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Aliases
Splittings
Subgroups
4 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 5851 points:
(2,3,5)(4,7,12)(6,10,9)(8,14,22)(11,17,19)(13,20,16)(15,24,35)(18,27,32)(21,30,29)(23,33,26)(25,37,51)(28,40,48)(31,43,45)(34,46,42)(36,49,39)(38,53,70)(41,56,67)(44,59,64)(47,62,61)(50,65,58)(52,68,55)(54,72,92)(57,75,89)(60,78,86)(63,81,83)(66,84,80)(69,87,77)(71,90,74)(73,94,117)(76,97,114)(79,100,111)(82,103,108)(85,106,105)(88,109,102)(91,112,99)(93,115,96)(95,119,145)(98,122,142)(101,125,139)(104,128,136)(107,131,133)(110,134,130)(113,137,127)(116,140,124)(118,143,121)(120,147,176)(123,150,173)(126,153,170)(129,156,167)(132,159,164)(135,162,161)(138,165,158)(141,168,155)(144,171,152)(146,174,149)(148,178,210)(151,181,207)(154,184,204)(157,187,201)(160,190,198)(163,193,195)(166,196,192)(169,199,189)(172,202,186)(175,205,183)(177,208,180)(179,212,247)(182,215,244)(185,218,241)(188,221,238)(191,224,235)(194,227,232)(197,230,229)(200,233,226)(203,236,223)(206,239,220)(209,242,217)(211,245,214)(213,249,287)(216,252,284)(219,255,281)(222,258,278)(225,261,275)(228,264,272)(231,267,269)(234,270,266)(237,273,263)(240,276,260)(243,279,257)(246,282,254)(248,285,251)(250,289,330)(253,292,327)(256,295,324)(259,298,321)(262,301,318)(265,304,315)(268,307,312)(271,310,309)(274,313,306)(277,316,303)(280,319,300)(283,322,297)(286,325,294)(288,328,291)(290,332,376)(293,335,373)(296,338,370)(299,341,367)(302,344,364)(305,347,361)(308,350,358)(311,353,355)(314,356,352)(317,359,349)(320,362,346)(323,365,343)(326,368,340)(329,371,337)(331,374,334)(333,378,425)(336,381,422)(339,384,419)(342,387,416)(345,390,413)(348,393,410)(351,396,407)(354,399,404)(357,402,401)(360,405,398)(363,408,395)(366,411,392)(369,414,389)(372,417,386)(375,420,383)(377,423,380)(379,427,477)(382,430,474)(385,433,471)(388,436,468)(391,439,465)(394,442,462)(397,445,459)(400,448,456)(403,451,453)(406,454,450)(409,457,447)(412,460,444)(415,463,441)(418,466,438)(421,469,435)(424,472,432)(426,475,429)(428,479,532)(431,482,529)(434,485,526)(437,488,523)(440,491,520)(443,494,517)(446,497,514)(449,500,511)(452,503,508)(455,506,505)(458,509,502)(461,512,499)(464,515,496)(467,518,493)(470,521,490)(473,524,487)(476,527,484)(478,530,481)(480,534,590)(483,537,587)(486,540,584)(489,543,581)(492,546,578)(495,549,575)(498,552,572)(501,555,569)(504,558,566)(507,561,563)(510,564,560)(513,567,557)(516,570,554)(519,573,551)(522,576,548)(525,579,545)(528,582,542)(531,585,539)(533,588,536)(535,592,651)(538,595,648)(541,598,645)(544,601,642)(547,604,639)(550,607,636)(553,610,633)(556,613,630)(559,616,627)(562,619,624)(565,622,621)(568,625,618)(571,628,615)(574,631,612)(577,634,609)(580,637,606)(583