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Aliases
Splittings
Subgroups
40 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 526 points:
(4,5)(7,11,12,30,35,8,9,17,19,57)(10,24,25,87,92,14,15,46,48,154)(13,40,41,42,68,21,22,76,78,79)(16,53,54,94,187,27,28,49,103,169)(18,62,63,208,193,32,33,118,120,108)(20,70,71,29,69,37,38,72,36,56)(23,81,82,218,165,43,44,144,146,275)(26,96,97,290,130,50,51,174,176,225)(31,112,113,58,195,59,60,200,109,110)(34,125,126,347,349,65,66,220,221,256)(39,132,133,166,167,73,74,229,93,277)(45,151,152,351,315,84,85,222,252,428)(47,159,160,382,140,89,90,266,267,194)(52,181,182,310,276,99,100,304,306,401)(55,189,190,433,226,104,105,319,321,340)(61,205,206,155,381,115,116,332,257,258)(64,216,217,80,239,122,123,278,141,142)(67,86,224,213,214,128,129,147,121,280)(75,234,235,316,317,135,136,333,188,430)(77,185,98,299,300,139,102,178,179,196)(83,248,202,203,138,148,149,114,295,237)(88,260,261,111,325,156,157,386,197,198)(91,271,272,497,479,162,163,397,398,380)(95,284,285,199,279,171,172,406,168,327)(101,223,311,426,429,127,184,353,412,366)(106,219,323,461,402,124,191,345,344,482)(107,119,231,281,282,117,192,210,170,212)(131,232,137,296,297,227,134,209,177,201)(143,367,268,269,431,240,241,161,376,395)(145,370,354,483,246,244,245,474,475,324)(150,374,313,183,404,249,250,186,308,309)(153,377,378,389,238,253,254,262,438,364)(158,391,392,259,484,263,264,493,383,384)(164,242,400,301,302,233,274,307,180,405)(173,409,410,385,432,287,288,494,318,486)(175,416,417,419,443,292,293,508,509,326)(204,446,368,346,487,329,330,243,464,465)(207,451,413,414,373,334,335,291,498,478)(211,455,456,467,468,337,338,434,350,403)(215,457,339,449,488,341,342,357,387,463)(228,362,289,439,440,355,236,348,322,388)(230,454,460,485,294,358,359,394,473,328)(247,361,408,356,365,265,372,286,283,298)(251,399,444,305,515,273,375,371,424,425)(255,396,481,511,499,270,379,418,462,526)(303,513,336,521,514,420,421,452,453,423)(312,442,510,500,314,422,427,466,518,363)(320,517,490,491,369,435,436,390,469,445)(331,520,470,471,476,447,448,352,489,360)(343,522,437,501,502,458,459,450,407,512)(393,492,505,506,480,495,496,415,472,525)(411,516,441,523,477,503,504,507,519,524);(1,2)(3,4,5)(6,7,10,16,29,30,58,111,199,166,87,155,259,385,316,94,170,283,355,227,38,72,128,65,32,9,13,23,45,86,60,114,204,331,449,157,262,390,492,501,172,286,406,476,358,74,134,233,162,89,15,26,52,101,125,116,207,336,454,455,264,393,410,493,517,288,411,502,481,416,136,236,363,313,185,28,55,106,122,62,119,211,339,133,231,361,477,504,456,190,322,441,505,413,97,177,298,364,237,41,56,107,115,59,12,20,39,75,137,63,121,215,343,460,160,221,350,469,509,179,120,212,340,225,79,57,108,194,139,22,42,80,143,242,123,218,344,462,521,269,351,321,438,518,302,214,187,315,429,142,110,196,324,244,44,83,150,251,271,219,346,466,508,451,396,471,440,386,487,421,342,317,431,515,241,198,326,444,370,85,153,255,268,159,189,320,437,235,332,377,480,519,488,323,442,459,432,514,182,307,327,445,368,82,147,247,263,156,25,49,95,173,289,126,222,352,472,520,272,353,473,484,526,309,217,277,403,478,149,113,201,328,292,51,98,180,303,422,223,354,398,498,446,399,475,267,381,482,401,275,154,256,380,250,203,290,412,424,100,183,310,306,308,181,305,426,176,295,374,479,349,92,165,276,402,258,382,483,375,330,414,497,474,184,312,420,301,178,96,175,294,297,200,248,373,468,167,278,404,499,384,485,311,397,448,506,470,152,220,348,287,171,54,46,88,158,265,224,144,243,369,279,400,304,423,486,522,427,345,463,523,525,254,206,333,450,435,105,90,161,270,253,151,245,371,443,325,367,425,395,430,457,513,465,261,388,489,379,335,417,510,464,191,163,273,249,148,81,145,246,300,195,239,366,428,169,280,405,500,389,433,252,376,453,511,461,146,216,274,240,141,78,40,77,140,193,35,68,130,226,282,208,299,419,491,467,347,266,394,458,341,213,118,209,135,73,37,17,31,61,117,69,76,138,238,365,296,174,291,415,507,439,319,434,516,524,372,210,229,357,337,192,33,64,124,104,53,102,186,314,362,234,293,418,512,503,409,436,392,494,495,391,338,359,452,334,205,66,127,99,50,24,47,91,164,232,132,230,360,285,408,284,407,496,490,378,260,387,447,329,202,112,129,84,43,21,11,18,34,67,71,70,131,228,356,281,103,188,318,383,257,48,93,168,197,109,19,36,27,14,8)
Conjugacy classes & character table
342 conjugacy classes. The character table is too large to display.
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31260, 19);
Finite Group Databasebeta