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Aliases
Splittings
Subgroups
40 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 546 points:
(4,5)(7,11,12,30,35,8,9,17,19,59)(10,24,25,92,97,14,15,46,48,170)(13,40,41,42,70,21,22,80,82,84)(16,53,54,109,148,27,28,108,79,205)(18,64,65,244,226,32,33,130,132,120)(20,74,75,71,72,37,38,76,36,83)(23,86,87,253,181,43,44,157,159,313)(26,102,103,330,140,50,51,191,193,259)(29,114,115,357,69,56,57,213,215,139)(31,124,125,60,228,61,62,233,121,122)(34,137,91,296,297,67,68,167,168,302)(39,146,129,182,183,77,78,242,98,315)(45,164,165,414,269,89,90,290,264,418)(47,175,176,216,204,94,95,232,308,227)(49,185,186,141,142,99,100,320,73,261)(52,198,199,350,314,105,106,344,346,460)(55,208,190,440,260,111,112,291,329,411)(58,220,221,505,507,117,118,376,378,544)(63,239,240,171,403,127,128,396,250,303)(66,251,252,85,278,134,135,316,154,155)(81,272,104,339,340,150,151,195,196,229)(88,286,236,237,149,161,162,126,335,270)(93,304,305,123,388,172,173,292,230,231)(96,310,311,298,462,178,179,421,448,449)(101,326,327,317,318,188,189,471,184,464)(107,351,352,539,419,201,202,483,485,481)(110,214,279,177,262,206,156,369,143,309)(113,363,359,509,461,210,211,484,446,511)(116,371,372,312,412,217,218,503,457,458)(119,383,384,444,445,223,224,382,295,532)(131,243,323,324,277,180,246,187,247,153)(133,322,174,265,284,248,249,145,234,160)(136,406,407,405,468,254,255,397,321,523)(138,354,355,475,426,257,203,489,490,528)(144,267,256,336,337,263,147,245,194,235)(152,424,209,447,479,274,275,361,343,455)(158,429,356,370,360,281,282,492,493,387)(163,437,422,200,463,287,288,273,348,349)(166,442,443,456,271,293,294,306,474,420)(169,451,452,459,517,299,300,467,391,529)(192,225,477,478,513,332,333,386,494,389)(197,469,334,410,465,341,342,268,404,347)(207,377,438,430,466,358,289,506,319,502)(212,499,500,497,480,365,366,543,514,345)(219,488,504,521,510,374,375,540,400,385)(222,450,508,431,432,380,381,533,283,522)(238,518,427,408,441,393,394,280,524,525)(241,512,301,476,436,398,399,331,454,530)(258,501,495,482,535,409,367,362,534,538)(266,276,515,373,368,415,416,390,491,392)(285,401,473,428,470,434,435,328,325,338)(307,519,379,439,417,433,395,453,402,413)(353,520,472,545,423,486,487,526,536,516)(364,542,541,546,425,498,496,537,531,527);(1,2)(3,4,5)(6,7,10,16,29,58,119,225,255,408,526,189,328,471,530,162,125,235,392,115,216,370,500,366,498,363,497,513,388,369,503,434,284,157,280,428,323,185,321,159,251,404,409,257,137,139,67,32,9,13,23,45,91,169,301,103,194,338,378,329,474,536,546,288,237,330,475,218,373,489,542,495,361,208,360,340,228,278,426,507,517,282,430,317,182,92,171,248,130,245,254,134,64,131,178,94,15,26,52,107,203,356,494,196,132,247,402,165,292,441,504,438,394,476,537,375,486,351,484,358,206,108,204,226,35,70,140,260,412,432,521,398,239,173,306,435,246,242,127,61,12,20,39,79,28,55,113,212,367,502,539,342,249,320,467,294,240,397,520,221,379,451,534,346,348,198,345,481,418,205,357,277,72,80,149,271,421,519,393,236,124,234,391,457,310,416,274,150,22,42,85,156,57,116,219,199,347,464,508,479,403,468,535,445,399,477,483,381,448,296,447,341,195,102,192,334,267,146,266,417,142,151,273,423,515,176,230,121,19,36,73,143,175,307,431,281,44,88,163,289,118,222,382,349,252,315,462,297,97,181,314,461,510,383,509,444,293,164,291,188,99,46,93,174,75,74,144,264,262,275,425,527,424,309,414,263,38,76,145,172,25,49,101,190,90,166,295,446,224,385,511,460,313,170,302,449,183,316,463,384,380,220,377,287,161,86,158,283,433,95,177,141,71,30,60,123,232,390,516,422,272,261,413,415,78,147,268,332,51,104,197,343,168,298,450,352,386,512,532,538,523,303,455,533,318,465,344,374,217,114,214,154,82,40,81,152,276,179,312,459,265,62,126,238,395,311,420,270,41,83,153,215,148,269,419,480,106,200,350,482,300,453,376,487,407,396,442,452,186,322,469,485,466,501,365,210,111,53,109,77,37,17,31,63,129,243,401,443,304,128,241,400,522,458,411,259,84,59,120,227,54,110,207,359,202,353,488,541,454,518,506,540,525,305,290,439,324,244,339,478,492,354,201,105,50,24,47,96,180,33,66,136,256,65,133,250,48,98,184,319,429,529,544,528,155,122,229,387,112,209,362,496,355,491,371,490,193,335,437,531,545,456,440,505,470,336,191,331,299,167,89,43,21,11,18,34,69,68,138,258,410,135,253,405,100,187,325,427,87,160,285,372,279,231,389,514,211,364,499,543,493,308,213,368,337,233,286,436,327,473,326,472,524,406,333,223,117,56,27,14,8)
Conjugacy classes & character table
354 conjugacy classes. The character table is too large to display.
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32460, 36);
Finite Group Databasebeta