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D₃×D₄₂₁⋊C₇ #47977906

• 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 424 points:

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

Conjugacy classes & character table

132 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35364, 36);