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Aliases
Splittings
Subgroups
4 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 6361 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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4,1252,1082,1163,1246,1331,1419,1510,1604,1701,1801,1904,2010,2119,2231,2346,2464,2585,2709,2836,2966,3099,3235,3374,3516,3661,3809,3959,4108,4251,4388,4519,4644,4763,4876,4983,5084,5179,5268,5351,5428,5325,5140,4931,4698,4441,4160,3859,3563,3279,3007,2747,2499,2262,2377,2495,2616,2740,2867,2997,3130,3266,3405,3547,3692,3840,3990,3878,4029,4177,4319,4455,4585,4709,4827,4939,5045,5145,5239,5327,5409,5485,5556,5624,5689,5751,5810,5866,5919,5969,6016,6060,6101,6139,6174,6206,6235,6261,6284,6304,6321,6335,6346,6354,6359,6361,6352,6331,6298,6253,6196,6127,6046,5953,5848,5731,5602,5461,5299,5113,4902,4667,4408,4125,3823,3527,3243,2971,2711,2463,2227,2003,1791,1591,1403,1227,1063,911,771,643,527,423,330,373,419,468,520,575,633,694,758,825,895,968,1044,1123,1205,1290,1378,1469,1563,1660,1760,1863,1969,2078,2190,2305,2423,2544,2668,2795,2925,3058,3194,3333,3475,3620,3768,3918,4068,4213,4352,4485,4612,4733,4848,4957,5060,5157,5248,5333,5412,5486,5427,5264,5077,4866,4631,4372,4089,3787,3491,3207,2935,2675,2427,2191,1967,1755,1555,1367,1191,1027,875,735,607,491,387,295,215,147,177,209,243,280,320,363,409,458,510,565,623,684,748,815,885,958,1034,1113,1195,1280,1368,1459,1553,1650,1750,1853,1959,2068,2180,2295,2413,2534,2658,2785,2915,3048,3184,3323,3465,3610,3758,3908,4058,4203,4342,4475,4602,4723,4838,4947,5050,5058,4843,4604,4341,4054,3751,3455,3171,2899,2639,2391,2155,1931,1719,1821,1925,2031,2140,2252,2367,2485,2606,2730,2857,2987,3120,3256,3395,3537,3682,3830,3980,4129,4272,4409,4540,4665,4784,4897,5004,5105,5200,5289,5372,5449,5520,5588,5653,5715,5774,5830,5883,5808,5685,5550,5400,5226,5028,4807,4562,4293,4000,3699,3409,3131,2865,2611,2369,2139,1921,1715,1520,1614,1711,1811,1914,2020,2129,2241,2356,2474,2595,2719,2846,2976,3109,3245,3384,3526,3671,3819,3969,4118,4261,4398,4529,4654,4773,4886,4993,5094,5189,5278,5361,5438,5509,5577,5642,5704,5765,5823,5878,5930,5979,6025,6068,6108,6145,6179,6210,6238,6263,6285,6270,6219,6156,6081,5994,5895,5784,5661,5525,5374,5199,5000,4777,4530,4259,3964,3663,3373,3095,2829,2575,2333,2103,1885,1679,1485,1303,1133,975,829,695,573,463,365,279,205,143,92,114,139,167,198,232,269,309,352,398,447,499,554,612,673,737,804,874,947,1023,1102,1184,1269,1357,1448,1542,1639,1739,1842,1948,2057,2169,2284,2402,2523,2647,2774,2904,3037,3173,3312,3454,3599,3747,3897,4047,4192,4331,4464,4591,4712,4828,4741,4494,4223,3928,3627,3337,3059,2793,2539,2297,2067,1849,1643,1449,1267,1097,939,793,659,537,427,478,531,586,644,705,769,836,906,979,1055,1134,1216,1301,1389,1480,1574,1671,1771,1874,1980,2089,2201,2316,2434,2555,2679,2806,2936,3069,3205,3344,3486,3631,3779,3929,4078,4221,4358,4175,3874,3577,3722,3870,4020,4168,4310,4446,4576,4700,4818,4930,5036,5136,5230,5147,4943,4716,4465,4190,3892,3591,3301,3023,2757,2503,2626,2751,2878,3008,3141,3277,3416,3558,3703,3851,4001,4149,4291,4427,4557,4682,4801,4914,5021,5122,5217,5306,5389,5466,5537,5605,5670,5732,5791,5847,5900,5950,5997,6041,6082,6120,6155,6187,6137,6056,5963,5858,5741,5612,5471,5309,5123,4913,4679,4421,4139,3838,3542,3258,2986,2726,2478,2242,2018,1806,1606,1418,1242,1078,925,998,1074,1153,1235,1320,1408,1499,1593,1690,1790,1893,1999,2108,2220,2335,2453,2574,2698,2825,2955,3088,3224,3363,3505,3650,3798,3948,4097,4240,4377,4508,4633,4752,4865,4972,5073,5168,5259,5344,5423,5496,5566,5633,5697,5758,5816,5871,5923,5972,6018,6061,6032,5938,5832,5714,5584,5442,5279,5092,4881,4646,4387,4104,3802,3506,3222,2950,2690,2442,2206,1982,1770,1570,1382,1206,1042,890,750,622,506,402,310,230,162,106,62,30,10)
Polycyclic presentation:
3,6361|b^a=b^1858
Conjugacy classes & character table
2123 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19083, 1);
Finite Group Databasebeta