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C₁₁⋊(D₄₀₉⋊C₃) #41008815

• metacyclic
• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

Splittings

Subgroups

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

Polycyclic presentation:

2,3,11,409|c^a=c^10,d^a=d^408,d^b=d^355

Conjugacy classes & character table

769 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26994, 12);