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(C₆₃₁⋊C₃)⋊C₇ #27210393

• metacyclic
• supersolvable
• metabelian
• solvable
• monolithic
• monomial
• stem
• Frobenius

Aliases

Splittings

Subgroups

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 631 points:

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

Polycyclic presentation:

3,7,631|c^a=c^587,c^b=c^269

Conjugacy classes & character table

51 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13251, 1);