Finite Group Databasebeta

?

← Prev (#27163182) Next (#27163184) →

#27163183

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

62 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 413 points:

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

Polycyclic presentation:

2^5,397|a^2=d,d^2=e,f^a=f^334,c^b=ce,f^d=f^396

Conjugacy classes & character table

515 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12704, 233);