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D₃×D₆₀₁⋊C₅ #49115147

• 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 604 points:

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

Conjugacy classes & character table

210 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36060, 24);