Finite Group Databasebeta

?

← Prev (#27162200) Next (#27162202) →

(C₂₉²⋊C₃)⋊C₅ #27162201

• metabelian
• solvable
• monolithic
• monomial
• stem
• Frobenius

Aliases

Splittings

Subgroups

10 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 435 points:

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

Polycyclic presentation:

3,5,29^2|c^a=c^7d^23,d^a=c^24d^21,c^b=c^6d^3,d^b=c^17d^28

Conjugacy classes & character table

71 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12615, 3);