Finite Group DatabasebetaFinite Group Databasebeta| order | 45643 |
| automorphism | ? |
| homology | Abelianization (H1) = C13 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C3511 ⋊ C13 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3511 | C13 |
| LCS | G ▷ C3511 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
| minimal degree | μ(G) = 3511 |
| transitive degree | μt(G) = 3511 |
A minimal faithful permutation representation — 2 generators on 3511 points:
(2,3,5,9,17,33,65,129,255,498,211,416,799)(4,7,13,25,49,97,192,380,733,1342,2223,2449,3125)(6,11,21,41,81,161,319,621,1158,1779,1955,2863,1453)(8,15,29,57,113,224,441,844,1522,2440,3226,3113,2584)(10,19,37,73,145,287,560,1055,1839,38,75,149,295)(12,23,45,89,177,351,681,1259,1294,1799,2732,515,975)(14,27,53,105,208,410,787,1432,2335,377,729,104,206)(16,31,61,121,240,472,899,1610,1325,2205,1218,2057,2953)(18,35,69,137,271,530,1003,379,731,1188,417,800,1454)(20,39,77,153,303,282,551,1041,1819,2617,2188,3064,3473)(22,43,85,169,335,651,1207,763,1393,1575,2500,3265,575)(24,47,93,184,365,709,1310,704,1301,572,1076,1744,2679)(26,51,101,200,395,760,1388,1893,308,599,1117,296,576)(28,55,109,216,426,816,1477,1431,2338,482,917,1636,1723)(30,59,117,232,456,869,717,1320,2199,3071,2367,802,407)(32,63,125,247,484,920,1641,415,797,1449,2357,2231,3096)(34,67,133,263,514,973,1720,2652,2664,944,421,807,1464)(36,71,141,279,546,1032,160,317,617,1044,1824,2756,2135)(40,79,157,311,605,1129,358,695,268,524,96,190,376)(42,83,165,327,635,1180,2007,2915,3428,1092,150,297,578)(44,87,173,343,318,619,1154,1970,2876,3102,3201,976,1724)(46,91,181,359,697,1287,2152,2729,871,1561,2485,207,408)(48,95,188,372,722,1330,2006,1364,2253,2382,3190,3082,3437)(50,99,196,388,747,1365,2255,3115,2977,3441,801,1455,2364)(52,103,204,403,775,1414,2317,3154,3340,406,781,1424,2329)(54,107,212,418,205,405,779,1420,1061,1847,2776,3381,1082)(56,111,220,433,830,1501,209,412,791,1438,2348,3175,3351)(58,115,228,448,855,1538,1327,2208,3078,3477,2968,577,1083)(60,119,236,464,884,1583,2511,806,1462,881,1578,2504,2656)(62,123,243,478,910,1627,2563,2303,3034,3269,3498,3507,783)(64,127,251,491,932,1659,2593,2750,1613,2263,3119,1971,2878)(66,131,259,506,959,1116,1916,554,499,945,429,822,1488)(68,135,267,522,989,1745,1005,909,1625,2224,3089,3231,1767)(70,139,275,538,1016,1781,2715,2458,3239,2714,2865,3012,2373)(72,143,283,553,1045,180,357,693,1280,2143,3025,2741,322)(74,147,291,567,1067,1856,2786,978,1727,76,151,299,582)(78,155,307,597,138,273,534,496,941,1673,1339,215,424)(80,159,315,613,1145,1961,765,1396,1626,2561,3092,2954,1838)(82,163,323,627,1167,1988,2186,3060,2351,2017,808,1465,943)(84,167,331,643,1193,2024,187,371,720,1326,2207,3077,1906)(86,171,339,659,264,516,977,883,1581,664,1230,1840,1085)(88,175,347,673,1245,1179,2005,2913,1423,2327,2810,2680,728)(90,179,355,689,1272,2132,2508,1233,2075,2772,1918,579,1086)(92,183,363,705,1303,838,1515,2040,2823,1947,752,1374,2270)(94