Finite Group Databasebeta

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#27136408

• 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 3089 points:

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9,1770,1887,1999,1912,1788,1667,1550,1437,1328,1432,1539,1648,1761,1878,1990,2085,2172,2255,2334,2409,2480,2547,2610,2669,2724,2775,2822,2865,2904,2939,2970,2997,3020,3007,2977,2943,2905,2863,2817,2767,2713,2654,2591,2524,2453,2378,2299,2216,2129,2038,1936,1820,1699,1582,1469,1360,1255,1154,1057,964,875,790,709,632,704,779,856,937,1022,1111,1204,1301,1402,1507,1616,1729,1846,1958,2056,2143,2226,2305,2380,2451,2518,2581,2640,2695,2679,2617,2551,2481,2407,2329,2247,2161,2070,1968,1852,1731,1614,1501,1392,1287,1186,1089,996,907,822,741,664,591,522,457,396,339,286,237,192,232,275,320,369,422,479,540,605,674,747,824,905,990,1079,1172,1269,1370,1475,1584,1697,1814,1926,2024,2111,2095,2000,1884,1763,1646,1533,1424,1319,1218,1121,1028,939,854,773,696,623,554,489,428,371,318,269,224,183,146,113,84,59,38,21,8,16,27,40,57,78,103,132,165,202,243,288,337,390,447,508,573,642,715,792,873,958,1047,1140,1237,1338,1443,1552,1665,1782,1903,1797,1680,1567,1458,1353,1252,1155,1062,973,888,807,730,657,588,523,462,405,352,303,258,217,180,147,118,91,116,145,178,215,256,301,350,403,460,521,586,655,728,805,886,971,1060,1153,1250,1351,1456,1565,1678,1795,1913,2014,2104,2190,2272,2350,2424,2434,2363,2288,2209,2126,2039,1941,1829,1712,1599,1490,1385,1284,1187,1094,1005,920,839,762,689,620,555,494,435,492,553,618,687,760,837,918,1003,1092,1185,1282,1383,1488,1597,1710,1827,1939,2037,2124,2207,2286,2361,2432,2502,2568,2630,2688,2742,2792,2838,2880,2890,2851,2808,2761,2710,2655,2596,2533,2466,2395,2320,2241,2158,2071,1973,1861,1744,1631,1522,1417,1316,1219,1126,1035,1124,1217,1314,1415,1520,1629,1742,1859,1971,2069,2156,2239,2318,2393,2464,2531,2594,2653,2708,2759,2806,2849,2888,2926,2960,2990,3016,3038,3056,3070,3080,3083,3076,3065,3050,3031,3008,2981,2950,2915,2876,2833,2786,2735,2680,2621,2558,2491,2420,2345,2266,2183,2096,2005,1891,2003,1914,1792,1671,1554,1441,1332,1227,1327,1430,1535,1644,1757,1874,1986,2082,2169,2252,2331,2406,2477,2544,2607,2666,2721,2772,2819,2862,2901,2936,2967,2994,2980,2946,2908,2866,2820,2770,2716,2658,2595,2528,2457,2382,2303,2220,2133,2042,1940,1824,1703,1586,1473,1364,1259,1158,1061,968,879,794,713,636,563,631,702,775,852,933,1018,1107,1200,1297,1398,1503,1612,1725,1842,1954,2052,2139,2222,2301,2376,2447,2514,2577,2636,2620,2554,2484,2410,2332,2250,2164,2074,1972,1856,1735,1618,1505,1396,1291,1190,1093,1000,911,826,745,668,595,526,461,400,343,290,241,196,155,191,230,271,316,365,418,475,536,601,670,743,820,901,986,1075,1168,1265,1366,1471,1580,1693,1810,1922,2020,2004,1888,1767,1650,1537,1428,1323,1222,1125,1032,943,858,777,700,627,558,493,432,375,322,273,228,187,150,117,88,63,42,25,12,3,7,14,23,36,53,74,99,128,161,198,239,284,333,386,443,504,569,638,711,788,869,954,1043,1136,1233,1334,1439,1548,1661,1778,1899,1801,1684,1571,1462,1357,1256,1159,1066,977,892,811,734,661,592,527,466,409,356,307,262,221,184,151,120,149,182,219,260,305,354,407,464,525,590,659,732,809,890,975,1064,1157,1254,1355,1460,1569,1682,1799,1915,2015,2105,2191,2273,2351,2425,2495,2505,2438,2367,2292,2213,2130,2043,1945,1833,1716,1603,1494,1389,1288,1191,1098,1009,924,843,766,693,624,559,496,557,622,691,764,841,922,1007,1096,1189,1286,1387,1492,1601,1714,1831,1943,2041,2128,2211,2290,2365,2436,2503,2569,2631,2689,2743,2793,2839,2881,2919,2929,2894,2855,2812,2765,2714,2659,2600,2537,2470,2399,2324,2245,2162,2075,1977,1865,1748,1635,1526,1421,1320,1223,1128,1221,1318,1419,1524,1633,1746,1863,1975,2073,2160,2243,2322,2397,2468,2535,2598,2657,2712,2763,2810,2853,2892,2927,2961,2991,3017,3039,3057,3071,3081,3087,3089,3085,3078,3067,3052,3033,3010,2983,2952,2917,2878,2835,2788,2737,2682,2623,2560,2493,2422,2347,2268,2185,2098,2007,1916,1796,1675,1558,1445,1336,1231,1130,1226,1325,1426,1531,1640,1753,1870,1982,2079,2166,2249,2328,2403,2474,2541,2604,2663,2718,2769,2816,2859,2898,2933,2964,2949,2911,2869,2823,2773,2719,2661,2599,2532,2461,2386,2307,2224,2137,2046,1944,1828,1707,1590,1477,1368,1263,1162,1065,972,883,798,717,640,567,498,562,629,698,771,848,929,1014,1103,1196,1293,1394,1499,1608,1721,1838,1950,2048,2135,2218,2297,2372,2443,2510,2573,2557,2487,2413,2335,2253,2167,2077,1976,1860,1739,1622,1509,1400,1295,1194,1097,1004,915,830,749,672,599,530,465,404,347,294,245,200,159,122,154,189,226,267,312,361,414,471,532,597,666,739,816,897,982,1071,1164,1261,1362,1467,1576,1689,1806,1894,1773,1656,1543,1434,1329,1228,1131,1038,949,864,783,706,633,564,499,438,381,328,279,234,193,156,123,94,69,48,31,18,9,4)

Polycyclic presentation:

2^2,3089|a^2=b,c^a=c^2696,c^b=c^3088

Conjugacy classes & character table

776 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12356, 3);