Finite Group Databasebeta

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#27166272

• metacyclic
• supersolvable
• metabelian
• solvable
• monolithic
• monomial
• stem
• Frobenius

Aliases

No aliases for this group.

Splittings

Subgroups

6 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 3221 points:

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53,2905,2853,2797,2738,2675,2608,2537,2462,2357,2224,2095,1970,1849,1732,1619,1510,1405,1304,1207,1114,1025,940,859,780,857,938,1023,1112,1205,1302,1403,1508,1617,1730,1847,1968,2093,2222,2355,2460,2535,2606,2673,2736,2695,2631,2563,2491,2415,2301,2168,2039,1914,1793,1676,1563,1454,1349,1248,1151,1058,969,884,803,726,653,584,519,458,401,348,299,254,213,176,143,114,89,66,87,112,141,174,211,252,297,346,399,456,517,582,651,724,801,882,967,1056,1149,1246,1347,1452,1561,1674,1791,1912,2037,2166,2299,2379,2243,2110,1981,1856,1735,1618,1505,1396,1291,1190,1093,1000,911,826,745,668,595,526,461,400,343,290,241,196,155,191,230,271,316,365,418,475,536,601,670,743,820,901,986,1075,1168,1265,1366,1471,1580,1693,1810,1931,2056,2185,2318,2428,2504,2576,2644,2708,2768,2824,2876,2924,2904,2849,2790,2727,2660,2589,2514,2435,2324,2187,2054,1925,1800,1679,1562,1449,1340,1235,1134,1037,1129,1224,1321,1422,1527,1636,1749,1866,1987,2112,2241,2373,2276,2145,2274,2398,2479,2554,2625,2692,2755,2814,2869,2920,2967,3010,3049,3084,3115,3142,3165,3184,3199,3210,3202,3190,3174,3154,3130,3102,3070,3034,2994,2950,2902,2850,2794,2734,2671,2604,2533,2458,2353,2220,2091,1966,1845,1728,1615,1506,1401,1300,1203,1110,1021,936,855,778,703,776,853,934,1019,1108,1201,1298,1399,1504,1613,1726,1843,1964,2089,2218,2351,2456,2531,2602,2669,2628,2560,2488,2412,2297,2164,2035,1910,1789,1672,1559,1450,1345,1244,1147,1054,965,880,799,722,649,580,515,454,397,344,295,250,209,172,139,110,85,64,45,62,83,108,137,170,207,248,293,342,395,452,513,578,647,720,797,878,963,1052,1145,1242,1343,1448,1557,1670,1787,1908,2033,2162,2295,2375,2239,2106,1977,1852,1731,1614,1501,1392,1287,1186,1089,996,907,822,741,664,591,522,457,396,339,286,237,192,232,275,320,369,422,479,540,605,674,747,824,905,990,1079,1172,1269,1370,1475,1584,1697,1814,1935,2060,2189,2322,2431,2507,2579,2647,2711,2771,2827,2879,2927,2971,2952,2901,2846,2787,2724,2657,2586,2511,2432,2320,2183,2050,1921,1796,1675,1558,1445,1336,1231,1130,1226,1325,1426,1531,1640,1753,1870,1991,2116,2245,2377,2272,2143,2016,2141,2270,2396,2478,2553,2624,2691,2754,2813,2868,2919,2966,3009,3048,3083,3114,3141,3164,3183,3198,3187,3171,3151,3127,3099,3067,3031,2991,2947,2899,2847,2791,2731,2667,2600,2529,2454,2349,2216,2087,1962,1841,1724,1611,1502,1397,1296,1199,1106,1017,932,851,774,701,630,699,772,849,930,1015,1104,1197,1294,1395,1500,1609,1722,1839,1960,2085,2214,2347,2452,2527,2598,2557,2485,2409,2293,2160,2031,1906,1785,1668,1555,1446,1341,1240,1143,1050,961,876,795,718,645,576,511,450,393,340,291,246,205,168,135,106,81,60,43,28,41,58,79,104,133,166,203,244,289,338,391,448,509,574,643,716,793,874,959,1048,1141,1238,1339,1444,1553,1666,1783,1904,2029,2158,2291,2371,2235,2102,1973,1848,1727,1610,1497,1388,1283,1182,1085,992,903,818,737,660,587,518,453,392,335,282,233