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Aliases
Splittings
Subgroups
12 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 2212 points:
(2,4)(3,7)(5,10)(6,13)(8,16)(9,15)(11,20)(12,23)(14,25)(17,29)(18,28)(19,27)(21,34)(22,37)(24,39)(26,41)(30,46)(31,45)(32,44)(33,43)(35,52)(36,55)(38,57)(40,59)(42,61)(47,67)(48,66)(49,65)(50,64)(51,63)(53,74)(54,77)(56,79)(58,81)(60,83)(62,85)(68,92)(69,91)(70,90)(71,89)(72,88)(73,87)(75,100)(76,103)(78,105)(80,107)(82,109)(84,111)(86,113)(93,121)(94,120)(95,119)(96,118)(97,117)(98,116)(99,115)(101,130)(102,133)(104,135)(106,137)(108,139)(110,141)(112,143)(114,145)(122,154)(123,153)(124,152)(125,151)(126,150)(127,149)(128,148)(129,147)(131,164)(132,167)(134,169)(136,171)(138,173)(140,175)(142,177)(144,179)(146,181)(155,191)(156,190)(157,189)(158,188)(159,187)(160,186)(161,185)(162,184)(163,183)(165,202)(166,205)(168,207)(170,209)(172,211)(174,213)(176,215)(178,217)(180,219)(182,221)(192,232)(193,231)(194,230)(195,229)(196,228)(197,227)(198,226)(199,225)(200,224)(201,223)(203,244)(204,247)(206,249)(208,251)(210,253)(212,255)(214,257)(216,259)(218,261)(220,263)(222,265)(233,277)(234,276)(235,275)(236,274)(237,273)(238,272)(239,271)(240,270)(241,269)(242,268)(243,267)(245,290)(246,293)(248,295)(250,297)(252,299)(254,301)(256,303)(258,305)(260,307)(262,309)(264,311)(266,313)(278,326)(279,325)(280,324)(281,323)(282,322)(283,321)(284,320)(285,319)(286,318)(287,317)(288,316)(289,315)(291,340)(292,343)(294,345)(296,347)(298,349)(300,351)(302,353)(304,355)(306,357)(308,359)(310,361)(312,363)(314,365)(327,379)(328,378)(329,377)(330,376)(331,375)(332,374)(333,373)(334,372)(335,371)(336,370)(337,369)(338,368)(339,367)(341,394)(342,397)(344,399)(346,401)(348,403)(350,405)(352,407)(354,409)(356,411)(358,413)(360,415)(362,417)(364,419)(366,421)(380,436)(381,435)(382,434)(383,433)(384,432)(385,431)(386,430)(387,429)(388,428)(389,427)(390,426)(391,425)(392,424)(393,423)(395,452)(396,455)(398,457)(400,459)(402,461)(404,463)(406,465)(408,467)(410,469)(412,471)(414,473)(416,475)(418,477)(420,479)(422,481)(437,497)(438,496)(439,495)(440,494)(441,493)(442,492)(443,491)(444,490)(445,489)(446,488)(447,487)(448,486)(449,485)(450,484)(451,483)(453,514)(454,517)(456,519)(458,521)(460,523)(462,525)(464,527)(466,529)(468,531)(470,533)(472,535)(474,537)(476,539)(478,541)(480,543)(482,545)(498,562)(499,561)(500,560)(501,559)(502,558)(503,557)(504,556)(505,555)(506,554)(507,553)(508,552)(509,551)(510,550)(511,549)(512,548)(513,547)(515,580)(516,583)(518,585)(520,587)(522,589)(524,591)(526,593)(528,595)(530,597)(532,599)(534,601)(536,603)(538,605)(540,607)(542,609)(544,611)(546,613)(563,631)(564,630)(565,629)(566,628)(567,627)(568,626)(569,625)(570,624)(571,623)(572,622)(573,621)(574,620)(575,619)(576,618)(577,617)(578,616)(579,615)(581,650)(582,653)(584,655)(586,657)(588,659)(590,661)(592,663)(594,665)(596,667)(598,669)(600,671)(602,673)(604,675)(606,677)(608,679)(610,681)(612,683)(614,685)(632,704)(633,703)(634,702)(635,701)(636,700)(637,699)(638,698)(639,697)(640,696)(641,695)(642,694)(643,693)(644,692)(645,691)(646,690)(647,689)(648,688)(649,687)(651,724)(652,727)(654,729)(656,731)(658,733)(660,735)(662,737)(664,739)(666,741)(668,743)(670,745)(672,747)(674,749)(676,751)(678,753)(680,755)(682,757)(684,759)(686,761)(705,781)(706,780)(707,779)(708,778)(709,777)(710,776)(711,775)(712,774)(713,773)(714,772)(715,771)(716,770)(717,769)(718,768)(719,767)(720,766)(721,765)(722,764)(723,763)(725,802)(726,805)(728,807)(730,809)(732,811)(734,813)(736,815)(738,817)(740,819)(742,821)(744,823)(746,825)(748,827)(750,829)(752,831)(754,833)(756,835)(758,837)(760,839)(762,841)(782,862)(783,861)(784,860)(785,859)(786,858)(787,857)(788,856)(789,855)(790,854)(791,853)(792,852)(793,851)(794,850)(795,849)(796,848)(797,847)(798,846)(799,845)(800,844)(801,843)(803,884)(804,887)(806,889)(808,891)(810,893)(812,895)(814,897)(816,899)(818,901)(820,903)(822,905)(824,907)(826,909)(828,911)(830,913)(832,915)(834,917)(836,919)(838,921)(840,923)(842,925)(863,947)(864,946)(865,945)(866,944)(867,943)(868,942)(869,941)(870,940)(871,939)(872,938)(873,937)(874,936)(875,935)(876,934)(877,933)(878,932)(879,931)(880,930)(881,929)(882,928)(883,927)(885,970)(886,973)(888,975)(890,977)(892,979)(894,981)(896,983)(898,985)(900,987)(902,989)(904,991)(906,993)(908,995)(910,997)(912,999)(914,1001)(916,1003)(918,1005)(920,1007)(922,1009)(924,1011)(926,1013)(948,1036)(949,1035)(950,1034)(951,1033)(952,1032)(953,1031)(954,1030)(955,1029)(956,1028)(957,1027)(958,1026)(959,1025)(960,1024)(961,1023)(962,1022)(963,1021)(964,1020)(965,1019)(966,1018)(967,1017)(968,1016)(969,1015)(971,1060)(972,1063)(974,1065)(976,1067)(978,1069)(980,1071)(982,1073)(984,1075)(986,1077)(988,1079)(990,1081)(992,1083)(994,1085)(996,1087)(998,1089)(1000,1091)(1002,1093)(1004,1095)(1006,1097)(1008,1099)(1010,1101)(1012,1103)(1014,1105)(1037,1129)(1038,1128)(1039,1127)(1040,1126)(1041,1125)(1042,1124)(1043,1123)(1044,1122)(1045,1121)(1046,1120)(1047,1119)(1048,1118)(1049,1117)(1050,1116)(1051,1115)(1052,1114)(1053,1113)(1054,1112)(1055,1111)(1056,1110)(1057,1109)(1058,1108)(1059,1107)(1061,1152)(1062,1154)(1064,1156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Conjugacy classes & character table
3318 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13254, 3);
Finite Group Databasebeta