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Aliases
Splittings
Subgroups
20 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 608 points:
(1,2)(3,4,5,6,7)(8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608);(4,7)(5,6)(9,608)(10,607)(11,606)(12,605)(13,604)(14,603)(15,602)(16,601)(17,600)(18,599)(19,598)(20,597)(21,596)(22,595)(23,594)(24,593)(25,592)(26,591)(27,590)(28,589)(29,588)(30,587)(31,586)(32,585)(33,584)(34,583)(35,582)(36,581)(37,580)(38,579)(39,578)(40,577)(41,576)(42,575)(43,574)(44,573)(45,572)(46,571)(47,570)(48,569)(49,568)(50,567)(51,566)(52,565)(53,564)(54,563)(55,562)(56,561)(57,560)(58,559)(59,558)(60,557)(61,556)(62,555)(63,554)(64,553)(65,552)(66,551)(67,550)(68,549)(69,548)(70,547)(71,546)(72,545)(73,544)(74,543)(75,542)(76,541)(77,540)(78,539)(79,538)(80,537)(81,536)(82,535)(83,534)(84,533)(85,532)(86,531)(87,530)(88,529)(89,528)(90,527)(91,526)(92,525)(93,524)(94,523)(95,522)(96,521)(97,520)(98,519)(99,518)(100,517)(101,516)(102,515)(103,514)(104,513)(105,512)(106,511)(107,510)(108,509)(109,508)(110,507)(111,506)(112,505)(113,504)(114,503)(115,502)(116,501)(117,500)(118,499)(119,498)(120,497)(121,496)(122,495)(123,494)(124,493)(125,492)(126,491)(127,490)(128,489)(129,488)(130,487)(131,486)(132,485)(133,484)(134,483)(135,482)(136,481)(137,480)(138,479)(139,478)(140,477)(141,476)(142,475)(143,474)(144,473)(145,472)(146,471)(147,470)(148,469)(149,468)(150,467)(151,466)(152,465)(153,464)(154,463)(155,462)(156,461)(157,460)(158,459)(159,458)(160,457)(161,456)(162,455)(163,454)(164,453)(165,452)(166,451)(167,450)(168,449)(169,448)(170,447)(171,446)(172,445)(173,444)(174,443)(175,442)(176,441)(177,440)(178,439)(179,438)(180,437)(181,436)(182,435)(183,434)(184,433)(185,432)(186,431)(187,430)(188,429)(189,428)(190,427)(191,426)(192,425)(193,424)(194,423)(195,422)(196,421)(197,420)(198,419)(199,418)(200,417)(201,416)(202,415)(203,414)(204,413)(205,412)(206,411)(207,410)(208,409)(209,408)(210,407)(211,406)(212,405)(213,404)(214,403)(215,402)(216,401)(217,400)(218,399)(219,398)(220,397)(221,396)(222,395)(223,394)(224,393)(225,392)(226,391)(227,390)(228,389)(229,388)(230,387)(231,386)(232,385)(233,384)(234,383)(235,382)(236,381)(237,380)(238,379)(239,378)(240,377)(241,376)(242,375)(243,374)(244,373)(245,372)(246,371)(247,370)(248,369)(249,368)(250,367)(251,366)(252,365)(253,364)(254,363)(255,362)(256,361)(257,360)(258,359)(259,358)(260,357)(261,356)(262,355)(263,354)(264,353)(265,352)(266,351)(267,350)(268,349)(269,348)(270,347)(271,346)(272,345)(273,344)(274,343)(275,342)(276,341)(277,340)(278,339)(279,338)(280,337)(281,336)(282,335)(283,334)(284,333)(285,332)(286,331)(287,330)(288,329)(289,328)(290,327)(291,326)(292,325)(293,324)(294,323)(295,322)(296,321)(297,320)(298,319)(299,318)(300,317)(301,316)(302,315)(303,314)(304,313)(305,312)(306,311)(307,310)(308,309)
Conjugacy classes & character table
3008 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12020, 18);
Finite Group Databasebeta