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C₁₁⋊(D₃₉₇⋊C₃) #39910666

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

Polycyclic presentation:

2,3,11,397|c^a=c^10,d^a=d^396,d^b=d^362

Conjugacy classes & character table

747 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26202, 17);