Finite Group Databasebeta

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C₇×#15691117 #36346249

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

254 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 632 points:

(1,2,6,17,42,4,8,19,44,89,14,25,50,95,161,38,63,108,174,255,83,128,194,275,360,5,9,20,45,90,15,26,51,96,162,39,64,109,175,256,84,129,195,276,361,153,219,300,385,460,16,27,52,97,163,40,65,110,176,257,85,130,196,277,362,154,220,301,386,461,242,323,408,483,538,41,66,111,177,258,86,131,197,278,363,155,221,302,387,462,243,324,409,484,539,342,427,502,557,590,87,132,198,279,364,156,222,303,388,463,244,325,410,485,540,343,428,503,558,591,439,514,569,602,617)(3,7,18,43,88,12,23,48,93,159,35,60,105,171,252,80,125,191,272,357,150,216,297,382,457,13,24,49,94,160,36,61,106,172,253,81,126,192,273,358,151,217,298,383,458,240,321,406,481,536,37,62,107,173,254,82,127,193,274,359,152,218,299,384,459,241,322,407,482,537,341,426,501,556,589,33,58,103,169,250,78,123,189,270,355,148,214,295,380,455,238,319,404,479,534,340,425,500,555,588,11,22,47,92,158,34,59,104,170,251,79,124,190,271,356,149,215,296,381,456,239,320,405,480,535)(10,21,46,91,157,30,55,100,166,247,73,118,184,265,350,142,208,289,374,449,232,313,398,473,528,31,56,101,167,248,74,119,185,266,351,143,209,290,375,450,233,314,399,474,529,335,420,495,550,583,75,120,186,267,352,144,210,291,376,451,234,315,400,475,530,336,421,496,551,584,436,511,566,599,614,29,54,99,165,246,72,117,183,264,349,141,207,288,373,448,231,312,397,472,527,334,419,494,549,582,32,57,102,168,249,77,122,188,269,354,147,213,294,379,454,237,318,403,478,533,339,424,499,554,587)(28,53,98,164,245,69,114,180,261,346,137,203,284,369,444,227,308,393,468,523,330,415,490,545,578,70,115,181,262,347,138,204,285,370,445,228,309,394,469,524,331,416,491,546,579,433,508,563,596,611,68,113,179,260,345,136,202,283,368,443,226,307,392,467,522,329,414,489,544,577,432,507,562,595,610,71,116,182,263,348,140,206,287,372,447,230,311,396,471,526,333,418,493,548,581,435,510,565,598,613,76,121,187,268,353,146,212,293,378,453,236,317,402,477,532,338,423,498,553,586,438,513,568,601,616)(67,112,178,259,344,134,200,281,366,441,224,305,390,465,520,327,412,487,542,575,430,505,560,593,608,133,199,280,365,440,223,304,389,464,519,326,411,486,541,574,429,504,559,592,607,515,570,603,618,622,135,201,282,367,442,225,306,391,466,521,328,413,488,543,576,431,506,561,594,609,516,571,604,619,623,139,205,286,371,446,229,310,395,470,525,332,417,492,547,580,434,509,564,597,612,517,572,605,620,624,145,211,292,377,452,235,316,401,476,531,337,422,497,552,585,437,512,567,600,615,518,573,606,621,625)(626,627,628,629,630,631,632);(1,3,10,28,67)(2,7,21,53,112)(4,12,30,69,134)(5,13,31,70,133)(6,18,46,98,178)(8,23,55,114,200)(9,24,56,115,199)(11,32,76,145,87)(14,35,73,137,224)(15,36,74,138,223)(16,37,75,68,135)(17,43,91,164,259)(19,48,100,180,281)(20,49,101,181,280)(22,57,121,211,132)(25,60,118,203,305)(26,61,119,204,304)(27,62,120,113,201)(29,71,139,41,33)(34,77,146,235,156)(38,80,142,227,327)(39,81,143,228,326)(40,82,144,136,225)(42,88,157,245,344)(44,93,166,261,366)(45,94,167,262,365)(47,102,187,292,198)(50,105,184,284,390)(51,106,185,285,389)(52,107,186,179,282)(54,116,205,66,58)(59,122,212,316,222)(63,125,208,308,412)(64,126,209,309,411)(65,127,210,202,306)(72,140,229,86,78)(79,147,236,337,244)(83,150,232,330,430)(84,151,233,331,429)(85,152,234,226,328)(89,159,247,346,441)(90,160,248,347,440)(92,168,268,377,279)(95,171,265,369,465)(96,172,266,370,464)(97,173,267,260,367)(99,182,286,111,103)(104,188,293,401,303)(108,191,289,393,487)(109,192,290,394,486)(110,193,291,283,391)(117,206,310,131,123)(124,213,317,422,325