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#27165836

• 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 433 points:

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

Polycyclic presentation:

2^5,401|a^2=b,b^2=c,c^2=d,d^2=e,f^a=f^268,f^b=f^45,f^c=f^20,f^d=f^400

Conjugacy classes & character table

82 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12832, 245);