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Aliases
Splittings
Subgroups
6 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 546 points:
(2,3,5,9,17)(4,7,13,25,47)(6,11,21,40,33)(8,15,29,55,99)(10,19,36,18,34)(12,23,43,77,84)(14,27,51,91,63)(16,31,59,67,37)(20,38,69,48,85)(22,41,74,73,64)(24,45,81,136,166)(26,49,87,35,65)(28,53,95,159,141)(30,57,103,173,114)(32,61,110,126,107)(39,71,122,100,167)(42,75,106,129,142)(44,79,132,152,115)(46,78,130,145,68)(50,89,148,86,143)(52,93,155,125,116)(54,97,163,251,256)(56,101,169,66,117)(58,105,177,273,220)(60,108,120,88,146)(62,112,183,206,235)(70,72,92,153,118)(76,127,200,213,257)(80,134,209,245,221)(82,138,216,266,189)(83,133,207,238,180)(90,150,231,168,258)(94,157,241,202,222)(96,161,248,234,190)(98,137,214,260,119)(102,171,263,144,223)(104,175,269,198,191)(109,182,195,170,261)(111,184,179,203,225)(113,187,284,312,372)(121,128,160,246,224)(123,151,174,267,192)(124,156,239,199,181)(131,204,228,147,226)(135,211,305,353,359)(139,218,315,381,318)(140,210,303,348,333)(149,229,154,236,193)(158,243,341,308,360)(162,250,351,344,319)(164,253,356,371,287)(165,217,313,375,278)(172,265,369,259,361)(176,271,378,295,320)(178,275,384,332,288)(185,281,293,309,363)(186,282,302,345,322)(188,247,346,325,230)(194,212,252,354,362)(196,244,274,382,321)(197,242,340,299,334)(201,249,349,336,279)(205,298,328,262,364)(208,300,339,296,323)(215,310,366,227,324)(219,306,402,445,460)(232,329,268,373,289)(233,270,376,292,280)(237,335,290,264,367)(240,337,277,297,326)(254,358,448,470,416)(255,316,413,473,425)(272,380,468,405,450)(276,386,476,434,417)(283,390,401,442,451)(285,391,412,471,418)(286,350,438,430,396)(291,342,432,409,461)(294,352,441,437,426)(301,399,431,406,452)(304,400,440,435,419)(307,357,446,463,388)(311,408,458,365,453)(314,410,466,395,420)(317,355,443,454,327)(330,393,383,472,421)(331,379,467,398,427)(338,429,394,407,455)(343,385,474,428,389)(347,436,422,368,456)(370,459,374,462,392)(377,464,387,397,423)(403,482,501,513,489)(404,449,502,514,491)(411,487,511,483,503)(414,488,516,495,490)(415,447,499,510,480)(424,469,512,486,508)(433,477,517,496,492)(439,497,494,484,504)(444,498,506,457,505)(465,509,479,485,507)(475,515,493,481,478)(500,519,521,518,520)(522,523,525,528,532,524,526,529,533,537,527,530,534,538,541,531,535,539,542,544,536,540,543,545,546);(1,2,4,8,16,32,62,113,188,286,101,170,262,365,410,49,88,147,227,300,19,37,68,119,184,3,6,12,24,46,83,140,219,317,415,171,264,368,457,487,89,149,230,327,399,38,70,121,194,281,7,14,28,54,98,165,255,341,431,494,265,370,231,328,422,150,232,330,315,412,71,123,196,209,302,15,30,58,106,179,277,387,432,69,120,193,289,329,423,103,174,268,374,413,51,92,154,237,303,21,31,60,109,183,5,10,20,39,72,124,197,291,393,478,175,270,377,465,488,93,156,240,338,400,41,61,111,185,282,11,22,42,76,128,201,294,273,381,470,271,379,173,266,371,157,242,99,166,256,75,112,186,283,390,23,44,80,135,212,307,404,382,471,513,380,469,267,372,460,243,342,167,257,359,127,187,285,305,401,45,82,139,200,293,394,479,472,122,195,290,392,373,461,177,274,383,258,360,95,160,247,347,402,43,78,131,205,284,13,26,50,90,151,233,331,424,462,508,275,385,475,361,450,161,249,350,439,482,79,133,208,301,391,27,52,94,158,244,343,433,384,473,514,386,477,269,375,463,250,352,169,260,362,134,210,304,251,353,53,96,162,159,245,344,434,474,91,152,234,332,376,47,84,141,220,261,363,451,211,306,403,354,442,97,164,254,246,345,435,495,515,153,235,333,425,464,85,142,221,318,364,452,163,252,355,444,443,81,137,215,311,346,29,56,102,172,236,334,426,491,509,143,222,319,416,453,503,253,357,447,500,498,138,217,314,411,436,57,104,176,272,335,427,492,476,516,223,320,417,378,466,510,358,449,263,366,454,218,316,414,356,445,105,178,276,248,348,437,496,517,155,238,336,428,467,87,145,224,321,367,455,136,213,308,405,446,77,129,202,295,349,40,73,125,198,239,17,33,63,114,146,225,322,418,456,504,214,309,406,483,499,130,203,296,395,438,59,107,180,278,337,34,64,115,189,226,323,419,489,505,520,310,407,484,518,519,204,297,396,480,497,108,181,279,388,429,65,116,190,287,324,420,490,468,511,521,408,485,369,458,506,298,397,481,448,501,182,280,389,351,440,117,191,288,241,339,430,493,512,148,228,325,421,459,507,216,312,409,486,502,132,206,299,398,441,74,126,199,292,340,36,67,118,192,229,326,55,100,168,259,313,25,48,86,144,207,9,18,35,66,110)
Polycyclic presentation:
5^2,521|a^5=b,c^a=c^25
Conjugacy classes & character table
545 conjugacy classes — view the full character table.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13025, 1);
Finite Group Databasebeta