Finite Group DatabasebetaFinite Group Databasebeta| order | 33594 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D16797 |
| unambiguous semidirect product | C3⋊D5599 |
| unambiguous semidirect product | C11⋊D1527 |
| unambiguous semidirect product | C509⋊D33 |
| Fitting, socle, derived, Hall | C3×C11×C509 ⋊ C2 |
| Hall | C11×C509 ⋊ D3 |
| Hall | C3×C509 ⋊ D11 |
| Sylow | C509 ⋊ D33 |
| Hall | C3×C11 ⋊ D509 |
| Sylow | C11 ⋊ D1527 |
| Sylow | C3 ⋊ D5599 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C11×C509 | C2 |
| LCS | G ▷ C3×C11×C509 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 523 |
| transitive degree | μt(G) = 16797 |
A minimal faithful permutation representation — 2 generators on 523 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);(2,3)(5,14)(6,13)(7,12)(8,11)(9,10)(16,523)(17,522)(18,521)(19,520)(20,519)(21,518)(22,517)(23,516)(24,515)(25,514)(26,513)(27,512)(28,511)(29,510)(30,509)(31,508)(32,507)(33,506)(34,505)(35,504)(36,503)(37,502)(38,501)(39,500)(40,499)(41,498)(42,497)(43,496)(44,495)(45,494)(46,493)(47,492)(48,491)(49,490)(50,489)(51,488)(52,487)(53,486)(54,485)(55,484)(56,483)(57,482)(58,481)(59,480)(60,479)(61,478)(62,477)(63,476)(64,475)(65,474)(66,473)(67,472)(68,471)(69,470)(70,469)(71,468)(72,467)(73,466)(74,465)(75,464)(76,463)(77,462)(78,461)(79,460)(80,459)(81,458)(82,457)(83,456)(84,455)(85,454)(86,453)(87,452)(88,451)(89,450)(90,449)(91,448)(92,447)(93,446)(94,445)(95,444)(96,443)(97,442)(98,441)(99,440)(100,439)(101,438)(102,437)(103,436)(104,435)(105,434)(106,433)(107,432)(108,431)(109,430)(110,429)(111,428)(112,427)(113,426)(114,425)(115,424)(116,423)(117,422)(118,421)(119,420)(120,419)(121,418)(122,417)(123,416)(124,415)(125,414)(126,413)(127,412)(128,411)(129,410)(130,409)(131,408)(132,407)(133,406)(134,405)(135,404)(136,403)(137,402)(138,401)(139,400)(140,399)(141,398)(142,397)(143,396)(144,395)(145,394)(146,393)(147,392)(148,391)(149,390)(150,389)(151,388)(152,387)(153,386)(154,385)(155,384)(156,383)(157,382)(158,381)(159,380)(160,379)(161,378)(162,377)(163,376)(164,375)(165,374)(166,373)(167,372)(168,371)(169,370)(170,369)(171,368)(172,367)(173,366)(174,365)(175,364)(176,363)(177,362)(178,361)(179,360)(180,359)(181,358)(182,357)(183,356)(184,355)(185,354)(186,353)(187,352)(188,351)(189,350)(190,349)(191,348)(192,347)(193,346)(194,345)(195,344)(196,343)(197,342)(198,341)(199,340)(200,339)(201,338)(202,337)(203,336)(204,335)(205,334)(206,333)(207,332)(208,331)(209,330)(210,329)(211,328)(212,327)(213,326)(214,325)(215,324)(216,323)(217,322)(218,321)(219,320)(220,319)(221,318)(222,317)(223,316)(224,315)(225,314)(226,313)(227,312)(228,311)(229,310)(230,309)(231,308)(232,307)(233,306)(234,305)(235,304)(236,303)(237,302)(238,301)(239,300)(240,299)(241,298)(242,297)(243,296)(244,295)(245,294)(246,293)(247,292)(248,291)(249,290)(250,289)(251,288)(252,287)(253,286)(254,285)(255,284)(256,283)(257,282)(258,281)(259,280)(260,279)(261,278)(262,277)(263,276)(264,275)(265,274)(266,273)(267,272)(268,271)(269,270)Polycyclic presentation:
2,3,11,509|b^a=b^2,c^a=c^10,d^a=d^5088400 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33594, 8);