Finite Group DatabasebetaFinite Group Databasebeta| order | 39941 |
| automorphism | ? |
| homology | Abelianization (H1) = C11 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C3631 ⋊ C11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3631 | C11 |
| LCS | G ▷ C3631 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
| minimal degree | μ(G) = 3631 |
| transitive degree | μt(G) = 3631 |
A minimal faithful permutation representation — 2 generators on 3631 points:
(2,3,5,9,17,33,65,129,256,502,947)(4,7,13,25,49,97,192,377,721,1308,1499)(6,11,21,41,81,160,315,609,1125,1927,1667)(8,15,29,57,113,224,439,834,1490,2397,3253)(10,19,37,73,144,285,557,1044,1816,948,1668)(12,23,45,89,176,345,662,1211,1844,2795,2408)(14,27,53,105,208,407,773,86,170,333,642)(16,31,61,121,240,470,890,1576,2491,3297,3087)(18,35,69,137,271,530,996,1743,503,949,1670)(20,39,77,152,300,82,162,319,617,1141,1957)(22,43,85,168,330,637,1175,2005,563,1054,1833)(24,47,93,184,361,690,1255,1897,2527,1288,2140)(26,51,101,200,392,748,1352,2224,1484,1669,2599)(28,55,109,216,423,802,1434,1733,2546,584,1090)(30,59,117,232,455,88,174,341,265,520,981)(32,63,125,248,486,918,1622,324,625,1156,1982)(34,67,133,264,518,978,1718,257,504,951,1674)(36,71,141,279,545,1022,1783,1740,1309,2171,1952)(38,75,148,293,571,1066,1850,2802,1928,2653,2601)(40,79,156,307,112,222,435,826,1476,2374,1359)(42,83,164,323,624,1154,1978,2928,2766,1671,2602)(44,87,172,337,648,572,1067,1851,915,1616,2542)(46,91,180,353,676,1234,919,595,239,468,886)(48,95,188,369,706,1279,1636,2131,2567,3065,3563)(50,99,196,385,734,1328,2193,2755,950,1672,2358)(52,103,204,399,759,1012,1196,2030,2977,1958,2906)(54,107,212,415,788,1204,1016,1776,2721,1834,2783)(56,111,220,431,818,1460,2032,1367,1254,2029,2975)(58,115,228,447,428,812,1450,2342,1938,2600,3365)(60,119,236,462,875,1018,1780,2727,1821,2770,1885)(62,123,244,478,903,1597,2516,2847,1233,2078,1723)(64,127,252,494,933,187,367,702,1273,102,202)(66,131,260,510,962,1694,130,258,506,954,1679)(68,135,209,409,777,1093,334,643,1182,78,154)(70,139,275,538,1011,1767,2135,1126,1929,2870,2606)(72,143,283,553,1036,1802,199,391,746,1349,2220)(74,146,289,564,1055,1835,2027,1817,2477,1675,2607)(76,150,297,579,1080,1870,2826,2947,2796,3466,2901)(80,158,311,601,1035,789,1413,2042,1797,2744,3445)(84,166,327,631,1165,1730,2673,3133,1142,1959,2903)(90,178,349,669,1222,2065,3010,3020,2389,2603,3366)(92,182,357,683,1245,253,496,937,1649,1091,1886)(94,186,365,698,1267,2119,2885,3426,3397,982,1570)(96,190,373,714,1295,2118,3051,2714,1717,2657,2933)(98,194,381,197,387,738,444,505,952,1676,1930)(100,198,389,742,1341,1654,2584,3355,2172,3093,2919)(104,206,403,189,371,710,1287,2139,3068,3232,2240)(106,210,411,781,1399,576,1075,1863,2819,2604,2500)(108,214,419,795,1424,1987,2205,1520,1731,2543,3333)(110,218,427,810,1448,2340,2915,768,1380,887,1571)(114,226,443,842,1505,2415,1678,2611,1673,2335,471)(116,230,451,855,1248,844,957,1684,2619,2907,346)(118,234,458,868,578,1078,1557,1134,1943,2784,3461)(120,238,466,882,1563,2207,3119,2438,2302,3181,3538)(122,242,474,895,1584,2499,898,1010,1765,2710,3428)(124,246,482,910,1608,2532,3325,1456,2349,2112,2841)(126,250,490,430,816,1457,1179,2011,1762,2705,2665)(128,254,498,941,1656,1782,2345,942,1658,2588,2825)(132,262,514,970,1705,2642,378,722,1310,2074,1471)(134,266,522,985,1729,2672,610,1127,1715,2654,2612)(136,269,