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Aliases
Splittings
Subgroups
24 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 696 points:
(2,3,5)(4,7,12)(6,10,9)(8,14,22)(11,17,19)(13,20,16)(15,24,35)(18,27,32)(21,30,29)(23,33,26)(25,37,51)(28,40,48)(31,43,45)(34,46,42)(36,49,39)(38,53,70)(41,56,67)(44,59,64)(47,62,61)(50,65,58)(52,68,55)(54,72,92)(57,75,89)(60,78,86)(63,81,83)(66,84,80)(69,87,77)(71,90,74)(73,94,117)(76,97,114)(79,100,111)(82,103,108)(85,106,105)(88,109,102)(91,112,99)(93,115,96)(95,119,145)(98,122,142)(101,125,139)(104,128,136)(107,131,133)(110,134,130)(113,137,127)(116,140,124)(118,143,121)(120,147,176)(123,150,173)(126,153,170)(129,156,167)(132,159,164)(135,162,161)(138,165,158)(141,168,155)(144,171,152)(146,174,149)(148,178,210)(151,181,207)(154,184,204)(157,187,201)(160,190,198)(163,193,195)(166,196,192)(169,199,189)(172,202,186)(175,205,183)(177,208,180)(179,212,247)(182,215,244)(185,218,241)(188,221,238)(191,224,235)(194,227,232)(197,230,229)(200,233,226)(203,236,223)(206,239,220)(209,242,217)(211,245,214)(213,249,287)(216,252,284)(219,255,281)(222,258,278)(225,261,275)(228,264,272)(231,267,269)(234,270,266)(237,273,263)(240,276,260)(243,279,257)(246,282,254)(248,285,251)(250,289,330)(253,292,327)(256,295,324)(259,298,321)(262,301,318)(265,304,315)(268,307,312)(271,310,309)(274,313,306)(277,316,303)(280,319,300)(283,322,297)(286,325,294)(288,328,291)(290,332,376)(293,335,373)(296,338,370)(299,341,367)(302,344,364)(305,347,361)(308,350,358)(311,353,355)(314,356,352)(317,359,349)(320,362,346)(323,365,343)(326,368,340)(329,371,337)(331,374,334)(333,378,420)(336,380,421)(339,383,418)(342,386,415)(345,389,412)(348,392,409)(351,395,406)(354,398,403)(357,401,400)(360,404,397)(363,407,394)(366,410,391)(369,413,388)(372,416,385)(375,419,382)(377,422,379)(381,426,463)(384,428,464)(387,430,462)(390,433,459)(393,436,456)(396,439,453)(399,442,450)(402,445,447)(405,448,444)(408,451,441)(411,454,438)(414,457,435)(417,460,432)(423,465,427)(424,466,425)(429,469,502)(431,470,503)(434,472,501)(437,475,498)(440,478,495)(443,481,492)(446,484,489)(449,487,486)(452,490,483)(455,493,480)(458,496,477)(461,499,474)(467,504,468)(471,505,535)(473,506,536)(476,508,534)(479,511,531)(482,514,528)(485,517,525)(488,520,522)(491,523,519)(494,526,516)(497,529,513)(500,532,510)(507,537,564)(509,538,565)(512,540,563)(515,543,560)(518,546,557)(521,549,554)(524,552,551)(527,555,548)(530,558,545)(533,561,542)(539,566,590)(541,567,591)(544,569,589)(547,572,586)(550,575,583)(553,578,580)(556,581,577)(559,584,574)(562,587,571)(568,592,613)(570,593,614)(573,595,612)(576,598,609)(579,601,606)(582,604,603)(585,607,600)(588,610,597)(594,615,633)(596,616,634)(599,618,632)(602,621,629)(605,624,626)(608,627,623)(611,630,620)(617,635,650)(619,636,651)(622,638,649)(625,641,646)(628,644,643)(631,647,640)(637,652,664)(639,653,665)(642,655,663)(645,658,660)(648,661,657)(654,666,675)(656,667,676)(659,669,674)(662,672,671)(668,677,683)(670,678,684)(673,680,682)(679,685,688)(681,686,689)(687,690,691)(695,696);(1,2,4,8,15,25,38,54,73,95,120,148,179,213,250,290,333,371,285,210,244,281,321,364,409,453,492,525,554,580,603,623,640,635,593,540,475,389,298,218,150,94,118,144,172,203,237,274,314,357,402,446,485,518,547,573,596,617,630,584,526,451,359,273,199,137,87,49,22,32,45,61,80,102,127,155,186,220,257,297,340,385,378,424,467,504,422,330,373,418,462,501,534,563,589,612,632,649,663,674,682,677,653,618,572,514,439,347,261,187,125,75,37,52,69,88,110,135,163,194,228,265,305,348,393,437,476,509,539,561,496,410,319,239,171,115,70,89,111,136,164,195,229,266,306,349,394,438,477,510,505,428,335,249,288,329,372,417,461,500,533,562,588,611,631,648,662,673,681,687,686,669,641,601,549,484,398,307,227,159,103,59,27,7,13,21,31,44,60,79,101,126,154,185,219,256,296,339,384,429,460,368,282,208,145,173,204,238,275,315,358,403,447,486,519,548,574,597,592,538,472,386,295,215,147,177,209,243,280,320,363,408,452,491,524,553,579,602,622,639,654,661,627,581,523,448,356,270,196,134,84,46,20,5,9,16,26,39,55,74,96,121,149,180,214,251,291,334,379,425,419,328,247,284,324,367,412,456,495,528,557,583,606,626,643,657,652,616,569,511,436,344,258,184,122,72,93,116,141,169,200,234,271,311,354,399,443,482,515,544,570,594,610,558,493,407,316,236,168,112,68,35,48,64,83,105,130,158,189,223,260,300,343,388,432,426,332,377,423,466,376,421,464,503,536,565,591,614,634,651,665,676,684,689,685,667,638,598,546,481,395,304,224,156,100,56,24,36,50,66,85,107,132,160,191,225,262,302,345,390,434,473,507,532,457,365,279,205,143,92,114,139,167,198,232,269,309,352,397,441,480,513,542,537,470,383,292,212,248,286,326,369,414,458,497,530,559,585,608,628,645,659,670,679,680,658,624,578,520,445,353,267,193,131,81,43,17,3,6,11,18,28,41,57,76,98,123,151,182,216,253,293,336,381,416,325,245,176,207,241,278,318,361,406,450,489,522,551,577,600,620,615,567,508,433,341,255,181,119,146,175,206,240,277,317,360,405,449,488,521,550,576,599,619,637,647,607,555,490,404,313,233,165,109,65,33,12,19,29,42,58,77,99,124,152,183,217,254,294,337,382,427,468,465,374,287,327,370,415,459,498,531,560,586,609,629,646,660,671,666,636,595,543,478,392,301,221,153,97,53,71,91,113,138,166,197,231,268,308,351,396,440,479,512,541,568,587,529,454,362,276,202,140,90,51,67,86,108,133,161,192,226,263,303,346,391,435,474,469,380,289,331,375,420,463,502,535,564,590,613,633,650,664,675,683,688,691,690,678,655,621,575,517,442,350,264,190,128,78,40,14,23,34,47,63,82,104,129,157,188,222,259,299,342,387,431,471,499,413,322,242,174,117,142,170,201,235,272,312,355,400,444,483,516,545,571,566,506,430,338,252,178,211,246,283,323,366,411,455,494,527,556,582,605,625,642,656,668,672,644,604,552,487,401,310,230,162,106,62,30,10)(692,693,694)
Conjugacy classes & character table
1398 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12438, 11);
Finite Group Databasebeta