,186,369,716,1319,2198,1399,336,653,1210,2045,1457,784)(98,194,384,740,1355,2242,708,1309,2189,1677,812,1472,2383)(100,198,392,755,1380,2278,3130,3486,1481,2394,2757,3373,3020)(102,202,399,768,507,960,1699,1949,2603,1384,1056,1611,2546)(106,210,414,795,1445,2352,3178,3424,1735,2668,298,580,1088)(108,214,422,809,694,1282,2145,3026,2918,574,1080,1725,2657)(110,218,430,824,1111,1911,2174,3049,1689,1033,1806,409,785)(112,222,437,837,1513,2430,1114,276,540,1020,1787,2545,3292)(114,226,444,849,1529,2448,2220,1035,1810,2743,1456,2365,3183)(116,230,452,862,1548,2470,3245,1495,2408,2860,3009,2330,3161)(118,234,460,876,1569,2100,2984,2130,3013,3225,1953,2861,1880)(120,238,468,891,1596,2528,1815,2748,1352,2238,2642,2914,3427)(122,242,476,906,1620,2556,2310,667,680,1257,1269,1084,1881)(124,245,481,915,1633,312,607,1133,1940,1239,2083,144,285)(126,249,487,926,447,853,1535,550,1040,1817,2751,2921,1427)(128,253,495,939,488,928,1653,905,1618,2554,1999,2908,3342)(130,257,502,951,700,1293,2162,256,500,947,459,874,1566)(132,261,510,965,1706,2325,3157,2784,1343,2225,3091,3234,3104)(134,265,518,981,1732,2665,3341,3329,1976,2292,2868,2692,2403)(136,269,526,995,1754,1731,1624,2560,3300,3227,3497,3047,2298)(140,277,542,1024,1793,2726,2257,1898,400,770,1405,982,1734)(142,281,549,1038,1814,1780,2293,2479,1052,730,1340,231,454)(146,289,563,1060,1845,2774,535,606,1131,1937,823,1489,744)(148,293,571,1074,1868,2796,2897,2246,1912,2826,3066,3474,2704)(152,301,586,1097,201,397,764,1394,2294,2965,1871,2691,626)(154,305,593,646,1198,2032,2934,2717,2834,1118,1919,583,1093)(156,309,601,1121,328,637,1183,2011,2644,3335,1637,2573,2659)(158,313,609,1137,389,749,1369,614,1147,1964,2873,1458,813)(162,321,624,1163,1983,774,1412,2315,3151,1678,827,1496,2410)(164,325,631,1173,1996,2904,3380,2959,1796,1825,2758,3374,2709)(166,329,639,1048,952,1684,1306,2183,3057,561,1057,1841,1676)(168,333,647,1200,2035,2675,2677,771,1407,2309,191,378,630)(170,337,655,1213,2049,1530,2450,1273,455,867,300,584,1094)(172,341,663,1228,568,1069,1859,2789,1855,1860,2790,1728,2660)(174,345,670,1206,628,1168,1990,896,1605,2540,3257,425,814)(176,349,677,1251,2103,2945,2038,2939,3110,2828,1717,2648,2769)(178,353,685,1266,2122,2971,2402,2911,1984,2892,1466,2374,2884)(182,361,701,1295,741,1357,1109,1908,2092,2978,3382,2770,1883)(185,367,712,1314,750,1371,2264,1252,2105,2688,3354,1087,1884)(189,374,725,1334,2215,3084,2940,2721,2851,3404,604,1127,1428)(193,382,737,956,1692,2622,2423,3215,946,1433,833,1505,1256)(195,386,471,897,1607,767,1400,1565,2489,3090,1113,1914,986)(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3457,2348,3176,3460,3264,3497,3145,3285,489,930,87,174,346,216,427,819,1483,1276,2138,1729,2662,3339,603,1126,627,878,1573,2498,2780,768,1402,1351,2237,3102,3178,1200,2012,135,268,525,994,1753,2691,3356,709,899,1611,2547,3293,3032,3418,1674,710,371,721,1329,828,1498,2413,3208,2700,3359,2560,3230,981,1733,2667,333,648,1203,2038,2878,2309,3