Finite Group DatabasebetaFinite Group Databasebeta| order | 19587 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C6529⋊C3 |
| Fitting, socle, derived, Sylow | C6529 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C6529 | C3 |
| LCS | G ▷ C6529 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
| minimal degree | μ(G) = 6529 |
| transitive degree | μt(G) = 6529 |
A minimal faithful permutation representation — 2 generators on 6529 points:
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878,4004,4124,4240,4353,4229,3989,3727,3443,3159,2887,2627,2753,2881,3011,3144,3280,3419,3561,3703,3841,3973,4099,4219,4335,4448,4558,4665,4769,4870,4968,5063,5155,5244,5330,5413,5493,5570,5644,5715,5783,5848,5910,5969,6025,6078,6128,6175,6219,6260,6298,6333,6365,6394,6420,6443,6463,6480,6495,6507,6516,6496,6462,6416,6358,6288,6206,6112,6006,5888,5758,5616,5462,5296,5118,4928,4726,4512,4286,4047,3786,3503,3219,2947,2687,2439,2203,1979,1767,1567,1379,1203,1039,887,747,619,503,399,307,227,159,103,59,27,7,13,21,31,44,60,79,101,126,154,185,219,256,296,339,385,434,486,541,599,660,724,791,861,934,1010,1089,1171,1256,1344,1435,1529,1626,1726,1829,1935,2044,2156,2271,2389,2510,2634,2761,2891,3024,3160,3299,3441,3583,3722,3563,3279,3007,2747,2499,2262,2377,2495,2616,2740,2867,2997,3130,3266,3405,3547,3689,3827,3959,4085,4205,4321,4434,4544,4651,4755,4856,4954,5049,5141,5230,5316,5399,5479,5556,5630,5701,5769,5834,5896,5955,6011,6064,6114,6161,6205,6246,6284,6319,6351,6308,6231,6142,6041,5929,5805,5669,5521,5361,5189,5005,4809,4601,4381,4149,3900,3627,3340,3062,2796,2542,2300,2070,1852,1646,1452,1270,1100,942,796,662,540,430,332,377,424,473,525,580,638,699,763,830,900,973,1049,1128,1210,1295,1383,1474,1568,1665,1765,1868,1974,2083,2195,2310,2428,2549,2673,2800,2930,3063,3199,3338,3480,3622,3760,3892,4018,4138,4254,4367,4477,4584,4688,4789,4887,4983,5076,5166,5065,4869,4661,4441,4209,3960,3687,3400,3122,2856,2602,2360,2130,1912,1706,1512,1330,1160,1001,1077,1156,1238,1323,1411,1502,1596,1693,1793,1896,2002,2111,2223,2338,2456,2577,2701,2828,2958,3091,3227,3366,3508,3650,3788,3920,4046,4166,4282,4395,4505,4612,4716,4817,4915,5010,5102,5191,5277,5360,5440,5517,5591,5662,5580,5425,5258,5079,4889,4687,4473,4247,4008,3747,3464,3180,2908,2648,2400,2164,1940,1728,1528,1340,1164,1248,1334,1422,1513,1607,1704,1804,1907,2013,2122,2234,2349,2467,2588,2712,2839,2969,3102,3238,3377,3519,3661,3799,3931,4057,4177,4293,4406,4516,4623,4727,4828,4926,5021,5113,5202,5288,5371,5451,5528,5602,5673,5741,5806,5868,5927,5984,6038,6089,6027,5909,5779,5637,5483,5317,5139,4949,4747,4533,4307,4068,3807,3524,3240,2968,2708,2460,2224,2000,1788,1588,1400,1224,1060,908,768,640,524,420,328,247,284,324,367,413,462,514,569,627,688,752,819,889,962,1038,1117,1199,1284,1372,1463,1557,1654,1754,1857,1963,2072,2184,2299,2417,2538,2662,2789,2919,3052,3188,3327,3469,3611,3749,3881,4007,4127,4243,4356,4466,4345,4112,3862,3588,3301,3023,2