← Prev (#27190402) Next (#27190404) →
Aliases
Splittings
Subgroups
20 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 499 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)(250,289,329)(253,292,326)(256,295,323)(259,298,320)(262,301,317)(265,304,314)(268,307,312)(271,310,309)(274,290,306)(277,315,303)(280,318,300)(283,321,297)(286,324,294)(288,327,291)(293,332,368)(296,335,365)(299,338,362)(302,341,359)(305,344,356)(308,347,354)(311,350,352)(313,333,349)(316,355,346)(319,357,343)(322,360,340)(325,363,337)(328,366,334)(330,369,331)(336,372,402)(339,375,399)(342,378,396)(345,381,393)(348,384,391)(351,386,390)(353,373,388)(358,392,383)(361,394,380)(364,397,377)(367,400,374)(370,403,371)(376,406,430)(379,409,427)(382,412,424)(385,415,422)(387,417,421)(389,407,420)(395,423,414)(398,425,411)(401,428,408)(404,431,405)(410,434,452)(413,437,449)(416,440,447)(418,442,446)(419,435,445)(426,448,439)(429,450,436)(432,453,433)(438,456,468)(441,459,466)(443,461,465)(444,457,464)(451,467,458)(454,469,455)(460,472,479)(462,474,478)(463,473,477)(470,480,471)(475,481,485)(476,482,484)(483,486,487)(491,492,494,493,495,497,496,498,499);(1,2,4,8,15,25,38,54,73,95,120,148,179,213,250,290,233,165,109,65,33,12,19,29,42,58,77,99,124,152,183,217,254,294,334,371,392,315,236,168,112,68,35,48,64,83,105,130,158,189,223,260,300,340,377,408,433,448,394,318,239,171,115,70,89,111,136,164,195,229,266,306,346,383,414,439,458,471,480,450,397,321,242,174,117,142,170,201,235,272,312,352,388,332,249,288,328,367,401,429,451,453,400,324,245,176,207,241,278,317,356,391,421,445,406,335,252,178,211,246,283,322,361,395,403,327,247,284,323,362,396,424,447,465,477,456,409,338,255,181,119,146,175,206,240,277,316,329,368,402,430,452,468,479,485,487,481,459,412,341,258,184,122,72,93,116,141,169,200,234,271,311,351,387,418,443,462,475,482,461,415,344,261,187,125,75,37,52,69,88,110,135,163,194,228,265,305,345,382,413,438,457,417,347,264,190,128,78,40,14,23,34,47,63,82,104,129,157,188,222,259,299,339,376,407,350,267,193,131,81,43,17,3,6,11,18,28,41,57,76,98,123,151,182,216,253,293,333,270,196,134,84,46,20,5,9,16,26,39,55,74,96,121,149,180,214,251,291,331,355,273,199,137,87,49,22,32,45,61,80,102,127,155,186,220,257,297,337,374,405,423,357,276,202,140,90,51,67,86,108,133,161,192,226,263,303,343,380,411,436,455,467,425,360,279,205,143,92,114,139,167,198,232,269,309,349,289,330,370,404,432,454,470,469,428,363,282,208,145,173,204,238,275,314,354,390,420,372,292,212,248,286,325,364,398,426,431,366,285,210,244,281,320,359,393,422,446,464,434,375,295,215,147,177,209,243,280,319,358,369,287,326,365,399,427,449,466,478,484,472,437,378,298,218,150,94,118,144,172,203,237,274,313,353,389,419,444,463,476,483,486,474,440,381,301,221,153,97,53,71,91,113,138,166,197,231,268,308,348,385,416,441,460,473,442,384,304,224,156,100,56,24,36,50,66,85,107,132,160,191,225,262,302,342,379,410,435,386,307,227,159,103,59,27,7,13,21,31,44,60,79,101,126,154,185,219,256,296,336,373,310,230,162,106,62,30,10)(488,489,490)
Conjugacy classes & character table
1485 conjugacy classes. The character table is too large to display.
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13149, 8);
Finite Group Databasebeta