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#27189807

• metacyclic
• supersolvable
• metabelian
• solvable
• monomial

Aliases

No aliases for this group.

Splittings

Subgroups

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 441 points:

(2,3,4,7,5,8,10,16)(6,12,13,28,14,29,31,63)(9,19,20,45,21,46,48,37)(11,24,25,56,26,57,23,54)(15,33,34,75,35,76,78,141)(17,38,39,83,40,18,42,43)(22,50,51,103,52,104,106,121)(27,59,60,116,61,36,70,80)(30,66,67,128,68,129,131,82)(32,71,72,134,73,135,55,110)(41,85,86,163,69,65,125,126)(44,89,90,64,91,122,169,123)(47,94,95,176,96,177,98,109)(49,99,100,184,101,113,87,165)(53,93,108,88,58,114,115,167)(62,117,118,208,119,174,147,252)(74,137,138,237,139,238,133,229)(77,143,144,239,145,247,249,157)(79,148,149,254,150,255,111,200)(81,153,154,102,155,185,264,186)(84,159,160,112,161,202,158,203)(92,171,172,142,173,244,283,245)(97,179,180,261,181,201,192,152)(105,188,189,236,190,294,225,198)(107,193,194,297,195,232,166,278)(120,209,210,162,211,271,207,272)(124,214,215,319,216,127,218,219)(130,221,222,217,223,321,183,199)(132,226,187,293,227,205,168,280)(136,233,234,281,235,175,285,170)(140,240,241,316,242,336,253,352)(146,213,251,317,204,305,306,274)(151,257,258,358,259,359,230,320)(156,265,266,228,267,301,367,329)(164,262,191,231,275,333,269,332)(178,288,289,354,279,287,197,277)(182,290,291,304,270,373,206,308)(196,298,299,390,300,335,263,364)(212,313,314,309,315,328,366,382)(220,322,323,246,312,342,276,343)(224,325,326,344,327,387,296,331)(243,338,339,318,340,372,310,393)(248,345,346,392,347,363,292,303)(250,337,349,402,350,307,282,381)(256,355,356,384,357,286,334,284)(260,360,361,403,362,405,353,341)(268,369,370,351,371,389,398,348)(273,374,375,311,376,377,383,394)(295,368,388,404,365,399,302,379)(324,400,330,401,391,386,385,380)(378,406,397,396,407,395,409,408)(410,411,412,416,413,417,420,426,414,418,421,427,423,429,432,436,415,419,422,428,424,430,433,437,425,431,434,438,435,439,440,441);(1,2,6,15,36,81,156,268,372,219,189,67,132,228,330,234,334,361,241,118,34,79,151,260,363,401,293,117,173,91,38,3,9,22,53,57,113,205,307,336,266,368,221,324,388,289,115,206,309,349,244,143,248,348,350,249,281,169,209,312,214,85,12,30,69,40,16,37,82,157,238,335,390,325,346,222,95,20,49,102,187,122,213,318,397,375,172,284,251,313,327,223,129,33,77,146,203,54,109,198,235,135,232,264,366,405,400,288,94,178,194,100,39,84,162,273,377,381,403,340,242,139,73,31,70,133,230,332,110,199,216,123,63,121,163,274,359,404,297,179,149,72,25,4,11,27,62,120,212,316,396,407,323,275,125,153,263,365,294,200,303,339,210,80,152,262,357,255,354,184,290,355,233,114,19,47,97,182,202,304,208,311,395,370,358,218,265,300,195,106,192,296,389,342,229,331,343,245,141,167,83,158,269,190,104,50,105,191,160,43,88,75,142,246,344,237,322,369,326,180,51,107,196,301,215,320,398,406,394,252,308,159,270,181,96,46,93,175,286,373,165,277,148,256,333,261,116,207,310,392,254,188,295,299,185,86,164,276,378,408,352,315,211,119,61,26,10,23,55,111,201,278,379,257,317,126,103,28,64,124,217,134,231,258,138,60,13,32,74,140,243,341,402,374,376,272,161,42,87,166,279,177,287,386,360,314,154,193,71,136,236,176,56,112,204,145,76,66,130,224,328,306,384,283,383,409,393,305,89,168,186,101,48,98,183,292,387,364,298,137,239,128,45,7,17,41,68,29,65,127,220,271,90,170,144,250,351,347,247,171,282,382,291,108,197,302,391,321,399,367,240,337,226,99,24,58,52,21,8,18,44,92,174,280,380,345,362,259,150,78,147,253,353,356,285,385,329,227,131,225,319,338,371,267,155,59,35,14,5)

Polycyclic presentation:

2^5,409|a^2=b,b^2=c,c^2=d,d^2=e,f^a=f^31,f^b=f^143,f^c=f^408

Conjugacy classes & character table

236 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13088, 236);