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Aliases
Splittings
Subgroups
40 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 608 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)(286,405,406,343,344,466)(288,403,404,346,342,397)(291,336,402,348,349,398)(298,413,414,355,356,393)(305,420,421,362,363,388)(312,427,428,369,370,383)(317,434,435,375,376,378)(322,440,432,380,381,373)(327,445,425,385,386,366)(331,450,418,390,391,359)(334,455,411,394,395,352)(345,410,464,350,401,467)(347,468,469,408,407,463)(357,472,473,415,416,459)(364,479,480,422,423,454)(371,486,487,429,430,449)(377,493,494,436,437,444)(382,500,498,441,442,439)(387,505,491,446,447,433)(392,510,484,451,452,426)(396,515,477,456,457,419)(399,520,471,460,461,412)(409,525,526,470,465,527)(417,528,529,474,475,524)(424,530,531,481,482,519)(431,534,535,488,489,514)(438,541,542,495,496,509)(443,548,549,501,502,504)(448,554,546,506,507,499)(453,559,539,511,512,492)(458,564,533,516,517,485)(462,569,476,521,522,478)(483,570,571,532,523,572)(490,573,574,536,537,568)(497,575,576,543,544,563)(503,579,580,550,551,558)(508,586,584,555,556,553)(513,591,578,560,561,547)(518,596,538,565,566,540)(545,597,598,577,567,599)(552,600,601,581,582,595)(557,602,603,587,588,590)(562,605,583,592,593,585)(589,606,607,604,594,608);(1,2)(8,9,12,18,26,39,58,81,110,145,186,233,286,345,348,289,236,189,148,113,84,61,42,29,14,13,19,28,41,60,83,112,147,188,235,288,347,409,471,411,351,292,239,192,151,116,87,52,22,33,21,32,47,67,92,122,157,198,245,298,357,417,476,477,418,358,299,246,199,158,119,75,35,50,51,34,49,70,96,127,163,205,252,305,364,424,483,533,484,425,365,306,253,202,154,104,54,73,89,74,53,72,99,131,168,210,258,312,371,431,490,538,539,491,432,372,309,249,195,139,77,102,124,118,103,76,101,134,172,215,263,317,377,438,497,545,578,546,498,435,368,302,242,180,106,137,165,160,153,138,105,136,175,219,268,322,382,443,503,552,583,584,549,494,428,361,295,227,141,178,212,207,201,194,179,140,177,222,272,327,387,448,508,557,589,603,580,542,487,421,354,280,182,225,265,260,255,248,241,226,181,224,275,331,392,453,513,562,594,607,601,576,535,480,414,339,229,278,324,319,314,308,301,294,279,228,277,334,396,458,518,567,582,588,593,598,574,531,473,404,282,337,389,384,379,374,367,360,353,338,281,336,399,462,523,537,544,551,556,561,566,571,529,469,341,402,455,450,445,440,434,427,420,413,403,340,401,465,475,482,489,496,502,507,512,517,522,526,406,467,520,515,510,505,500,493,486,479,472,468,405,344,407,416,423,430,437,442,447,452,457,461,464,466,527,569,564,559,554,548,541,534,530,528,525,410,285,342,356,363,370,376,381,386,391,395,398,400,463,524,572,596,591,586,579,575,573,570,521,460,349,232,283,297,304,311,316,321,326,330,333,335,397,459,519,568,599,605,602,600,597,565,516,456,394,290,185,230,244,251,257,262,267,271,274,276,332,393,454,514,563,595,608,606,592,560,511,451,390,329,237,144,183,197,204,209,214,218,221,223,273,328,388,449,509,558,590,604,587,555,506,446,385,325,270,190,109,142,156,162,167,171,174,176,220,269,323,383,444,504,553,585,581,550,501,441,380,320,266,217,149,80,107,121,126,130,133,135,173,216,264,318,378,439,499,547,577,543,495,436,375,315,261,213,170,114,57,78,91,95,98,100,132,169,211,259,313,373,433,492,540,536,488,429,369,310,256,208,166,129,85,38,55,66,69,71,97,128,164,206,254,307,366,426,485,532,481,422,362,303,250,203,161,125,94,62,25,36,46,48,68,93,123,159,200,247,300,359,419,478,474,415,355,296,243,196,155,120,90,65,43,17,23,31,45,64,88,117,152,193,240,293,352,412,470,408,346,287,234,187,146,111,82,59,40,27,11,15,20,30,44,63,86,115,150,191,238,291,350,343,284,231,184,143,108,79,56,37,24,16,10)
Conjugacy classes & character table
1060 conjugacy classes. The character table is too large to display.
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36060, 38);
Finite Group Databasebeta