Finite Group DatabasebetaFinite Group Databasebeta| order | 33668 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic8417 |
| unambiguous semidirect product | C19⋊Dic443 |
| unambiguous semidirect product | C443⋊Dic19 |
| derived, Hall | C19×C443 ⋊ C4 |
| Sylow | C443 ⋊ Dic19 |
| Sylow | C19 ⋊ Dic443 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D8417 |
| commutator, hypocenter | C19×C443 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C19×C443 | C2 |
| LCS | G ▷ C19×C443 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 466 |
| transitive degree | μt(G) = 33668 |
A minimal faithful permutation representation — 2 generators on 466 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);(1,3,2,4)(6,23)(7,22)(8,21)(9,20)(10,19)(11,18)(12,17)(13,16)(14,15)(25,466)(26,465)(27,464)(28,463)(29,462)(30,461)(31,460)(32,459)(33,458)(34,457)(35,456)(36,455)(37,454)(38,453)(39,452)(40,451)(41,450)(42,449)(43,448)(44,447)(45,446)(46,445)(47,444)(48,443)(49,442)(50,441)(51,440)(52,439)(53,438)(54,437)(55,436)(56,435)(57,434)(58,433)(59,432)(60,431)(61,430)(62,429)(63,428)(64,427)(65,426)(66,425)(67,424)(68,423)(69,422)(70,421)(71,420)(72,419)(73,418)(74,417)(75,416)(76,415)(77,414)(78,413)(79,412)(80,411)(81,410)(82,409)(83,408)(84,407)(85,406)(86,405)(87,404)(88,403)(89,402)(90,401)(91,400)(92,399)(93,398)(94,397)(95,396)(96,395)(97,394)(98,393)(99,392)(100,391)(101,390)(102,389)(103,388)(104,387)(105,386)(106,385)(107,384)(108,383)(109,382)(110,381)(111,380)(112,379)(113,378)(114,377)(115,376)(116,375)(117,374)(118,373)(119,372)(120,371)(121,370)(122,369)(123,368)(124,367)(125,366)(126,365)(127,364)(128,363)(129,362)(130,361)(131,360)(132,359)(133,358)(134,357)(135,356)(136,355)(137,354)(138,353)(139,352)(140,351)(141,350)(142,349)(143,348)(144,347)(145,346)(146,345)(147,344)(148,343)(149,342)(150,341)(151,340)(152,339)(153,338)(154,337)(155,336)(156,335)(157,334)(158,333)(159,332)(160,331)(161,330)(162,329)(163,328)(164,327)(165,326)(166,325)(167,324)(168,323)(169,322)(170,321)(171,320)(172,319)(173,318)(174,317)(175,316)(176,315)(177,314)(178,313)(179,312)(180,311)(181,310)(182,309)(183,308)(184,307)(185,306)(186,305)(187,304)(188,303)(189,302)(190,301)(191,300)(192,299)(193,298)(194,297)(195,296)(196,295)(197,294)(198,293)(199,292)(200,291)(201,290)(202,289)(203,288)(204,287)(205,286)(206,285)(207,284)(208,283)(209,282)(210,281)(211,280)(212,279)(213,278)(214,277)(215,276)(216,275)(217,274)(218,273)(219,272)(220,271)(221,270)(222,269)(223,268)(224,267)(225,266)(226,265)(227,264)(228,263)(229,262)(230,261)(231,260)(232,259)(233,258)(234,257)(235,256)(236,255)(237,254)(238,253)(239,252)(240,251)(241,250)(242,249)(243,248)(244,247)(245,246)Polycyclic presentation:
2,19,443,2|a^2=d,b^a=b^18,c^a=c^4428420 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33668, 4);