,640,603)(586,643,600)(589,646,597)(591,649,594)(593,653,715)(596,656,712)(599,659,709)(602,662,706)(605,665,703)(608,668,700)(611,671,697)(614,674,694)(617,677,691)(620,680,688)(623,683,685)(626,686,682)(629,689,679)(632,692,676)(635,695,673)(638,698,670)(641,701,667)(644,704,664)(647,707,661)(650,710,658)(652,713,655)(654,717,782)(657,720,779)(660,723,776)(663,726,773)(666,729,770)(669,732,767)(672,735,764)(675,738,761)(678,741,758)(681,744,755)(684,747,752)(687,750,749)(690,753,746)(693,756,743)(696,759,740)(699,762,737)(702,765,734)(705,768,731)(708,771,728)(711,774,725)(714,777,722)(716,780,719)(718,784,852)(721,787,849)(724,790,846)(727,793,843)(730,796,840)(733,799,837)(736,802,834)(739,805,831)(742,808,828)(745,811,825)(748,814,822)(751,817,819)(754,820,816)(757,823,813)(760,826,810)(763,829,807)(766,832,804)(769,835,801)(772,838,798)(775,841,795)(778,844,792)(781,847,789)(783,850,786)(785,854,925)(788,857,922)(791,860,919)(794,863,916)(797,866,913)(800,869,910)(803,872,907)(806,875,904)(809,878,901)(812,881,898)(815,884,895)(818,887,892)(821,890,889)(824,893,886)(827,896,883)(830,899,880)(833,902,877)(836,905,874)(839,908,871)(842,911,868)(845,914,865)(848,917,862)(851,920,859)(853,923,856)(855,927,1001)(858,930,998)(861,933,995)(864,936,992)(867,939,989)(870,942,986)(873,945,983)(876,948,980)(879,951,977)(882,954,974)(885,957,971)(888,960,968)(891,963,965)(894,966,962)(897,969,959)(900,972,956)(903,975,953)(906,978,950)(909,981,947)(912,984,944)(915,987,941)(918,990,938)(921,993,935)(924,996,932)(926,999,929)(928,1003,1080)(931,1006,1077)(934,1009,1074)(937,1012,1071)(940,1015,1068)(943,1018,1065)(946,1021,1062)(949,1024,1059)(952,1027,1056)(955,1030,1053)(958,1033,1050)(961,1036,1047)(964,1039,1044)(967,1042,1041)(970,1045,1038)(973,1048,1035)(976,1051,1032)(979,1054,1029)(982,1057,1026)(985,1060,1023)(988,1063,1020)(991,1066,1017)(994,1069,1014)(997,1072,1011)(1000,1075,1008)(1002,1078,1005)(1004,1082,1162)(1007,1085,1159)(1010,1088,1156)(1013,1091,1153)(1016,1094,1150)(1019,1097,1147)(1022,1100,1144)(1025,1103,1141)(1028,1106,1138)(1031,1109,1135)(1034,1112,1132)(1037,1115,1129)(1040,1118,1126)(1043,1121,1123)(1046,1124,1120)(1049,1127,1117)(1052,1130,1114)(1055,1133,1111)(1058,1136,1108)(1061,1139,1105)(1064,1142,1102)(1067,1145,1099)(1070,1148,1096)(1073,1151,1093)(1076,1154,1090)(1079,1157,1087)(1081,1160,1084)(1083,1164,1247)(1086,1167,1244)(1089,1170,1241)(1092,11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1092,1174,1259,1347,1438,1532,1629,1729,1832,1938,2047,2159,2274,2392,2513,2637,2764,2894,3027,3163,3302,3444,3589,3737,3885,4030,4169,3932,3633,3343,3065,2799,2545,2303,2073,1855,1649,1455,1273,1103,945,799,665,543,433,335,249,288,329,372,418,467