Finite Group DatabasebetaFinite Group Databasebeta| order | 33932 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic8483 |
| unambiguous semidirect product | C499⋊Dic17 |
| derived, Hall | C17×C499 ⋊ C4 |
| Sylow | C499 ⋊ Dic17 |
| Sylow | C17 ⋊ Dic499 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D8483 |
| commutator, hypocenter | C17×C499 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C17×C499 | C2 |
| LCS | G ▷ C17×C499 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 520 |
| transitive degree | μt(G) = 33932 |
A minimal faithful permutation representation — 2 generators on 520 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);(1,3,2,4)(6,21)(7,20)(8,19)(9,18)(10,17)(11,16)(12,15)(13,14)(23,520)(24,519)(25,518)(26,517)(27,516)(28,515)(29,514)(30,513)(31,512)(32,511)(33,510)(34,509)(35,508)(36,507)(37,506)(38,505)(39,504)(40,503)(41,502)(42,501)(43,500)(44,499)(45,498)(46,497)(47,496)(48,495)(49,494)(50,493)(51,492)(52,491)(53,490)(54,489)(55,488)(56,487)(57,486)(58,485)(59,484)(60,483)(61,482)(62,481)(63,480)(64,479)(65,478)(66,477)(67,476)(68,475)(69,474)(70,473)(71,472)(72,471)(73,470)(74,469)(75,468)(76,467)(77,466)(78,465)(79,464)(80,463)(81,462)(82,461)(83,460)(84,459)(85,458)(86,457)(87,456)(88,455)(89,454)(90,453)(91,452)(92,451)(93,450)(94,449)(95,448)(96,447)(97,446)(98,445)(99,444)(100,443)(101,442)(102,441)(103,440)(104,439)(105,438)(106,437)(107,436)(108,435)(109,434)(110,433)(111,432)(112,431)(113,430)(114,429)(115,428)(116,427)(117,426)(118,425)(119,424)(120,423)(121,422)(122,421)(123,420)(124,419)(125,418)(126,417)(127,416)(128,415)(129,414)(130,413)(131,412)(132,411)(133,410)(134,409)(135,408)(136,407)(137,406)(138,405)(139,404)(140,403)(141,402)(142,401)(143,400)(144,399)(145,398)(146,397)(147,396)(148,395)(149,394)(150,393)(151,392)(152,391)(153,390)(154,389)(155,388)(156,387)(157,386)(158,385)(159,384)(160,383)(161,382)(162,381)(163,380)(164,379)(165,378)(166,377)(167,376)(168,375)(169,374)(170,373)(171,372)(172,371)(173,370)(174,369)(175,368)(176,367)(177,366)(178,365)(179,364)(180,363)(181,362)(182,361)(183,360)(184,359)(185,358)(186,357)(187,356)(188,355)(189,354)(190,353)(191,352)(192,351)(193,350)(194,349)(195,348)(196,347)(197,346)(198,345)(199,344)(200,343)(201,342)(202,341)(203,340)(204,339)(205,338)(206,337)(207,336)(208,335)(209,334)(210,333)(211,332)(212,331)(213,330)(214,329)(215,328)(216,327)(217,326)(218,325)(219,324)(220,323)(221,322)(222,321)(223,320)(224,319)(225,318)(226,317)(227,316)(228,315)(229,314)(230,313)(231,312)(232,311)(233,310)(234,309)(235,308)(236,307)(237,306)(238,305)(239,304)(240,303)(241,302)(242,301)(243,300)(244,299)(245,298)(246,297)(247,296)(248,295)(249,294)(250,293)(251,292)(252,291)(253,290)(254,289)(255,288)(256,287)(257,286)(258,285)(259,284)(260,283)(261,282)(262,281)(263,280)(264,279)(265,278)(266,277)(267,276)(268,275)(269,274)(270,273)(271,272)Polycyclic presentation:
2,17,499,2|a^2=d,b^a=b^16,c^a=c^4988486 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33932, 4);