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Aliases
Splittings
Subgroups
16 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 438 points:
(2,6,7,3,4,8)(5,14,15,9,10,24)(11,27,28,17,18,41)(12,26,22,20,16,13)(19,46,47,30,31,64)(21,44,45,33,29,38)(23,25,43,35,36,39)(32,69,70,49,50,93)(34,67,68,52,48,61)(37,42,66,54,55,62)(40,82,80,58,59,57)(51,98,99,72,73,128)(53,96,97,75,71,90)(56,65,95,77,78,91)(60,111,112,83,84,86)(63,117,109,87,88,81)(74,133,134,101,102,169)(76,131,132,104,100,125)(79,94,130,106,107,126)(85,146,147,113,114,121)(89,153,151,118,119,116)(92,158,144,122,123,110)(103,174,175,136,137,216)(105,172,173,139,135,166)(108,129,171,141,142,167)(115,187,188,148,149,162)(120,194,195,154,155,157)(124,200,192,159,160,152)(127,205,185,163,164,145)(138,221,222,177,178,269)(140,219,220,180,176,213)(143,170,218,182,183,214)(150,234,235,189,190,209)(156,241,242,196,197,204)(161,248,246,201,202,199)(165,253,239,206,207,193)(168,258,232,210,211,186)(179,274,275,224,225,328)(181,272,273,227,223,266)(184,217,271,229,230,267)(191,287,288,236,237,262)(198,294,295,243,244,257)(203,301,302,249,250,252)(208,307,299,254,255,247)(212,312,292,259,260,240)(215,317,285,263,264,233)(226,333,334,277,278,392)(228,331,332,280,276,325)(231,270,330,282,283,326)(238,345,346,289,290,321)(245,352,353,296,297,316)(251,359,360,303,304,311)(256,366,364,308,309,306)(261,371,357,313,314,300)(265,376,350,318,319,293)(268,381,343,322,323,286)(279,396,342,336,337,398)(281,394,395,338,335,389)(284,329,393,340,341,390)(291,401,402,347,348,385)(298,406,407,354,355,380)(305,411,412,361,362,375)(310,416,417,367,368,370)(315,420,414,372,373,365)(320,423,409,377,378,358)(324,426,404,382,383,351)(327,429,399,386,387,344)(339,432,400,391,397,433)(349,430,405,388,403,431)(356,427,410,384,408,428)(363,424,415,379,413,425)(369,421,419,374,418,422)(434,435,436,437,438);(1,2,5,11,19,32,51,74,103,138,179,226,279,278,335,348,355,362,368,373,378,383,387,390,392,433,399,343,285,232,185,144,109,80,45,15,26,14,25,40,60,85,115,150,191,238,291,349,386,283,178,223,237,244,250,255,260,264,267,269,325,385,428,409,357,299,246,195,147,97,47,66,82,67,46,65,92,124,161,203,251,305,363,377,318,263,183,102,135,149,155,160,164,167,169,213,262,316,375,422,417,360,295,235,173,99,130,158,153,146,131,98,129,168,212,261,315,374,367,308,254,206,163,107,50,71,84,88,91,93,125,162,204,252,306,365,415,407,346,273,175,218,258,253,248,241,234,219,174,217,268,324,384,354,296,243,196,154,118,87,55,18,29,39,41,61,86,116,152,193,240,293,351,405,395,275,330,381,376,371,366,359,352,345,331,274,329,391,338,280,227,180,139,104,75,52,33,20,4,8,13,23,37,56,79,108,143,184,231,284,342,337,397,403,408,413,418,421,424,427,430,432,396,398,340,282,229,182,141,106,77,54,35,22,7,6,12,21,34,53,76,105,140,181,228,281,339,341,225,276,290,297,304,309,314,319,323,326,328,389,431,404,350,292,239,192,151,112,68,28,43,44,27,42,63,89,120,156,198,245,298,356,382,322,230,137,176,190,197,202,207,211,214,216,266,321,380,425,414,364,302,242,188,132,70,95,117,111,96,69,94,127,165,208,256,310,369,372,313,259,210,142,73,100,114,119,123,126,128,166,209,257,311,370,419,412,353,288,220,134,171,205,200,194,187,172,133,170,215,265,320,379,361,303,249,201,159,122,78,31,48,59,62,64,90,121,157,199,247,300,358,410,402,332,222,271,317,312,307,301,294,287,272,221,270,327,388,347,289,236,189,148,113,83,58,36,10,16,24,38,57,81,110,145,186,233,286,344,400,334,393,429,426,423,420,416,411,406,401,394,333,336,277,224,177,136,101,72,49,30,17,9,3)
Conjugacy classes & character table
390 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12990, 10);
Finite Group Databasebeta