,519,574,632,693,757,824,894,967,1043,1122,1204,1289,1377,1468,1562,1659,1759,1862,1968,2077,2189,2304,2422,2543,2667,2794,2924,3057,3193,3332,3474,3619,3767,3915,4060,4199,4332,4459,4580,4695,4804,4907,5004,5095,5180,5259,5112,4921,4706,4467,4204,3917,3618,3328,3050,2784,2530,2288,2058,1840,1634,1440,1258,1088,930,784,853,924,997,1073,1152,1234,1319,1407,1498,1592,1689,1789,1892,1998,2107,2219,2334,2452,2573,2697,2824,2954,3087,3223,3362,3504,3649,3796,3943,4086,4165,3873,3577,3722,3869,4016,4158,4294,4424,4548,4666,4778,4884,4984,5078,5166,5248,5324,5394,5458,5516,5568,5614,5526,5407,5264,5097,4906,4691,4452,4189,3902,3603,3313,3035,2769,2515,2273,2043,1825,1619,1718,1819,1922,2028,2137,2249,2364,2482,2603,2727,2854,2984,3117,3253,3392,3534,3679,3826,3973,4115,4251,4381,4506,4625,4738,4845,4946,5041,5130,5213,5255,5082,4885,4664,4419,4150,3858,3563,3279,3007,2747,2499,2262,2377,2495,2616,2740,2867,2997,3130,3266,3405,3547,3692,3839,3986,4128,4264,4394,4518,4636,4748,4854,4676,4437,4174,3887,3588,3298,3020,2754,2883,3014,3147,3283,3422,3564,3709,3856,4003,4145,4281,4411,4535,4653,4765,4871,4971,5065,5153,5235,5311,5381,5446,5505,5558,5605,5646,5681,5711,5737,5750,5692,5615,5514,5389,5240,5067,4870,4649,4404,4135,3843,3548,3264,2992,2732,2484,2248,2024,1812,1612,1424,1247,1332,1420,1511,1605,1702,1802,1905,2011,2120,2232,2347,2465,2586,2710,2837,2967,3100,3236,3375,3517,3662,3809,3956,4099,4236,4367,4492,4611,4724,4832,4935,5032,5123,5208,5287,5360,5427,5488,5543,5592,5635,5672,5704,5732,5757,5779,5798,5814,5827,5837,5840,5818,5785,5740,5682,5604,5502,5376,5226,5052,4855,4634,4389,4120,3828,3533,3249,2977,2717,2469,2233,2009,1797,1597,1409,1233,1069,917,777,649,532,587,645,706,770,837,907,980,1056,1135,1217,1302,1390,1481,1575,1672,1772,1875,1981,2090,2202,2317,2435,2556,2680,2807,2937,3070,3206,3345,3487,3632,3780,3928,4073,4212,4345,4472,4593,4708,4817,4920,5017,5108,5193,5272,5345,5412,5473,5528,5577,5595,5492,5366,5216,5042,4844,4622,4376,4106,3813,3518,3234,2962,2702,2454,2218,1994,1782,1582,1394,1218,1054,902,762,634,518,414,322,242,174,117,142,170,201,235,272,312,355,401,450,502,557,615,676,740,807,877,950,1026,1105,1187,1272,1360,1451,1545,1642,1742,1845,1951,2060,2172,2287,2405,2526,2650,2777,2907,3040,3176,3315,3457,3602,3750,3898,4043,4182,4315,4442,4563,4678,4787,4833,4609,4362,4091,3798,3503,3219,2947,2687,2439,2203,1979,1767,1567,1379,1203,1039,887,747,619,503,399,307,227,159,103,59,27,7,13,21,31,44,60,79,101,126,154,185,219,256,296,339,385,434,486,541,599,660,724,791,861,934,1010,1089,1171,1256,1344,1435,1529,1626,1726,1829,1935,2044,2156,2271,2389,2510,2634,2761,2891,3024,3160,3299,3441,3586,3734,3882,4027,3784,3488,3204,2932,2672,2424,2188,1964,1752,1552,1364