Finite Group Databasebeta

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C₂×(D₆₀₁⋊C₃)⋊C₅ #49115144

• metacyclic
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 603 points:

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

Conjugacy classes & character table

100 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36060, 21);