Finite Group Databasebeta

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D₃×D₅₂₁⋊C₅ #44530450

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

Splittings

Subgroups

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 524 points:

(1,2,3)(5,9,10,28,33,6,7,15,17,55)(8,22,23,85,90,12,13,44,46,152)(11,38,39,40,66,19,20,74,76,77)(14,51,52,92,185,25,26,47,101,167)(16,60,61,206,191,30,31,116,118,106)(18,68,69,27,67,35,36,70,34,54)(21,79,80,216,163,41,42,142,144,273)(24,94,95,288,128,48,49,172,174,223)(29,110,111,56,193,57,58,198,107,108)(32,123,124,345,347,63,64,218,219,254)(37,130,131,164,165,71,72,227,91,275)(43,149,150,349,313,82,83,220,250,426)(45,157,158,380,138,87,88,264,265,192)(50,179,180,308,274,97,98,302,304,399)(53,187,188,431,224,102,103,317,319,338)(59,203,204,153,379,113,114,330,255,256)(62,214,215,78,237,120,121,276,139,140)(65,84,222,211,212,126,127,145,119,278)(73,232,233,314,315,133,134,331,186,428)(75,183,96,297,298,137,100,176,177,194)(81,246,200,201,136,146,147,112,293,235)(86,258,259,109,323,154,155,384,195,196)(89,269,270,495,477,160,161,395,396,378)(93,282,283,197,277,169,170,404,166,325)(99,221,309,424,427,125,182,351,410,364)(104,217,321,459,400,122,189,343,342,480)(105,117,229,279,280,115,190,208,168,210)(129,230,135,294,295,225,132,207,175,199)(141,365,266,267,429,238,239,159,374,393)(143,368,352,481,244,242,243,472,473,322)(148,372,311,181,402,247,248,184,306,307)(151,375,376,387,236,251,252,260,436,362)(156,389,390,257,482,261,262,491,381,382)(162,240,398,299,300,231,272,305,178,403)(171,407,408,383,430,285,286,492,316,484)(173,414,415,417,441,290,291,506,507,324)(202,444,366,344,485,327,328,241,462,463)(205,449,411,412,371,332,333,289,496,476)(209,453,454,465,466,335,336,432,348,401)(213,455,337,447,486,339,340,355,385,461)(226,360,287,437,438,353,234,346,320,386)(228,452,458,483,292,356,357,392,471,326)(245,359,406,354,363,263,370,284,281,296)(249,397,442,303,513,271,373,369,422,423)(253,394,479,509,497,268,377,416,460,524)(301,511,334,519,512,418,419,450,451,421)(310,440,508,498,312,420,425,464,516,361)(318,515,488,489,367,433,434,388,467,443)(329,518,468,469,474,445,446,350,487,358)(341,520,435,499,500,456,457,448,405,510)(391,490,503,504,478,493,494,413,470,523)(409,514,439,521,475,501,502,505,517,522);(2,3)(4,5,8,14,27,28,56,109,197,164,85,153,257,383,314,92,168,281,353,225,36,70,126,63,30,7,11,21,43,84,58,112,202,329,447,155,260,388,490,499,170,284,404,474,356,72,132,231,160,87,13,24,50,99,123,114,205,334,452,453,262,391,408,491,515,286,409,500,479,414,134,234,361,311,183,26,53,104,120,60,117,209,337,131,229,359,475,502,454,188,320,439,503,411,95,175,296,362,235,39,54,105,113,57,10,18,37,73,135,61,119,213,341,458,158,219,348,467,507,177,118,210,338,223,77,55,106,192,137,20,40,78,141,240,121,216,342,460,519,267,349,319,436,516,300,212,185,313,427,140,108,194,322,242,42,81,148,249,269,217,344,464,506,449,394,469,438,384,485,419,340,315,429,513,239,196,324,442,368,83,151,253,266,157,187,318,435,233,330,375,478,517,486,321,440,457,430,512,180,305,325,443,366,80,145,245,261,154,23,47,93,171,287,124,220,350,470,518,270,351,471,482,524,307,215,275,401,476,147,111,199,326,290,49,96,178,301,420,221,352,396,496,444,397,473,265,379,480,399,273,152,254,378,248,201,288,410,422,98,181,308,304,306,179,303,424,174,293,372,477,347,90,163,274,400,256,380,481,373,328,412,495,472,182,310,418,299,176,94,173,292,295,198,246,371,466,165,276,402,497,382,483,309,395,446,504,468,150,218,346,285,169,52,44,86,156,263,222,142,241,367,277,398,302,421,484,520,425,343,461,521,523,252,204,331,448,433,103,88,159,268,251,149,243,369,441,323,365,423,393,428,455,511,463,259,386,487,377,333,415,508,462,189,161,271,247,146,79,143,244,298,193,237,364,426,167,278,403,498,387,431,250,374,451,509,459,144,214,272,238,139,76,38,75,138,191,33,66,128,224,280,206,297,417,489,465,345,264,392,456,339,211,116,207,133,71,35,15,29,59,115,67,74,136,236,363,294,172,289,413,505,437,317,432,514,522,370,208,227,355,335,190,31,62,122,102,51,100,184,312,360,232,291,416,510,501,407,434,390,492,493,389,336,357,450,332,203,64,125,97,48,22,45,89,162,230,130,228,358,283,406,282,405,494,488,376,258,385,445,327,200,110,127,82,41,19,9,16,32,65,69,68,129,226,354,279,101,186,316,381,255,46,91,166,195,107,17,34,25,12,6)

Conjugacy classes & character table

186 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31260, 16);