,1188,1024,872,732,604,488,384,292,212,248,286,326,369,415,464,516,571,629,690,754,821,891,964,1040,1119,1201,1286,1374,1465,1559,1656,1756,1859,1965,2074,2186,2301,2419,2540,2664,2791,2921,3054,3190,3329,3471,3616,3764,3912,4057,4196,4329,4456,4577,4692,4801,4904,5001,5092,5177,5021,4818,4591,4340,4065,3769,3473,3189,2917,2657,2409,2173,1949,1737,1537,1349,1173,1009,857,717,783,851,921,994,1070,1149,1231,1316,1404,1495,1589,1686,1786,1889,1995,2104,2216,2331,2449,2570,2694,2821,2951,3084,3220,3359,3501,3646,3793,3940,4023,3725,3872,4019,4161,4297,4427,4551,4669,4781,4887,4987,5081,5169,5251,5327,5397,5461,5519,5571,5617,5657,5578,5471,5340,5185,5006,4803,4576,4325,4050,3754,3458,3174,2902,2642,2394,2158,1934,1722,1522,1618,1716,1816,1919,2025,2134,2246,2361,2479,2600,2724,2851,2981,3114,3250,3389,3531,3676,3823,3970,4112,4248,4379,4504,4623,4736,4843,4944,5039,5128,5173,4988,4779,4546,4289,4008,3711,3421,3143,2877,2623,2380,2498,2619,2743,2870,3000,3133,3269,3408,3550,3695,3842,3989,4131,4267,4397,4521,4639,4751,4857,4957,4788,4561,4310,4035,3739,3443,3159,2887,2627,2753,2881,3011,3144,3280,3419,3561,3706,3853,4000,4142,4278,4408,4532,4650,4762,4868,4968,5062,5150,5232,5308,5379,5444,5503,5556,5603,5644,5679,5709,5724,5658,5569,5456,5319,5158,4973,4764,4531,4274,3993,3696,3406,3128,2862,2608,2366,2136,1918,1712,1518,1335,1423,1514,1608,1705,1805,1908,2014,2123,2235,2350,2468,2589,2713,2840,2970,3103,3239,3378,3520,3665,3812,3959,4102,4239,4370,4495,4614,4727,4834,4936,5033,5124,5209,5288,5361,5428,5489,5544,5593,5636,5673,5705,5733,5758,5780,5799,5815,5828,5838,5845,5847,5831,5804,5765,5714,5647,5557,5443,5305,5143,4958,4749,4516,4259,3978,3681,3391,3113,2847,2593,2351,2121,1903,1697,1503,1321,1151,993,847,713,590,648,709,773,840,910,983,1059,1138,1220,1305,1393,1484,1578,1675,1775,1878,1984,2093,2205,2320,2438,2559,2683,2810,2940,3073,3209,3348,3490,3635,3783,3931,4076,4215,4348,4475,4596,4711,4820,4923,5020,5111,5196,5275,5348,5415,5476,5531,5580,5623,5638,5547,5433,5295,5133,4947,4737,4503,4245,3963,3666,3376,3098,2832,2578,2336,2106,1888,1682,1488,1306,1136,978,832,698,576,466,368,282,208,145,173,204,238,275,315,358,404,453,505,560,618,679,743,810,880,953,1029,1108,1190,1275,1363,1454,1548,1645,1745,1848,1954,2063,2175,2290,2408,2529,2653,2780,2910,3043,3179,3318,3460,3605,3753,3901,4046,4185,4318,4445,4566,4681,4790,4893,4937,4725,4490,4231,3948,3651,3361,3083,2817,2563,2321,2091,1873,1667,1473,1291,1121,963,817,683,561,451,353,267,193,131,81,43,17,3,6,11,18,28,41,57,76,98,123,151,182,216,253,293,336,382,431,483,538,596,657,721,788,858,931,1007,1086,1168,1253,1341,1432,1526,1623,1723,1826,1932,2041,2153,2268,2386,2507,2631,2758,2888,3021,3157,3296,3438,3583,3731,3879,3636