149,2165,3041,2687,3353,2938,1412,551,1042,1629,701,1296,2166,3042,2192,2259,1642,2470,3246,3498,2929,1210,2046,1340,2222,214,423,812,433,831,1503,2419,2145,3027,2673,3348,1781,426,817,1173,1592,2522,733,1343,1409,1682,2249,3112,127,252,494,938,293,572,1077,1873,2802,3393,3485,1314,1614,1783,2717,2457,1191,2021,2847,1320,836,1512,2429,1511,2427,1390,2290,3138,3488,265,519,984,1488,2403,695,1284,2149,2233,3098,1036,1812,2747,3371,843,1133,1941,2374,1096,1897,2571,1307,2186,3061,3453,1706,2636,2583,3247,3499,2939,3341,2052,2949,2439,3225,462,881,1579,837,1514,2431,3195,997,1757,753,1377,2275,824,1491,2000,2534,504,956,1693,2313,2632,565,1064,619,1155,1973,2881,595,1111,1912,2827,1827,2759,3107,2194,2553,1963,2872,3261,2067,2963,2992,2208,1602,2537,3287,2436,3223,2296,3142,2703,3360,540,1021,1788,2410,3207,1317,2195,1711,2642,3315,1817,1814,1872,2800,1444,1950,2857,2556,1929,2841,3308,1436,2345,3173,3492,2640,2134,321,625,1165,1586,2471,2953,3437,3292,2258,37,74,148,294,574,1081,1245,1800,2733,1407,2310,3150,1497,2411,2910,3289,979,1730,2664,3151,3333,1083,1880,1430,2337,1990,2898,1135,1944,2852,2798,2761,3376,2824,1175,1999,847,1524,2443,2976,1983,2891,2353,157,312,608,1136,1946,2855,2980,3368,2529,1040,1818,2654,3212,3124,99,197,391,754,1379,2277,2751,2812,3397,2368,2864,3409,3299,2866,3411,484,921,1643,1718,2650,2912,3019,637,1184,2013,2521,3249,3438,3370,617,1151,85,170,338,658,1220,2060,2099,2755,3372,2327,3159,3310,405,780,1423,2328,384,741,1358,2247,3111,1633,2501,2482,3256,2902,2278,81,162,322,626,1166,1987,2895,2019,2923,1541,2446,3233,3449,2893,1974,2883,347,674,1248,2098,2983,3260,3447,3509,502,952,1685,47,94,187,210,415,798,1452,1268,2127,3011,3306,3502,3187,3413,622,860,331,644,926,762,1392,2293,2342,3169,1380,1195,2028,2931,3279,2035,2600,3123,1255,2107,181,360,700,1294,2163,3030,1694,2625,3324,238,469,894,811,1471,2382,3191,751,1373,2269,3125,975,1723,2656,285,557,1051,1834,169,336,654,1212,2048,2945,3084,2936,2698,2472,3219,1618,691,1277,2140,3021,410,788,1435,2344,3172,3385,3327,3489,962,931,1658,175,348,676,428,821,1487,2402,2139,3020,2663,3340,3507,1127,1933,1168,1574,663,1229,1655,1403,2304,2238,3103,3482,530,1004,1766,269,527,998,1759,2697,1442,2351,369,717,1321,2201,3072,3464,2396,2612,1312,414,796,1448,1499,2415,3211,2352,271,531,1005,1767,1734,303,590,649,1204,2039,2940,343,667,1236,2080,2968,3354,1770,2705,2316,1043,1823,2567,1297,2168,2122,3004,795,1446,2354,2950,3436,3510,3423,2047,1709,1454,1839,424,813,1473,832,1504,1012,1776,2711,3362,3349,1110,1910,818,1481,1997,2523,1243,1344,2227,2312,1699,2631,3330,253,496,942,1675,573,1079,1877,2806,3396,2361,3182,725,1335,2216,3085,3239,2022,2926,3183,2200,805,1461,2369,2428,3218,2291,3140,538,1017,520,986,1740,597,1114,1285,2150,1480,2393,673,1246,2094,2979,3444,681,1260,2113,2993,456,855,1539,2187,3063,3008)Polycyclic presentation:
13,3511|b^a=b^494283 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(45643, 1);