757,2503,2626,2751,2878,3008,3141,3277,3416,3558,3700,3838,3970,4096,4216,4332,4445,4555,4662,4766,4867,4965,5060,5152,5241,5327,5410,5490,5567,5641,5712,5780,5845,5907,5966,6022,6075,6125,6172,6216,6257,6295,6330,6362,6391,6417,6440,6460,6478,6493,6505,6482,6442,6390,6326,6250,6162,6062,5950,5826,5690,5542,5382,5210,5026,4830,4622,4402,4170,3921,3648,3361,3083,2817,2563,2321,2091,1873,1667,1473,1291,1121,963,817,683,561,451,353,267,193,131,81,43,17,3,6,11,18,28,41,57,76,98,123,151,182,216,253,293,336,382,431,483,538,596,657,721,788,858,931,1007,1086,1168,1253,1341,1432,1526,1623,1723,1826,1932,2041,2153,2268,2386,2507,2631,2758,2888,3021,3157,3296,3438,3580,3421,3143,2877,2623,2380,2498,2619,2743,2870,3000,3133,3269,3408,3550,3692,3830,3962,4088,4208,4324,4437,4547,4654,4758,4859,4957,5052,5144,5233,5319,5402,5482,5559,5633,5704,5772,5837,5899,5958,6014,6067,6117,6164,6208,6249,6287,6322,6354,6383,6343,6272,6189,6094,5988,5870,5740,5598,5444,5278,5100,4910,4708,4494,4268,4029,3768,3485,3201,2929,2669,2421,2185,1961,1749,1549,1361,1185,1021,869,729,601,485,381,289,331,375,421,470,522,577,635,696,760,827,897,970,1046,1125,1207,1292,1380,1471,1565,1662,1762,1865,1971,2080,2192,2307,2425,2546,2670,2797,2927,3060,3196,3335,3477,3619,3757,3889,4015,4135,4251,4364,4474,4581,4685,4786,4885,4981,5074,4970,4768,4554,4328,4089,3828,3545,3261,2989,2729,2481,2245,2021,1809,1609,1421,1245,1080,1159,1241,1326,1414,1505,1599,1696,1796,1899,2005,2114,2226,2341,2459,2580,2704,2831,2961,3094,3230,3369,3511,3653,3791,3923,4049,4169,4285,4398,4508,4615,4719,4820,4918,5013,5105,5194,5280,5363,5443,5520,5594,5665,5733,5654,5505,5344,5171,4987,4791,4583,4363,4131,3882,3609,3322,3044,2778,2524,2282,2052,1834,1628,1434,1252,1082,1163,1246,1331,1419,1510,1604,1701,1801,1904,2010,2119,2231,2346,2464,2585,2709,2836,2966,3099,3235,3374,3516,3658,3796,3928,4054,4174,4290,4403,4513,4620,4724,4825,4923,5018,5110,5199,5285,5368,5448,5525,5599,5670,5738,5803,5865,5925,5982,6036,5971,5847,5711,5563,5403,5231,5047,4851,4643,4423,4191,3942,3669,3382,3104,2838,2584,2342,2112,1894,1688,1494,1312,1142,984,838,704,582,472,374,287,327,370,416,465,517,572,630,691,755,822,892,965,1041,1120,1202,1287,1375,1466,1560,1657,1757,1860,1966,2075,2187,2302,2420,2541,2665,2792,2922,3055,3191,3330,3472,3614,3752,3884,4010,4130,4246,4359,4469,4576,4458,4231,3991,3729,3446,3162,2890,2630,2382,2502,2624,2748,2875,3005,3138,3274,3413,3555,3697,3835,3967,4093,4213,4329,4442,4552,4659,4763,4864,4962,5057,5149,5238,5324,5407,5487,5564,5638,5709,5777,5842,5904,5963,6019,6072,6122,6169,6213,6254,6292,6327,6359,6388,6414,6437,6458,6476,6491,6465,6419,6361,6291,6209,6115,6009,5891,5761,5619,5465,5299,5121,4931,4729,4515,4289,4050,3789,3506,3222,2950,2690,2442,2206,1982,1770,1570,1382,1206,1042,890,750,622,506,402,310,230,162,106,62,30,10)Polycyclic presentation:
3,6529|b^a=b^60372179 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19587, 1);