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