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Aliases
Splittings
Subgroups
40 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 548 points:
(3,4,5,6,7)(9,13,14,10,11,15)(12,21,22,16,17,31)(18,34,35,24,25,48)(19,33,29,27,23,20)(26,53,54,37,38,71)(28,51,52,40,36,45)(30,32,50,42,43,46)(39,76,77,56,57,100)(41,74,75,59,55,68)(44,49,73,61,62,69)(47,89,87,65,66,64)(58,105,106,79,80,135)(60,103,104,82,78,97)(63,72,102,84,85,98)(67,118,119,90,91,93)(70,124,116,94,95,88)(81,140,141,108,109,176)(83,138,139,111,107,132)(86,101,137,113,114,133)(92,153,154,120,121,128)(96,160,158,125,126,123)(99,165,151,129,130,117)(110,181,182,143,144,223)(112,179,180,146,142,173)(115,136,178,148,149,174)(122,194,195,155,156,169)(127,201,202,161,162,164)(131,207,199,166,167,159)(134,212,192,170,171,152)(145,228,229,184,185,276)(147,226,227,187,183,220)(150,177,225,189,190,221)(157,241,242,196,197,216)(163,248,249,203,204,211)(168,255,253,208,209,206)(172,260,246,213,214,200)(175,265,239,217,218,193)(186,281,282,231,232,335)(188,279,280,234,230,273)(191,224,278,236,237,274)(198,294,295,243,244,269)(205,301,302,250,251,264)(210,308,309,256,257,259)(215,314,306,261,262,254)(219,319,299,266,267,247)(222,324,292,270,271,240)(233,340,341,284,285,400)(235,338,339,287,283,332)(238,277,337,289,290,333)(245,353,354,296,297,328)(252,360,361,303,304,323)(258,367,368,310,311,318)(263,374,372,315,316,313)(268,379,365,320,321,307)(272,384,358,325,326,300)(275,389,351,329,330,293)(286,405,406,343,344,465)(288,403,404,346,342,397)(291,336,402,348,349,398)(298,417,418,355,356,393)(305,424,425,362,363,388)(312,429,430,369,370,383)(317,436,437,375,376,378)(322,442,434,380,381,373)(327,447,409,385,386,366)(331,452,422,390,391,359)(334,457,415,394,395,352)(345,453,454,408,392,504)(347,467,468,410,407,463)(350,401,466,412,413,464)(357,472,473,419,420,460)(364,477,478,426,427,456)(371,482,483,431,432,451)(377,487,488,438,439,446)(382,494,492,443,444,441)(387,499,470,448,449,435)(396,508,414,458,459,423)(399,510,471,461,462,416)(411,505,506,469,455,512)(421,513,514,474,475,511)(428,515,516,479,480,509)(433,519,520,484,485,507)(440,524,525,489,490,503)(445,529,518,495,496,498)(450,533,476,500,501,493)(481,534,535,517,502,539)(486,540,541,521,522,538)(491,542,543,526,527,537)(497,545,523,530,531,536)(528,546,547,544,532,548);(1,2)(8,9,12,18,26,39,58,81,110,145,186,233,286,345,409,365,306,253,202,154,104,54,73,89,74,53,72,99,131,168,210,258,312,371,433,486,523,525,483,425,354,280,182,225,265,260,255,248,241,226,181,224,275,331,392,455,475,480,485,490,496,501,506,406,466,510,508,504,499,494,487,482,477,472,467,405,458,394,290,185,230,244,251,257,262,267,271,274,276,332,393,456,507,537,544,526,489,438,375,315,261,213,170,114,57,78,91,95,98,100,132,169,211,259,313,373,435,469,410,346,287,234,187,146,111,82,59,40,27,11,15,20,30,44,63,86,115,150,191,238,291,350,414,422,358,299,246,199,158,119,75,35,50,51,34,49,70,96,127,163,205,252,305,364,428,481,518,488,430,361,295,227,141,178,212,207,201,194,179,140,177,222,272,327,387,450,502,522,527,531,535,514,468,341,402,457,452,447,442,436,429,424,417,403,340,401,461,349,232,283,297,304,311,316,321,326,330,333,335,397,460,509,538,548,546,530,495,443,380,320,266,217,149,80,107,121,126,130,133,135,173,216,264,318,378,441,493,474,419,355,296,243,196,155,120,90,65,43,17,23,31,45,64,88,117,152,193,240,293,352,416,471,415,351,292,239,192,151,116,87,52,22,33,21,32,47,67,92,122,157,198,245,298,357,421,476,492,437,368,302,242,180,106,137,165,160,153,138,105,136,175,219,268,322,382,445,497,532,547,541,516,473,404,282,337,389,384,379,374,367,360,353,338,281,336,399,413,285,342,356,363,370,376,381,386,391,395,398,400,463,511,539,545,542,540,534,500,448,385,325,270,190,109,142,156,162,167,171,174,176,220,269,323,383,446,498,517,479,426,362,303,250,203,161,125,94,62,25,36,46,48,68,93,123,159,200,247,300,359,423,412,348,289,236,189,148,113,84,61,42,29,14,13,19,28,41,60,83,112,147,188,235,288,347,411,470,434,372,309,249,195,139,77,102,124,118,103,76,101,134,172,215,263,317,377,440,491,528,543,520,478,418,339,229,278,324,319,314,308,301,294,279,228,277,334,396,344,407,420,427,432,439,444,449,454,459,462,464,465,512,533,529,524,519,515,513,505,453,390,329,237,144,183,197,204,209,214,218,221,223,273,328,388,451,503,536,521,484,431,369,310,256,208,166,129,85,38,55,66,69,71,97,128,164,206,254,307,366,408,343,284,231,184,143,108,79,56,37,24,16,10)
Conjugacy classes & character table
960 conjugacy classes. The character table is too large to display.
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32460, 38);
Finite Group Databasebeta