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Aliases
Splittings
Subgroups
8 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 638 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)(250,289,329)(253,291,326)(256,294,323)(259,297,320)(262,300,317)(265,303,314)(268,306,311)(271,309,308)(274,312,305)(277,315,302)(280,318,299)(283,321,296)(286,324,293)(288,327,290)(292,332,369)(295,334,366)(298,337,363)(301,340,360)(304,343,357)(307,346,354)(310,349,351)(313,352,348)(316,355,345)(319,358,342)(322,361,339)(325,364,336)(328,367,333)(330,370,331)(335,373,407)(338,375,404)(341,378,401)(344,381,398)(347,384,395)(350,387,392)(353,390,389)(356,393,386)(359,396,383)(362,399,380)(365,402,377)(368,405,374)(371,408,372)(376,411,442)(379,413,439)(382,416,436)(385,419,433)(388,422,430)(391,425,427)(394,428,424)(397,431,421)(400,434,418)(403,437,415)(406,440,412)(409,443,410)(414,446,474)(417,448,471)(420,451,468)(423,454,465)(426,457,462)(429,460,459)(432,463,456)(435,466,453)(438,469,450)(441,472,447)(444,475,445)(449,478,503)(452,480,500)(455,483,497)(458,486,494)(461,489,491)(464,492,488)(467,495,485)(470,498,482)(473,501,479)(476,504,477)(481,507,529)(484,509,526)(487,512,523)(490,515,520)(493,518,517)(496,521,514)(499,524,511)(502,527,508)(505,530,506)(510,533,552)(513,535,549)(516,538,546)(519,541,543)(522,544,540)(525,547,537)(528,550,534)(531,553,532)(536,556,572)(539,558,569)(542,561,566)(545,564,563)(548,567,560)(551,570,557)(554,573,555)(559,576,589)(562,578,586)(565,581,583)(568,584,580)(571,587,577)(574,590,575)(579,593,603)(582,595,600)(585,598,597)(588,601,594)(591,604,592)(596,607,614)(599,609,611)(602,612,608)(605,615,606)(610,618,622)(613,620,619)(616,623,617)(621,626,627)(624,628,625)(629,631,630)(632,633,634,635,636,637,638);(1,2,4,8,15,25,38,54,73,95,120,148,179,213,250,289,330,371,409,444,476,505,531,554,574,591,605,616,624,629,628,612,584,544,492,428,352,270,196,134,84,46,20,5,9,16,26,39,55,74,96,121,149,180,214,251,290,331,332,249,288,328,368,406,441,473,502,528,551,571,588,602,613,621,623,601,567,521,463,393,312,233,165,109,65,33,12,19,29,42,58,77,99,124,152,183,217,254,293,333,372,373,291,212,248,286,325,365,403,438,470,499,525,548,568,585,599,610,615,587,547,495,431,355,273,199,137,87,49,22,32,45,61,80,102,127,155,186,220,257,296,336,374,410,411,334,252,178,211,246,283,322,362,400,435,467,496,522,545,565,582,596,604,570,524,466,396,315,236,168,112,68,35,48,64,83,105,130,158,189,223,260,299,339,377,412,445,446,375,294,215,147,177,209,243,280,319,359,397,432,464,493,519,542,562,579,590,550,498,434,358,276,202,140,90,51,67,86,108,133,161,192,226,263,302,342,380,415,447,477,478,413,337,255,181,119,146,175,206,240,277,316,356,394,429,461,490,516,539,559,573,527,469,399,318,239,171,115,70,89,111,136,164,195,229,266,305,345,383,418,450,479,506,507,448,378,297,218,150,94,118,144,172,203,237,274,313,353,391,426,458,487,513,536,553,501,437,361,279,205,143,92,114,139,167,198,232,269,308,348,386,421,453,482,508,532,533,480,416,340,258,184,122,72,93,116,141,169,200,234,271,310,350,388,423,455,484,510,530,472,402,321,242,174,117,142,170,201,235,272,311,351,389,424,456,485,511,534,555,556,509,451,381,300,221,153,97,53,71,91,113,138,166,197,231,268,307,347,385,420,452,481,504,440,364,282,208,145,173,204,238,275,314,354,392,427,459,488,514,537,557,575,576,535,483,419,343,261,187,125,75,37,52,69,88,110,135,163,194,228,265,304,344,382,417,449,475,405,324,245,176,207,241,278,317,357,395,430,462,491,517,540,560,577,592,593,558,512,454,384,303,224,156,100,56,24,36,50,66,85,107,132,160,191,225,262,301,341,379,414,443,367,285,210,244,281,320,360,398,433,465,494,520,543,563,580,594,606,607,578,538,486,422,346,264,190,128,78,40,14,23,34,47,63,82,104,129,157,188,222,259,298,338,376,408,327,247,284,323,363,401,436,468,497,523,546,566,583,597,608,617,618,595,561,515,457,387,306,227,159,103,59,27,7,13,21,31,44,60,79,101,126,154,185,219,256,295,335,370,287,326,366,404,439,471,500,526,549,569,586,600,611,619,625,626,609,581,541,489,425,349,267,193,131,81,43,17,3,6,11,18,28,41,57,76,98,123,151,182,216,253,292,329,369,407,442,474,503,529,552,572,589,603,614,622,627,630,631,620,598,564,518,460,390,309,230,162,106,62,30,10)
Conjugacy classes & character table
1491 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13251, 4);
Finite Group Databasebeta