← Prev (#72212488) Next (#72212490) →
D7044 #72212489
Aliases
Splittings
Subgroups
32 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 594 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);(2,4)(6,7)(9,594)(10,593)(11,592)(12,591)(13,590)(14,589)(15,588)(16,587)(17,586)(18,585)(19,584)(20,583)(21,582)(22,581)(23,580)(24,579)(25,578)(26,577)(27,576)(28,575)(29,574)(30,573)(31,572)(32,571)(33,570)(34,569)(35,568)(36,567)(37,566)(38,565)(39,564)(40,563)(41,562)(42,561)(43,560)(44,559)(45,558)(46,557)(47,556)(48,555)(49,554)(50,553)(51,552)(52,551)(53,550)(54,549)(55,548)(56,547)(57,546)(58,545)(59,544)(60,543)(61,542)(62,541)(63,540)(64,539)(65,538)(66,537)(67,536)(68,535)(69,534)(70,533)(71,532)(72,531)(73,530)(74,529)(75,528)(76,527)(77,526)(78,525)(79,524)(80,523)(81,522)(82,521)(83,520)(84,519)(85,518)(86,517)(87,516)(88,515)(89,514)(90,513)(91,512)(92,511)(93,510)(94,509)(95,508)(96,507)(97,506)(98,505)(99,504)(100,503)(101,502)(102,501)(103,500)(104,499)(105,498)(106,497)(107,496)(108,495)(109,494)(110,493)(111,492)(112,491)(113,490)(114,489)(115,488)(116,487)(117,486)(118,485)(119,484)(120,483)(121,482)(122,481)(123,480)(124,479)(125,478)(126,477)(127,476)(128,475)(129,474)(130,473)(131,472)(132,471)(133,470)(134,469)(135,468)(136,467)(137,466)(138,465)(139,464)(140,463)(141,462)(142,461)(143,460)(144,459)(145,458)(146,457)(147,456)(148,455)(149,454)(150,453)(151,452)(152,451)(153,450)(154,449)(155,448)(156,447)(157,446)(158,445)(159,444)(160,443)(161,442)(162,441)(163,440)(164,439)(165,438)(166,437)(167,436)(168,435)(169,434)(170,433)(171,432)(172,431)(173,430)(174,429)(175,428)(176,427)(177,426)(178,425)(179,424)(180,423)(181,422)(182,421)(183,420)(184,419)(185,418)(186,417)(187,416)(188,415)(189,414)(190,413)(191,412)(192,411)(193,410)(194,409)(195,408)(196,407)(197,406)(198,405)(199,404)(200,403)(201,402)(202,401)(203,400)(204,399)(205,398)(206,397)(207,396)(208,395)(209,394)(210,393)(211,392)(212,391)(213,390)(214,389)(215,388)(216,387)(217,386)(218,385)(219,384)(220,383)(221,382)(222,381)(223,380)(224,379)(225,378)(226,377)(227,376)(228,375)(229,374)(230,373)(231,372)(232,371)(233,370)(234,369)(235,368)(236,367)(237,366)(238,365)(239,364)(240,363)(241,362)(242,361)(243,360)(244,359)(245,358)(246,357)(247,356)(248,355)(249,354)(250,353)(251,352)(252,351)(253,350)(254,349)(255,348)(256,347)(257,346)(258,345)(259,344)(260,343)(261,342)(262,341)(263,340)(264,339)(265,338)(266,337)(267,336)(268,335)(269,334)(270,333)(271,332)(272,331)(273,330)(274,329)(275,328)(276,327)(277,326)(278,325)(279,324)(280,323)(281,322)(282,321)(283,320)(284,319)(285,318)(286,317)(287,316)(288,315)(289,314)(290,313)(291,312)(292,311)(293,310)(294,309)(295,308)(296,307)(297,306)(298,305)(299,304)(300,303)(301,302)
Polycyclic presentation:
2^3,3,587|b^2=c,b^a=bc,d^a=d^2,e^a=e^586
Conjugacy classes & character table
3525 conjugacy classes. The character table is too large to display.
Relationships
GAP
Past the SmallGroups library coverage — no SmallGroups id. Construct it from its polycyclic presentation:
gap> F := FreeGroup(IsSyllableWordsFamily, "a", "b", "c", "d", "e");;
gap> coll := SingleCollector(F, [2, 2, 2, 3, 587]);;
gap> SetPower(coll, 2, F.3);;
gap> SetConjugate(coll, 2, 1, F.2*F.3);;
gap> SetConjugate(coll, 4, 1, F.4^2);;
gap> SetConjugate(coll, 5, 1, F.5^586);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);
Finite Group Databasebeta