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D₃×D₄₃₁⋊C₅ #39905503

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

Splittings

Subgroups

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 434 points:

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

Conjugacy classes & character table

159 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25860, 14);