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Aliases
Splittings
Subgroups
4 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 5857 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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233,2009,1797,1597,1409,1233,1069,917,777,649,532,587,645,706,770,837,907,980,1056,1135,1217,1302,1390,1481,1575,1672,1772,1875,1981,2090,2202,2317,2435,2556,2680,2807,2937,3070,3205,3339,3467,3589,3705,3815,3922,4026,4127,4225,4320,4412,4501,4587,4672,4754,4833,4909,4982,4914,4760,4594,4416,4226,4024,3810,3581,3328,3056,2790,2536,2294,2064,1846,1640,1446,1264,1094,936,790,656,534,591,650,711,775,842,912,985,1061,1140,1222,1307,1395,1486,1580,1677,1777,1880,1986,2095,2207,2322,2440,2561,2685,2812,2942,3075,3210,3344,3472,3594,3710,3820,3927,4031,4132,4230,4325,4417,4506,4592,4675,4579,4396,4201,3994,3775,3534,3269,2998,2738,2490,2254,2030,1818,1617,1714,1814,1917,2023,2132,2244,2359,2477,2598,2722,2849,2979,3112,3247,3381,3509,3631,3747,3857,3964,4068,4169,4267,4362,4454,4543,4629,4712,4792,4869,4943,5014,5082,5147,5209,5268,5324,5377,5427,5474,5518,5561,5601,5638,5672,5703,5677,5607,5525,5431,5325,5207,5077,4935,4781,4615,4437,4247,4045,3831,3602,3349,3077,2811,2557,2315,2085,1867,1661,1467,1285,1115,957,811,677,555,445,347,261,187,125,75,37,52,69,88,110,135,163,194,228,265,305,348,394,443,495,550,608,669,733,800,870,943,1019,1098,1180,1265,1353,1444,1538,1635,1735,1838,1944,2053,2165,2280,2398,2519,2643,2770,2900,3033,3168,3302,3432,3556,3674,3672,3426,3158,2887,2627,2753,2881,3011,3144,3279,3412,3540,3662,3778,3888,3995,4099,4200,4298,4393,4485,4574,4660,4743,4823,4900,4974,5045,5113,5178,5240,5299,5355,5408,5458,5505,5549,5590,5628,5663,5695,5724,5750,5773,5793,5810,5824,5798,5753,5696,5627,5546,5452,5346,5228,5098,4956,4802,4636,4458,4268,4066,3852,3623,3370,3098,2832,2578,2336,2106,1888,1682,1488,1306,1136,978,832,698,576,466,368,282,208,145,173,204,238,275,315,358,404,453,505,560,618,679,743,810,880,953,1029,1108,1190,1275,1363,1454,1548,1645,1745,1848,1954,2063,2175,2290,2408,2529,2653,2780,2910,3043,3178,3312,3440,3562,3678,3790,3899,4005,4108,4208,4113,3905,3685,3444,3179,2908,2648,2400,2164,1940,1728,1528,1340,1164,1248,1334,1422,1513,1607,1704,1804,1907,2013,2122,2234,2349,2467,2588,2712,2839,2969,3102,3237,3371,3499,3621,3737,3847,3954,4058,4159,4257,4352,4444,4533,4619,4702,4782,4859,4933,5004,5072,5137,5199,5258,5314,5245,5116,4975,4822,4657,4479,4289,4087,3873,3644,3391,3119,2853,2599,2357,2127,1909,1703,1509,1327,1157,999,852,922,995,1071,1150,1232,1317,1405,1496,1590,1687,1787,1890,1996,2105,2217,2332,2450,2571,2695,2822,2952,3085,3220,3354,3482,3604,3720,3830,3937,4041,4142,4240,4335,4427,4516,4602,4685,4765,4842,4916,4987,5057,5124,5188,5249,5307,5254,5130,4994,4846,4686,4514,4330,4134,3926,3706,3465,3200,2929,2669,2421,2185,1961,1749,1549,1361,1185,1021,869,729,601,485,381,289,331,375,421,470,522,577,635,696,760,827,897,970,1046,1125,1207,1292,1380,1471,1565,1662,1762,1865,1971,2080,2192,2307,2425,2546,2670,2797,2927,3060,3195,3329,3457,3579,3695,3805,3912,4016,4117,4215,4104,3891,3663,3411,3140,2874,2620,2378,2147,2259,2374,2492,2613,2737,2864,2994,3127,3262,3396,3524,3646,3762,3872,3979,4083,4184,4282,4377,4469,4558,4644,4727,4807,4884,4958,5029,5097,5162,5224,5283,5339,5392,5442,5489,5533,5574,5612,5647,5679,5708,5736,5761,5783,5802,5818,5807,5767,5715,5651,5575,5487,5387,5275,5151,5015,4867,4707,4535,4351,4155,3947,3727,3486,3221,2950,2690,2442,2206,1982,1770,1570,1382,1206,1042,890,750,622,506,402,310,230,162,106,62,30,10)
Polycyclic presentation:
3,5857|b^a=b^4592
Conjugacy classes & character table
1955 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17571, 1);
Finite Group Databasebeta