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Aliases
Splittings
Subgroups
12 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 678 points:
(2,3,4,6)(5,8,9,15)(7,12,13,11)(10,17,18,28)(14,21,22,24)(16,25,26,20)(19,30,31,45)(23,34,35,41)(27,38,39,37)(29,42,43,33)(32,47,48,66)(36,51,52,62)(40,55,56,58)(44,59,60,54)(46,63,64,50)(49,68,69,91)(53,72,73,87)(57,76,77,83)(61,80,81,79)(65,84,85,75)(67,88,89,71)(70,93,94,120)(74,97,98,116)(78,101,102,112)(82,105,106,108)(86,109,110,104)(90,113,114,100)(92,117,118,96)(95,122,123,153)(99,126,127,149)(103,130,131,145)(107,134,135,141)(111,138,139,137)(115,142,143,133)(119,146,147,129)(121,150,151,125)(124,155,156,190)(128,159,160,186)(132,163,164,182)(136,167,168,178)(140,171,172,174)(144,175,176,170)(148,179,180,166)(152,183,184,162)(154,187,188,158)(157,192,193,231)(161,196,197,227)(165,200,201,223)(169,204,205,219)(173,208,209,215)(177,212,213,211)(181,216,217,207)(185,220,221,203)(189,224,225,199)(191,228,229,195)(194,233,234,276)(198,237,238,272)(202,241,242,268)(206,245,246,264)(210,249,250,260)(214,253,254,256)(218,257,258,252)(222,261,262,248)(226,265,266,244)(230,269,270,240)(232,273,274,236)(235,278,279,325)(239,282,283,321)(243,286,287,317)(247,290,291,313)(251,294,295,309)(255,298,299,305)(259,302,303,301)(263,306,307,297)(267,310,311,293)(271,314,315,289)(275,318,319,285)(277,322,323,281)(280,327,328,378)(284,331,332,374)(288,335,336,370)(292,339,340,366)(296,343,344,362)(300,347,348,358)(304,351,352,354)(308,355,356,350)(312,359,360,346)(316,363,364,342)(320,367,368,338)(324,371,372,334)(326,375,376,330)(329,380,381,435)(333,384,385,431)(337,388,389,427)(341,392,393,423)(345,396,397,419)(349,400,401,415)(353,404,405,411)(357,408,409,407)(361,412,413,403)(365,416,417,399)(369,420,421,395)(373,424,425,391)(377,428,429,387)(379,432,433,383)(382,437,438,496)(386,441,442,492)(390,445,446,488)(394,449,450,484)(398,453,454,480)(402,457,458,476)(406,461,462,472)(410,465,466,468)(414,469,470,464)(418,473,474,460)(422,477,478,456)(426,481,482,452)(430,485,486,448)(434,489,490,444)(436,493,494,440)(439,498,499,561)(443,502,503,557)(447,506,507,553)(451,510,511,549)(455,514,515,545)(459,518,519,541)(463,522,523,537)(467,526,527,533)(471,530,531,529)(475,534,535,525)(479,538,539,521)(483,542,543,517)(487,546,547,513)(491,550,551,509)(495,554,555,505)(497,558,559,501)(500,563,564,588)(504,567,568,617)(508,571,572,615)(512,575,576,613)(516,579,580,611)(520,565,583,609)(524,586,587,605)(528,590,591,601)(532,594,595,597)(536,598,599,593)(540,602,603,589)(544,606,607,585)(548,610,608,582)(552,612,604,578)(556,614,600,574)(560,616,596,570)(562,618,592,566)(569,619,620,633)(573,622,623,637)(577,625,626,636)(581,628,629,635)(584,621,631,634)(624,638,639,649)(627,641,642,652)(630,644,645,651)(632,640,647,650)(643,653,654,661)(646,656,657,663)(648,655,659,662)(658,664,665,669)(660,666,667,670)(668,671,672,673)(674,675,676,677,678);(1,2,5,10,19,32,49,70,95,124,157,194,235,280,329,382,439,500,565,514,449,388,331,278,326,377,430,487,548,607,543,482,425,372,323,276,321,370,423,480,541,605,618,558,493,432,375,322,273,228,187,150,117,88,63,42,25,12,3,7,14,23,36,53,74,99,128,161,198,239,284,333,386,443,504,569,621,579,510,445,384,327,379,434,491,552,603,539,478,421,368,319,274,231,272,317,366,419,476,537,601,616,554,489,428,371,318,269,224,183,146,113,84,59,38,21,8,16,27,40,57,78,103,132,165,202,243,288,337,390,447,508,573,624,640,628,575,506,441,380,436,495,556,599,535,474,417,364,315,270,229,190,227,268,313,362,415,472,533,597,614,550,485,424,367,314,265,220,179,142,109,80,55,34,17,29,44,61,82,107,136,169,206,247,292,341,394,451,512,577,627,643,655,644,625,571,502,437,497,560,595,531,470,413,360,311,266,225,188,153,186,223,264,309,358,411,468,529,593,612,546,481,420,363,310,261,216,175,138,105,76,51,30,46,65,86,111,140,173,210,251,296,345,398,455,516,581,630,646,658,666,656,641,622,567,498,562,591,527,466,409,356,307,262,221,184,151,120,149,182,219,260,305,354,407,464,525,589,610,542,477,416,359,306,257,212,171,134,101,72,47,67,90,115,144,177,214,255,300,349,402,459,520,584,632,648,660,668,671,664,653,638,619,563,587,523,462,405,352,303,258,217,180,147,118,91,116,145,178,215,256,301,350,403,460,521,585,606,538,473,412,355,302,253,208,167,130,97,68,92,119,148,181,218,259,304,353,406,463,524,588,633,649,661,669,673,672,667,659,647,631,583,519,458,401,348,299,254,213,176,143,114,89,66,87,112,141,174,211,252,297,346,399,456,517,582,602,534,469,408,351,298,249,204,163,126,93,121,152,185,222,263,308,357,410,467,528,592,561,617,637,652,663,670,665,657,645,629,580,515,454,397,344,295,250,209,172,139,110,85,64,45,62,83,108,137,170,207,248,293,342,395,452,513,578,598,530,465,404,347,294,245,200,159,122,154,189,226,267,312,361,414,471,532,596,559,496,557,615,636,651,662,654,642,626,576,511,450,393,340,291,246,205,168,135,106,81,60,43,28,41,58,79,104,133,166,203,244,289,338,391,448,509,574,594,526,461,400,343,290,241,196,155,191,230,271,316,365,418,475,536,600,555,494,435,492,553,613,635,650,639,623,572,507,446,389,336,287,242,201,164,131,102,77,56,39,26,15,24,37,54,75,100,129,162,199,240,285,334,387,444,505,570,590,522,457,396,339,286,237,192,232,275,320,369,422,479,540,604,551,490,433,378,431,488,549,611,634,620,568,503,442,385,332,283,238,197,160,127,98,73,52,35,22,13,6,11,20,33,50,71,96,125,158,195,236,281,330,383,440,501,566,586,518,453,392,335,282,233,277,324,373,426,483,544,608,547,486,429,376,325,374,427,484,545,609,564,499,438,381,328,279,234,193,156,123,94,69,48,31,18,9,4)
Conjugacy classes & character table
860 conjugacy classes. The character table is too large to display.
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13460, 6);
Finite Group Databasebeta