Finite Group Databasebeta

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#27159138

• 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 3109 points:

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945,1030,1119,1212,1309,1410,1515,1624,1737,1854,1975,2100,2229,2362,2499,2640,2785,2933,2812,2667,2526,2389,2256,2127,2002,1881,1764,1651,1540,1649,1762,1879,2000,2125,2254,2387,2524,2665,2810,2952,2969,2839,2690,2545,2404,2267,2134,2005,1880,1759,1642,1529,1420,1315,1214,1117,1024,935,850,769,692,619,550,485,424,367,314,265,220,179,142,109,80,55,34,17,29,44,61,82,107,136,169,206,247,292,341,394,451,512,577,646,719,796,877,962,1051,1144,1241,1342,1447,1556,1669,1786,1907,2032,2161,2294,2431,2572,2717,2866,2982,3010,3034,3020,2989,2872,2719,2570,2425,2284,2147,2279,2414,2551,2692,2837,2908,2760,2615,2474,2337,2204,2075,1950,1829,1712,1599,1490,1385,1284,1187,1094,1005,920,839,762,689,620,555,494,435,492,553,618,687,760,837,918,1003,1092,1185,1282,1383,1488,1597,1710,1827,1948,2073,2202,2335,2472,2613,2758,2906,2939,2787,2638,2493,2352,2215,2082,1953,1828,1707,1590,1477,1368,1263,1162,1065,972,883,798,717,640,567,498,562,629,698,771,848,929,1014,1103,1196,1293,1394,1499,1608,1721,1838,1959,2084,2213,2346,2483,2624,2769,2917,2828,2683,2542,2405,2272,2143,2016,2141,2270,2403,2540,2681,2826,2960,2998,2975,2857,2708,2563,2422,2285,2152,2023,1898,1777,1660,1547,1438,1333,1232,1135,1042,953,868,787,710,637,568,503,442,385,332,283,238,197,160,127,98,73,52,35,22,13,6,11,20,33,50,71,96,125,158,195,236,281,330,383,440,501,566,635,708,785,866,951,1040,1133,1230,1331,1436,1545,1658,1775,1896,2021,2150,2283,2420,2561,2706,2855,2887,2735,2586,2441,2300,2163,2030,1901,1776,1655,1771,1890,2011,2136,2265,2398,2535,2676,2821,2924,2776,2631,2490,2353,2220,2091,1966,1845,1728,1615,1506,1401,1300,1203,1110,1021,936,855,778,703,776,853,934,1019,1108,1201,1298,1399,1504,1613,1726,1843,1964,2089,2218,2351,2488,2629,2774,2922,2951,2803,2654,2509,2368,2231,2098,1969,1844,1723,1606,1493,1384,1279,1178,1081,988,899,814,733,656,583,514,449,388,331,278,326,377,430,487,548,613,682,755,832,913,998,1087,1180,1277,1378,1483,1592,1705,1822,1943,2068,2197,2330,2467,2608,2753,2901,2844,2699,2556,2697,2842,2968,3002,3029,3052,3071,3086,3075,3059,3039,3015,2987,2873,2724,2579,2438,2301,2168,2039,1914,1793,1676,1563,1454,1349,1248,1151,1058,969,884,803,726,653,584,519,458,401,348,299,254,213,176,143,114,89,66,87,112,141,174,211,252,297,346,399,456,517,582,651,724,801,882,967,1056,1149,1246,1347,1452,1561,1674,1791,1912,2037,2166,2299,2436,2577,2722,2871,2903,2751,2602,2457,2316,2179,2046,1917,1792,1671,1554,1441,1332,1227,1327,1430,1535,1644,1757,1874,1995,2120,2249,2382,2519,2660,2805,2940,2792,2647,2506,2369,2236,2107,1982,1861,1744,1631,1522,1417,1316,1219,1126,1035,1124,1217,1314,1415,1520,1629,1742,1859,1980,2105,2234,2367,2504,2645,2790,2938,2959,2819,2670,2525,2384,2247,2114,1985,1860,1739,1622,1509,1400,1295,1194,1097,1004,915,830,749,672,599,530,465,404,347,294,245,200,159,122,154,189,226,267,312,361,414,471,532,597,666,739,816,897,982,1071,1164,1261,1362,1467,1576,1689,1806,1927,2052,2181,2314,2451,2592,2737,2885,2996,3024,3048,3068,3084,3096,3104,3107,3100,3089,3074,3055,3032,3005,2974,2852,2888,2740,2595,2454,2317,2184,2055,1930,1809,1692,1579,1470,1365,1264,1167,1074,985,900,819,742,669,600,535,474,417,364,315,270,229,190,227,268,313,362,415,472,533,598,667,740,817,898,983,1072,1165,1262,1363,1468,1577,1690,1807,1928,2053,2182,2315,2452,2593,2738,2886,2919,2767,2618,2473,2332,2195,2062,1933,1808,1687,1570,1457,1348,1243,1142,1045,952,863,947,1034,1123,1216,1313,1414,1519,1628,1741,1858,1979,2104,2233,2366,2503,2644,2789,2937,2808,2663,2522,2385,2252,2123,1998,1877,1760,1647,1538,1431,1536,1645,1758,1875,1996,2121,2250,2383,2520,2661,2806,2950,2967,2835,2686,2541,2400,2263,2130,2001,1876,1755,1638,1525,1416,1311,1210,1113,1020,931,846,765,688,615,546,481,420,363,310,261,216,175,138,105,76,51,30,46,65,86,111,140,173,210,251,296,345,398,455,516,581,650,723,800,881,966,1055,1148,1245,1346,1451,1560,1673,1790,1911,2036,2165,2298,2435,2576,2721,2870,2985,3013,3037,3057,3044,3017,2986,2868,2715,2566,2421,2280,2416,2555,2696,2841,2904,2756,2611,2470,2333,2200,2071,1946,1825,1708,1595,1486,1381,1280,1183,1090,1001,916,835,758,685,616,551,490,433,378,431,488,549,614,683,756,833,914,999,1088,1181,1278,1379,1484,1593,1706,1823,1944,2069,2198,2331,2468,2609,2754,2902,2935,2783,2634,2489,2348,2211,2078,1949,1824,1703,1586,1473,1364,1259,1158,1061,968,879,794,713,636,563,631,702,775,852,933,1018,1107,1200,1297,1398,1503,1612,1725,1842,1963,2088,2217,2350,2487,2628,2773,2921,2824,2679,2538,2401,2268,2139,2014,1891,2012,2137,2266,2399,2536,2677,2822,2958,2853,2704,2559,2418,2281,2148,2019,1894,1773,1656,1543,1434,1329,1228,1131,1038,949,864,783,706,633,564,499,438,381,328,279,234,193,156,123,94,69,48,31,18,9,4)

Polycyclic presentation:

2^2,3109|a^2=b,c^a=c^727,c^b=c^3108

Conjugacy classes & character table

781 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12436, 3);