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C₂²⋊#16861332 #30654271

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

50 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 521 points:

(1,2,5,10,19,32,49,70,95,124,157,194,235,280,329,299,254,213,176,143,114,89,66,87,112,141,174,211,252,297,342,378,408,434,456,474,479,464,445,422,395,362,319,274,231,272,317,360,331,278,326,371,402,429,452,471,486,497,504,495,481,463,441,415,384,345,298,249,204,163,126,93,121,152,185,222,263,308,351,386,413,400,365,318,269,224,183,146,113,84,59,38,21,8,16,27,40,57,78,103,132,165,202,243,288,337,291,246,205,168,135,106,81,60,43,28,41,58,79,104,133,166,203,244,289,338,376,406,432,439,416,389,354,311,266,225,188,153,186,223,264,309,352,387,414,437,459,477,491,501,507,509,505,498,487,472,453,430,403,372,341,290,241,196,155,191,230,271,316,359,393,420,443,462,450,424,394,357,310,261,216,175,138,105,76,51,30,46,65,86,111,140,173,210,251,296,332,283,238,197,160,127,98,73,52,35,22,13,6,11,20,33,50,71,96,125,158,195,236,281,330,374,381,346,303,258,217,180,147,118,91,116,145,178,215,256,301,344,379,409,435,457,475,489,493,482,467,448,425,398,366,323,276,321,364,335,282,233,277,324,367,399,426,449,468,483,494,484,466,444,418,388,349,302,253,208,167,130,97,68,92,119,148,181,218,259,304,347,382,369,322,273,228,187,150,117,88,63,42,25,12,3,7,14,23,36,53,74,99,128,161,198,239,284,333,295,250,209,172,139,110,85,64,45,62,83,108,137,170,207,248,293,340,377,407,433,455,461,442,419,392,358,315,270,229,190,227,268,313,356,327,373,404,431,454,473,488,499,506,508,502,492,478,460,438,411,380,343,294,245,200,159,122,154,189,226,267,312,355,390,417,440,427,397,361,314,265,220,179,142,109,80,55,34,17,29,44,61,82,107,136,169,206,247,292,336,287,242,201,164,131,102,77,56,39,26,15,24,37,54,75,100,129,162,199,240,285,334,375,405,412,385,350,307,262,221,184,151,120,149,182,219,260,305,348,383,410,436,458,476,490,500,503,496,485,470,451,428,401,370,325,368,339,286,237,192,232,275,320,363,396,423,446,465,480,469,447,421,391,353,306,257,212,171,134,101,72,47,67,90,115,144,177,214,255,300,328,279,234,193,156,123,94,69,48,31,18,9,4)(511,513);(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)(235,278,279,325)(239,282,283,321)(243,286,287,317)(247,290,291,313)(251,294,295,309)(255,298,299,305)(259,302,303,301)(263,306,307,297)(267,310,311,293)(271,314,315,289)(275,318,319,285)(277,322,323,281)(280,327,328,372)(284,331,332,368)(288,335,336,364)(292,339,337,360)(296,341,333,356)(300,343,329,352)(304,345,346,348)(308,349,350,344)(312,353,354,342)(316,357,358,340)(320,361,362,338)(324,365,366,334)(326,369,370,330)(347,380,381,387)(351,384,385,383)(355,388,389,379)(359,391,392,378)(363,394,395,377)(367,397,398,376)(371,400,401,375)(373,382,403,374)(386,411,412,414)(390,415,416,410)(393,418,419,409)(396,421,422,408)(399,424,425,407)(402,427,428,406)(404,413,430,405)(417,438,439,437)(420,441,442,436)(423,444,445,435)(426,447,448,434)(429,450,451,433)(431,440,453,432)(443,460,461,459)(446,463,464,458)(449,466,467,457)(452,469,470,456)(454,462,472,455)(465,478,479,477)(468,481,482,476)(471,484,485,475)(473,480,487,474)(483,492,493,491)(486,495,496,490)(488,494,498,489)(497,502,503,501)(499,504,505,500)(506,508,509,507)(510,511)(512,513)(514,515,516,518,517,519,520,521)

Polycyclic presentation:

2^5,509|a^2=d,d^2=e,b^a=bc,f^a=f^301,f^d=f^508

Conjugacy classes & character table

1036 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16288, 202);