)(128,216,313,415,505)(129,217,314,416,504)(130,218,315,307,413)(141,230,332,155,148)(149,237,338,437,343)(153,240,335,433,515)(154,241,336,329,431)(158,249,353,452,364)(161,252,350,444,520)(162,253,351,445,519)(163,254,352,345,442)(165,263,371,177,169)(170,269,378,476,388)(174,272,374,468,542)(175,273,375,469,541)(176,274,376,368,466)(183,287,395,197,189)(190,294,402,497,410)(194,297,398,490,560)(195,298,399,491,559)(196,299,400,392,488)(207,311,417,221,214)(215,318,423,512,428)(219,321,420,508,570)(220,322,421,414,506)(231,333,434,243,238)(239,339,438,518,439)(242,341,436,432,516)(246,348,446,258,250)(251,354,453,531,463)(255,357,449,523,575)(256,358,450,524,574)(257,359,451,443,521)(264,372,470,278,270)(271,379,477,552,485)(275,382,473,545,593)(276,383,474,546,592)(277,384,475,467,543)(288,396,492,302,295)(296,403,498,567,503)(300,406,495,563,603)(301,407,496,489,561)(312,418,509,324,319)(320,424,513,573,514)(323,426,511,507,571)(334,435,517,342,340)(349,447,525,363,355)(356,454,532,585,540)(360,457,528,578,608)(361,458,529,579,607)(362,459,530,522,576)(373,471,547,387,380)(381,478,553,600,558)(385,481,550,596,618)(386,482,551,544,594)(397,493,564,409,404)(405,499,568,606,569)(408,501,566,562,604)(419,510,572,427,425)(448,526,580,462,455)(456,533,586,615,591)(460,536,583,611,622)(461,537,584,577,609)(472,548,597,484,479)(480,554,601,621,602)(483,556,599,595,619)(494,565,605,502,500)(527,581,612,539,534)(535,587,616,625,617)(538,589,614,610,623)(549,598,620,557,555)(582,613,624,590,588);(3,11,33,37,13)(7,22,58,62,24)(10,29,31,32,75)(12,34,78,82,36)(18,47,103,107,49)(21,54,56,57,120)(23,59,123,127,61)(28,68,76,70,71)(30,72,74,77,144)(35,79,148,152,81)(43,92,169,173,94)(46,99,101,102,186)(48,104,189,193,106)(53,113,121,115,116)(55,117,119,122,210)(60,124,214,218,126)(67,133,135,139,145)(69,136,146,138,140)(73,141,143,147,234)(80,149,238,241,151)(88,158,250,254,160)(91,165,167,168,267)(93,170,270,274,172)(98,179,187,181,182)(100,183,185,188,291)(105,190,295,299,192)(112,199,201,205,211)(114,202,212,204,206)(118,207,209,213,315)(125,215,319,322,217)(134,223,225,229,235)(137,226,236,228,230)(142,231,233,237,336)(150,239,340,341,240)(157,246,248,249,352)(159,251,355,359,253)(164,260,268,262,263)(166,264,266,269,376)(171,271,380,384,273)(178,280,282,286,292)(180,283,293,285,287)(184,288,290,294,400)(191,296,404,407,298)(200,304,306,310,316)(203,307,317,309,311)(208,312,314,318,421)(216,320,425,426,321)(224,326,328,332,337)(227,329,338,331,333)(232,334,335,339,436)(245,345,353,347,348)(247,349,351,354,451)(252,356,455,459,358)(259,365,367,371,377)(261,368,378,370,372)(265,373,375,379,475)(272,381,479,482,383)(281,389,391,395,401)(284,392,402,394,396)(289,397,399,403,496)(297,405,500,501,406)(305,411,413,417,422)(308,414,423,416,418)(313,419,420,424,511)(327,429,431,434,437)(330,432,438,433,435)(344,440,442,446,452)(346,443,453,445,447)(350,448,450,454,530)(357,456,534,537,458)(366,464,466,470,476)(369,467,477,469,471)(374,472,474,478,551)(382,480,555,556,481)(390,486,488,492,497)(393,489,498,491,493)(398,494,495,499,566)(412,504,506,509,512)(415,507,513,508,510)(430,515,516,517,518)(441,519,521,525,531)(444,522,532,524,526)(449,527,529,533,584)(457,535,588,589,536)(465,541,543,547,552)(468,544,553,546,548)(473,549,550,554,599)(487,559,561,564,567)(490,562,568,563,565)(505,570,571,572,573)(520,574,576,580,585)(523,577,586,579,581)(528,582,583,587,614)(542,592,594,597,600)(545,595,601,596,598)(560,603,604,605,606)(575,607,609,612,615)(578,610,616,611,613)(593,618,619,620,621)(608,622,623,624,625)

Conjugacy classes & character table

5075 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21875, 60);