,277,324,373,426,483,544,609,678,751,828,909,994,1083,1176,1273,1374,1479,1588,1701,1818,1939,2064,2193,2326,2434,2510,2582,2650,2714,2774,2830,2882,2930,2974,3014,2996,2949,2898,2843,2784,2721,2654,2583,2508,2429,2316,2179,2046,1917,1792,1671,1554,1441,1332,1227,1327,1430,1535,1644,1757,1874,1995,2120,2249,2381,2268,2139,2014,1891,2012,2137,2266,2394,2477,2552,2623,2690,2753,2812,2867,2918,2965,3008,3047,3082,3113,3140,3163,3182,3168,3148,3124,3096,3064,3028,2988,2944,2896,2844,2788,2728,2664,2596,2525,2450,2345,2212,2083,1958,1837,1720,1607,1498,1393,1292,1195,1102,1013,928,847,770,697,628,561,626,695,768,845,926,1011,1100,1193,1290,1391,1496,1605,1718,1835,1956,2081,2210,2343,2448,2523,2482,2406,2289,2156,2027,1902,1781,1664,1551,1442,1337,1236,1139,1046,957,872,791,714,641,572,507,446,389,336,287,242,201,164,131,102,77,56,39,26,15,24,37,54,75,100,129,162,199,240,285,334,387,444,505,570,639,712,789,870,955,1044,1137,1234,1335,1440,1549,1662,1779,1900,2025,2154,2287,2367,2231,2098,1969,1844,1723,1606,1493,1384,1279,1178,1081,988,899,814,733,656,583,514,449,388,331,278,326,377,430,487,548,613,682,755,832,913,998,1087,1180,1277,1378,1483,1592,1705,1822,1943,2068,2197,2330,2437,2513,2585,2653,2717,2777,2833,2885,2933,2977,3017,3053,3036,2993,2946,2895,2840,2781,2718,2651,2580,2505,2426,2312,2175,2042,1913,1788,1667,1550,1437,1328,1432,1539,1648,1761,1878,1999,2124,2253,2385,2264,2135,2010,1889,1770,1887,2008,2133,2262,2392,2476,2551,2622,2689,2752,2811,2866,2917,2964,3007,3046,3081,3112,3139,3162,3145,3121,3093,3061,3025,2985,2941,2893,2841,2785,2725,2661,2593,2521,2446,2341,2208,2079,1954,1833,1716,1603,1494,1389,1288,1191,1098,1009,924,843,766,693,624,559,496,557,622,691,764,841,922,1007,1096,1189,1286,1387,1492,1601,1714,1831,1952,2077,2206,2339,2444,2403,2285,2152,2023,1898,1777,1660,1547,1438,1333,1232,1135,1042,953,868,787,710,637,568,503,442,385,332,283,238,197,160,127,98,73,52,35,22,13,6,11,20,33,50,71,96,125,158,195,236,281,330,383,440,501,566,635,708,785,866,951,1040,1133,1230,1331,1436,1545,1658,1775,1896,2021,2150,2283,2363,2227,2094,1965,1840,1719,1602,1489,1380,1275,1174,1077,984,895,810,729,652,579,510,445,384,327,379,434,491,552,617,686,759,836,917,1002,1091,1184,1281,1382,1487,1596,1709,1826,1947,2072,2201,2334,2440,2516,2588,2656,2720,2780,2836,2888,2936,2980,3020,3056,3088,3072,3033,2990,2943,2892,2837,2778,2715,2648,2577,2502,2423,2308,2171,2038,1909,1784,1663,1546,1433,1541,1652,1765,1882,2003,2128,2257,2389,2260,2131,2006,1885,1768,1653,1766,1883,2004,2129,2258,2390,2475,2550,2621,2688,2751,2810,2865,2916,2963,3006,3045,3080,3111,3138,3118,3090,3058,3022,2982,2938,2890,2838,2782,2722,2658,2590,2518,2442,2337,2204,2075,1950,1829,1712,1599,1490,1385,1284,1187,1094,1005,920,839,762,689,620,555,494,435,492,553,618,687,760,837,918,1003,1092,1185,1282,1383,1488,1597,1710,1827,1948,2073,2202,2335,2281,2148,2019,1894,1773,1656,1543,1434,1329,1228,1131,1038,949,864,783,706,633,564,499,438,381,328,279,234,193,156,123,94,69,48,31,18,9,4)

Polycyclic presentation:

2^2,3221|a^2=b,c^a=c^234,c^b=c^3220

Conjugacy classes & character table

809 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12884, 3);