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#27189778

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

38 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 425 points:

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

Polycyclic presentation:

2^5,409|a^2=d,b^2=e,d^2=e,b^a=bc,c^a=ce,f^a=f^143,d^b=de,f^d=f^408

Conjugacy classes & character table

827 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13088, 207);