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D619 #11927792
Aliases
Splittings
Subgroups
4 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 619 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619);(2,619)(3,618)(4,617)(5,616)(6,615)(7,614)(8,613)(9,612)(10,611)(11,610)(12,609)(13,608)(14,607)(15,606)(16,605)(17,604)(18,603)(19,602)(20,601)(21,600)(22,599)(23,598)(24,597)(25,596)(26,595)(27,594)(28,593)(29,592)(30,591)(31,590)(32,589)(33,588)(34,587)(35,586)(36,585)(37,584)(38,583)(39,582)(40,581)(41,580)(42,579)(43,578)(44,577)(45,576)(46,575)(47,574)(48,573)(49,572)(50,571)(51,570)(52,569)(53,568)(54,567)(55,566)(56,565)(57,564)(58,563)(59,562)(60,561)(61,560)(62,559)(63,558)(64,557)(65,556)(66,555)(67,554)(68,553)(69,552)(70,551)(71,550)(72,549)(73,548)(74,547)(75,546)(76,545)(77,544)(78,543)(79,542)(80,541)(81,540)(82,539)(83,538)(84,537)(85,536)(86,535)(87,534)(88,533)(89,532)(90,531)(91,530)(92,529)(93,528)(94,527)(95,526)(96,525)(97,524)(98,523)(99,522)(100,521)(101,520)(102,519)(103,518)(104,517)(105,516)(106,515)(107,514)(108,513)(109,512)(110,511)(111,510)(112,509)(113,508)(114,507)(115,506)(116,505)(117,504)(118,503)(119,502)(120,501)(121,500)(122,499)(123,498)(124,497)(125,496)(126,495)(127,494)(128,493)(129,492)(130,491)(131,490)(132,489)(133,488)(134,487)(135,486)(136,485)(137,484)(138,483)(139,482)(140,481)(141,480)(142,479)(143,478)(144,477)(145,476)(146,475)(147,474)(148,473)(149,472)(150,471)(151,470)(152,469)(153,468)(154,467)(155,466)(156,465)(157,464)(158,463)(159,462)(160,461)(161,460)(162,459)(163,458)(164,457)(165,456)(166,455)(167,454)(168,453)(169,452)(170,451)(171,450)(172,449)(173,448)(174,447)(175,446)(176,445)(177,444)(178,443)(179,442)(180,441)(181,440)(182,439)(183,438)(184,437)(185,436)(186,435)(187,434)(188,433)(189,432)(190,431)(191,430)(192,429)(193,428)(194,427)(195,426)(196,425)(197,424)(198,423)(199,422)(200,421)(201,420)(202,419)(203,418)(204,417)(205,416)(206,415)(207,414)(208,413)(209,412)(210,411)(211,410)(212,409)(213,408)(214,407)(215,406)(216,405)(217,404)(218,403)(219,402)(220,401)(221,400)(222,399)(223,398)(224,397)(225,396)(226,395)(227,394)(228,393)(229,392)(230,391)(231,390)(232,389)(233,388)(234,387)(235,386)(236,385)(237,384)(238,383)(239,382)(240,381)(241,380)(242,379)(243,378)(244,377)(245,376)(246,375)(247,374)(248,373)(249,372)(250,371)(251,370)(252,369)(253,368)(254,367)(255,366)(256,365)(257,364)(258,363)(259,362)(260,361)(261,360)(262,359)(263,358)(264,357)(265,356)(266,355)(267,354)(268,353)(269,352)(270,351)(271,350)(272,349)(273,348)(274,347)(275,346)(276,345)(277,344)(278,343)(279,342)(280,341)(281,340)(282,339)(283,338)(284,337)(285,336)(286,335)(287,334)(288,333)(289,332)(290,331)(291,330)(292,329)(293,328)(294,327)(295,326)(296,325)(297,324)(298,323)(299,322)(300,321)(301,320)(302,319)(303,318)(304,317)(305,316)(306,315)(307,314)(308,313)(309,312)(310,311)
Polycyclic presentation:
2,619|b^a=b^618
Conjugacy classes & character table
311 conjugacy classes — view the full character table.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1238, 1);
Finite Group Databasebeta