Finite Group Databasebeta

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#27210402

• 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 3313 points:

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56,1735,1618,1505,1396,1291,1190,1093,1000,911,826,745,668,595,526,461,400,343,290,241,196,155,191,230,271,316,365,418,475,536,601,670,743,820,901,986,1075,1168,1265,1366,1471,1580,1693,1810,1931,2056,2165,2256,2344,2428,2508,2584,2656,2724,2788,2772,2701,2626,2547,2464,2377,2286,2191,2078,1949,1824,1703,1586,1473,1364,1259,1158,1061,968,879,794,713,636,563,631,702,775,852,933,1018,1107,1200,1297,1398,1503,1612,1725,1842,1963,2088,2197,2288,2375,2458,2537,2612,2683,2750,2813,2872,2928,2980,3028,3072,3112,3148,3180,3164,3125,3082,3035,2984,2929,2870,2807,2740,2669,2594,2515,2432,2345,2254,2159,2046,1917,1792,1671,1554,1441,1332,1227,1327,1430,1535,1644,1757,1874,1995,2119,2226,2317,2404,2487,2566,2641,2712,2779,2842,2901,2956,3007,3054,3097,3136,3171,3202,3229,3253,3273,3289,3301,3309,3313,3312,3307,3299,3287,3271,3251,3227,3199,3168,3133,3094,3051,3004,2953,2898,2839,2776,2709,2638,2563,2484,2401,2314,2223,2114,1990,1869,1752,1639,1530,1425,1324,1225,1322,1423,1528,1637,1750,1867,1988,2113,2222,2313,2400,2483,2562,2637,2708,2775,2838,2897,2952,3003,3050,3093,3132,3167,3144,3108,3068,3024,2976,2924,2868,2808,2745,2678,2607,2532,2453,2370,2283,2192,2083,1958,1837,1720,1607,1498,1393,1292,1195,1102,1013,928,847,770,697,628,561,626,695,768,845,926,1011,1100,1193,1290,1391,1496,1605,1718,1835,1956,2081,2190,2281,2368,2451,2530,2605,2676,2743,2720,2652,2580,2504,2424,2340,2252,2160,2051,1926,1805,1688,1575,1466,1361,1260,1163,1070,981,896,815,738,665,596,531,470,413,360,311,266,225,188,153,186,223,264,309,358,411,468,529,594,663,736,813,894,979,1068,1161,1258,1359,1464,1573,1686,1803,1924,2049,2019,1894,1773,1656,1543,1434,1329,1228,1131,1038,949,864,783,706,633,564,499,438,381,328,279,234,193,156,123,94,69,48,31,18,9,4)

Polycyclic presentation:

2^2,3313|a^2=b,c^a=c^2906,c^b=c^3312

Conjugacy classes & character table

832 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13252, 3);