416,790,1415,2022,1864,1491,2398,3254,3308)(138,273,534,1003,1753,2697,1045,1818,2767,1680,2613)(140,277,424,804,1437,2249,2722,2047,2798,3467,304)(142,281,549,1029,1617,2544,3334,171,335,645,1185)(145,287,560,1049,1825,2774,1744,2685,955,1681,2615)(147,291,456,864,215,421,799,618,1143,155,305)(149,295,575,1073,1860,2815,3083,2954,1061,1845,2797)(151,299,583,1088,1881,2837,2278,3165,3320,2142,3071)(153,302,588,177,347,665,1216,2055,2391,2608,3369)(157,309,163,321,621,597,1107,817,521,983,1725)(159,313,605,1118,1916,1540,1087,1879,2481,1983,2934)(161,317,613,1133,1941,2884,2658,507,956,1683,2618)(165,325,627,1159,1335,846,965,1698,2636,2930,585)(167,329,635,1171,1999,2720,3388,3600,2375,2221,501)(169,331,639,1178,2010,2960,1682,2617,3290,301,586)(173,339,195,383,268,412,783,1402,469,888,1388)(175,343,658,539,1013,1770,975,1714,1979,2929,3521)(179,351,673,1228,2073,2912,3230,548,1027,1791,2739)(181,355,679,1239,515,972,1709,2647,3390,774,1389)(183,359,687,565,1056,1837,1691,2628,2785,2976,863)(185,363,694,1261,2111,3046,3018,2164,2880,3367,3616)(191,375,718,1128,1931,2682,3411,1846,382,729,396)(193,379,724,1313,2176,422,259,508,958,1686,1062)(201,394,752,666,243,476,899,1589,2506,2609,1760)(203,397,314,607,1121,1920,2865,2524,3317,2533,3326)(205,401,318,615,1137,1949,2896,1110,644,1183,2015)(207,405,769,659,1205,805,1439,1502,1954,2902,3011)(211,413,785,1406,2288,376,720,1306,1960,2908,3512)(213,417,792,1419,959,1688,2624,1896,408,775,1391)(217,425,806,1441,483,912,1610,2535,3246,3368,3305)(219,429,814,1453,2346,3014,1594,2106,2451,1887,2842)(221,433,822,1468,2365,3226,1522,2098,1518,1724,2486)(223,437,830,1483,2388,3245,2691,1699,2637,2703,3422)(225,441,838,1498,2406,3260,3252,953,1677,2610,2887)(227,445,845,1509,2421,3268,2872,3198,3094,3572,3518)(229,449,851,879,1558,2467,2488,3161,703,1274,892)(231,453,859,1528,2348,1303,1936,2876,3438,3596,3142)(233,457,866,336,647,1188,728,390,744,1345,894)(235,460,871,1545,1366,889,1574,2273,420,797,664)(237,464,878,1556,1990,2943,3526,2957,2998,1572,2487)(241,472,893,1581,2203,3115,3309,2254,2605,3205,896)(245,480,906,1602,2523,3316,3581,2120,30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18,616,1140,1956,1543,2453,3282,3532,2534,3328,2334,2807,2174,3096,3228,3486,3607,1166,1701,341,655,1200,2034,1232,103,205,402,765,640,832,1488,2394,1439,2327,3200,3364,2834,2384,3242,905,1601,2522,3315,2150,1711,2650,3393,2890,3504,2101,3039,2991,3113,3556,861,1533,2444,3277,1228,1755,2642,931,1640,2568,3345,302,589,1098,1895,790,1416,2302,3182,1552,1299,2157,462,876,1553,2463,1287,2028,2974,3109,2388,1831,884,1567,401,763,1375,2255,3012,945,1664,1905,2754,3339,2253,3150,3559,3331,1947,2894,3506,3564,399,760,1371,2251,868,1540,2451,3279,1608,2533,3327,1854,1310,2173,3095,2833,3298,2688,964,172,338,651,1196,673,1229,2074,1964,2912,3513,375,719,1305,2167,2314,3191,2592,3362,1478,2379,2503,1097,1893,2848,3321,968,1703,2641,3052,2949,1249,2098,3037,2199,3030,2052,2996,3546,3304,2712,1003,1754,484,915,1617,2545,1672,2604,3368,3617,3425,1352,2225,3130,2775,714,1296,2151,575,1074,1862,2818,1193,2025,2972,3537,1050,464,879,202,396,756,1366,2245,498,942,1659,1805,2752,1370,2249,3147,2537,1131,1938,2880,3500,1720,2662,3399,3619,1820,2210,2510,2443,2792,3316,2539,2652,721,1309,2172,3094,2492,3091,3571,85,169,332,641,349,670,1223,2067,3013,3523,127,253,497,940,1424,2311,1658