,3346,3068,2802,2548,2306,2076,1858,1652,1458,1276,1106,948,802,668,546,436,338,252,178,211,246,283,323,366,412,461,513,568,626,687,751,818,888,961,1037,1116,1198,1283,1371,1462,1556,1653,1753,1856,1962,2071,2183,2298,2416,2537,2661,2788,2918,3051,3187,3326,3468,3613,3761,3909,4054,4193,4326,4453,4574,4689,4798,4901,4998,5089,4924,4709,4470,4207,3920,3621,3331,3053,2787,2533,2291,2061,1843,1637,1443,1261,1091,933,787,653,716,781,848,918,991,1067,1146,1228,1313,1401,1492,1586,1683,1783,1886,1992,2101,2213,2328,2446,2567,2691,2818,2948,3081,3217,3356,3498,3643,3790,3875,4022,4164,4300,4430,4554,4672,4784,4890,4990,5084,5172,5254,5330,5400,5464,5522,5574,5620,5660,5694,5624,5529,5410,5267,5100,4909,4694,4455,4192,3905,3606,3316,3038,2772,2518,2276,2046,1828,1622,1428,1521,1616,1713,1813,1916,2022,2131,2243,2358,2476,2597,2721,2848,2978,3111,3247,3386,3528,3673,3820,3967,4109,4246,4377,4502,4621,4734,4841,4942,5037,5085,4888,4667,4422,4153,3861,3566,3282,3010,2750,2501,2622,2746,2873,3003,3136,3272,3411,3553,3698,3845,3992,4134,4270,4400,4524,4642,4754,4860,4960,5054,4894,4679,4440,4177,3890,3591,3301,3023,2757,2503,2626,2751,2878,3008,3141,3277,3416,3558,3703,3850,3997,4139,4275,4405,4529,4647,4759,4865,4965,5059,5147,5229,5306,5377,5442,5501,5554,5601,5642,5677,5695,5618,5517,5392,5243,5070,4873,4652,4407,4138,3846,3551,3267,2995,2735,2487,2251,2027,1815,1615,1426,1517,1611,1708,1808,1911,2017,2126,2238,2353,2471,2592,2716,2843,2973,3106,3242,3381,3523,3668,3815,3962,4105,4242,4373,4498,4617,4730,4837,4938,5034,5125,5210,5289,5362,5429,5490,5545,5594,5637,5674,5706,5734,5759,5781,5800,5816,5829,5839,5846,5850,5851,5841,5820,5787,5742,5684,5606,5504,5378,5228,5055,4858,4637,4392,4123,3831,3536,3252,2980,2720,2472,2236,2012,1800,1600,1412,1236,1072,920,780,651,712,776,843,913,986,1062,1141,1223,1308,1396,1487,1581,1678,1778,1881,1987,2096,2208,2323,2441,2562,2686,2813,2943,3076,3212,3351,3493,3638,3786,3934,4079,4218,4351,4478,4599,4714,4823,4926,5023,5114,5199,5278,5351,5418,5479,5534,5583,5626,5663,5675,5596,5494,5368,5218,5044,4846,4624,4378,4108,3816,3521,3237,2965,2705,2457,2221,1997,1785,1585,1397,1221,1057,905,765,637,521,417,325,245,176,207,241,278,318,361,407,456,508,563,621,682,746,813,883,956,1032,1111,1193,1278,1366,1457,1551,1648,1748,1851,1957,2066,2178,2293,2411,2532,2656,2783,2913,3046,3182,3321,3463,3608,3756,3904,4049,4188,4321,4448,4569,4684,4793,4896,4993,5035,4835,4612,4365,4094,3801,3506,3222,2950,2690,2442,2206,1982,1770,1570,1382,1206,1042,890,750,622,506,402,310,230,162,106,62,30,10)
Polycyclic presentation:
3,5851|b^a=b^5273
Conjugacy classes & character table
1953 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17553, 1);
Finite Group Databasebeta