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C₉⋊(D₄₀₁⋊C₅) #49115397

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

Aliases

Splittings

Subgroups

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 410 points:

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

Polycyclic presentation:

2,3,5,401,3|b^3=e^2,b^a=b^2e,d^a=d^400,e^a=e^2,d^c=d^72

Conjugacy classes & character table

390 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36090, 12);