,2589,1176,1811,2761,586,1093,1889,2844,508,959,1689,2626,1999,681,1243,2090,1329,2087,2926,3520,3593,2499,3303,1925,2421,238,467,885,1569,2485,3293,3533,3499,3427,995,1742,2684,3412,2671,3405,2868,293,572,1068,1853,648,1190,2021,2969,558,234,459,99,197,388,741,1340,252,495,936,1036,1803,2750,3248,3186,1610,1042,1813,2764,3082,2681,1874,2832,3372,3475,1326,2191,1530,2438,2790,1607,2531,787,1411,2296,3178,2110,2166,3089,41,82,163,322,176,346,664,1215,2054,2998,2467,3045,2294,2780,3332,2767,3212,2398,1350,1038,1806,2607,2797,1618,2546,799,1430,1503,2412,2117,351,674,1231,2077,1237,1973,2923,3518,2357,2918,3517,3630,111,221,434,825,1475,2373,3231,2871,2705,3423,2189,3105,3522,3217,3576,3549,2415,1512,1171,1709,2635,3384,2088,2721,3390,115,229,450,854,650,1194,2027,125,249,489,925,1633,2476,2390,2881,910,551,1033,1800,2156,1736,2679,3410,2932,2811,2128,2277,857,1525,2434,901,1594,2512,991,1739,2682,3312,1301,2161,3087,3563,307,595,1105,1902,795,1425,2313,3190,1556,2109,3044,1830,2540,1816,2766,2819,744,1346,2218,3127,1843,914,1615,419,796,1427,2316,1264,2115,3050,1911,2856,3494,1147,1969,2919,3326,1966,2915,3515,47,94,187,368,705,1278,2130,3042,1757,2700,1318,2183,2931,2349,3216,3592,3121,845,1510,970,1706,2644,3388,1774,2720,1915,2859,2356,3221,2633,660,1208,61,122,243,477,902,1596,1483,1937,2879,277,542,1019,1781,987,1733,2676,3054,1855,1274,1392,449,852,1518,2057,3002,1923,516,975,1715,2655,712,1292,2147,3075,1681,2616,3376,3620,2673,1869,2441,3276,2777,1258,2108,3043,2400,3255,3567,3396,387,739,1337,2207,1058,482,911,212,416,791,1418,694,1262,2112,2082,2007,2957,615,1138,1952,2901,1143,1961,2909,15,30,60,120,239,469,889,1575,1001,1751,2694,2566,1978,1452,2345,3213,2211,443,843,1507,2419,3267,3606,2938,3269,1111,1908,1460,2353,3218,313,606,29,58,116,231,454,862,1178,1129,1934,135,268,526,992,520,982,1724,2666,1067,700,1270,226,444,844,1508,2420,1121,1921,2867,1125,1928,367,703,1275,2127,2003,2952,3530,3505,3437,1064,1848,2800,3469,690,1256,2106,3041,3477,3073,3566,194,382,730,1323,564,244,479,105,209,410,780,361,691,1257,2107,1175,2006,2956,838,1499,2408,1090,1885,2841,3261,2295,1883,2839,1622,2551,1364,2242,1548,2459,2448,1635,2564,808,1446,2337,3207,224,440,837,1497,2405,3259,2556,2611,594,1104,1901,2579,3351,3579,3572,13,26,52,104,207,406,772,609,1126,1930,381,728,1320,2186,3103,1516,2426,3270,363,695,890,1577,1246,1991,2628,605,1119,1919,2864,3414,182,358,686,1250,1169,1997,2947,2888,2725,3435,2206,3118,3484,3229,3181,1591,2509,3310,2138,3067,2870,1845,2798,3468,3609,121,241,473,133,265,521,984,1728,1453,2070,2695,3420,2480,439,835,1493,581,1085,1877,2733,1408,2291,3174,2934,2821,2148,2284,871,1546,2457,924,1631,2561,1017,1779,2726,3314,1485,2391,3247,3101,2624,1626,2418,299,584,1091,1887,2843,3138,3578,5,10,20,40,80,159,314,608,1124,1926,192,378,723,1312,2175,3097,2330,2804,3156,3463,1918,2862,3387,1160,1688,311,602,1114,1912,2687,87,173,340,654,629,1163,1992,2945,1776,2722,1333,2201,2830,2369,2298,897,1588,2505,2692,3417,1927,1054,1834,2784,3462,2040,2985,3541,65,130,259,509,961,1693,1224,1750,2693,3418,2121,3055,3561,295,576,1076,1866,783,1403,2285,3169,1863,1291,1400,458,869,1542,2060,1283,2135,536,1008,1762,2706,828,1481,2385,2182,1686,2621,3379,143,284,556,1043,1815,2229,3132)Polycyclic presentation:
11,3631|b^a=b^2304341 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(39941, 1);