2154, -2159, 2161, -2165, 2167, 2169,
-2171, 2173, -2190, 2193, 2195, -2196, 2199, -2200, 2203, -2204, 2207, -2208,
2210, -2211, 2213, -2214, 2706, -2707, 2889, -2896, 2899, -2900, 2914, -2916,
2965, -2966, 3093, -3094, 3487, 3489 ], [ 4, -10, 15, -18, 23, -27, 29, -30,
35, 37, -40, 43, -47, 51, -62, 238, -242, 253, -272, 303, -304, 321, -322,
327, -330, 339, -340, 381, -382, 387, -394, 407, -408, 413, -420, 635, -636,
638, -642, 644, -647, 661, -669, 672, -673, 684, -687, 745, -754, 757, -758,
769, -771, 1237, -1239, 1935, -1936 ], [ 1, -2, 28, 31, -34 ] ] ),
frattFacs := rec( frattFacs := [ 17, 33, 50, 66, 82, 51, 67, 83, 196, 212,
228, 244, 149, 165, 181, 197, 213, 229, 774, 790, 806, 822, 838, 199, 215,
231, 247, 632, 648, 664, 680, 696, 712, 728, 744, 760, 776, 792, 808, 585,
601, 617, 633, 649, 665, 681, 697, 713, 729, 2922, 2938, 2954, 2970, 2986,
3002, 3018, 3034, 3050, 3066, 3082, 3098, 3114, 3130, 3146, 3162, 827, 843,
859, 875, 891, 2476, 2492, 2508, 2524, 2540, 2556, 2572, 2588, 2604, 2620,
2636, 2652, 2668, 2684, 2700, 2716, 2732, 2748, 2764, 2780, 2796, 2812, 2828,
2844, 2573, 2589, 2605, 2621, 2637, 2653, 2669, 2685, 2701, 2717, 2733, 2749,
2765, 2781, 2797, 2813, 2829, 11758, 11774, 11790, 11806, 11822, 11838, 11854
, 11870, 11886, 11902, 11918, 11934, 11950, 11966, 11982, 11998, 12014, 12030
, 12046, 12062, 12078, 12094, 12110, 12126, 12142, 12158, 12174, 12190, 12206
, 12222, 12238, 12254, 12270, 12286, 12302, 12318, 12334, 12350, 12366, 12382
, 12398, 12414, 11263, 11279, 11295, 11311, 11327, 11343, 11359, 11375, 11391
, 11407, 11423, 11439, 11455, 11471, 11487, 11503, 11519, 11535, 11551, 11567
, 11583, 11599, 11615, 11631, 11647, 11663, 11679, 11695, 11711, 11727, 11743
, 11759, 11775, 11791, 11807, 11823, 11839, 11855, 11871, 11887, 11903, 11919
, 11935, 11951, 11967, 11983, 11999, 12015, 12031, 12047, 12063, 12079, 12095
, 12111, 12127 ], pos := [ 1, 2, 3, 19, 27, 40, 47, 56, 59, 62, 72, 76, 77,
218, 237, 445, 557, 629, 630, 631, 632, 633, 634, 640, 647, 649, 653, 654,
659, 660, 699, 744, 783, 790, 943, 1000, 1130, 1200, 1236, 1239, 1241, 1348,
1448, 1496, 1506, 1602, 1714, 1746, 1778, 1779, 1790, 1811, 1812, 1813, 1814,
1827, 1842, 1855, 1856, 1862, 1881, 1900, 1913, 1920, 1929, 1930, 1931, 1932,
1933, 1934, 1936, 1939, 1953, 1963, 1977, 1992, 1995, 1999, 2077, 2095, 2131,
2143, 2173, 2194, 2215, 2229, 2346, 2454, 2508, 2538, 2598, 2668, 2688, 2704,
2705, 2706, 2707, 2708, 2709, 2725, 2750, 2758, 2783, 2799, 2815, 2816, 2832,
2848, 2864, 2880, 2888, 2892, 2896, 2898, 2900, 2902, 2905, 2907, 2909, 2911,
2913, 2916, 2924, 2928, 2934, 2940, 2945, 2964, 2966, 2969, 2971, 2973, 2975,
2978, 2981, 2983, 2985, 2991, 3003, 3007, 3017, 3024, 3027, 3029, 3034, 3038,
3041, 3051, 3061, 3067, 3074, 3076, 3080, 3083, 3086, 3089, 3092, 3093, 3094,
3095, 3096, 3097, 3098, 3105, 3112, 3119, 3126, 3131, 3136, 3143, 3148, 3155,
3160, 3167, 3172, 3177, 3178, 3180, 3182, 3184, 3185, 3204, 3243, 3262, 3272,
3275, 3278, 3281, 3284, 3287, 3290, 3293, 3300, 3307, 3314, 3321, 3339, 3366,
3376, 3403, 3421, 3439, 3442, 3452, 3462, 3472, 3482, 3486 ] ) );