Finite Group DatabasebetaFinite Group Databasebeta| order | 21022 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D10511 |
| unambiguous semidirect product | C23⋊D457 |
| unambiguous semidirect product | C457⋊D23 |
| Fitting, socle, derived, Hall | C23×C457 ⋊ C2 |
| Sylow | C457 ⋊ D23 |
| Sylow | C23 ⋊ D457 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C23×C457 | C2 |
| LCS | G ▷ C23×C457 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 480 |
| transitive degree | μt(G) = 10511 |
A minimal faithful permutation representation — 2 generators on 480 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);(2,23)(3,22)(4,21)(5,20)(6,19)(7,18)(8,17)(9,16)(10,15)(11,14)(12,13)(25,480)(26,479)(27,478)(28,477)(29,476)(30,475)(31,474)(32,473)(33,472)(34,471)(35,470)(36,469)(37,468)(38,467)(39,466)(40,465)(41,464)(42,463)(43,462)(44,461)(45,460)(46,459)(47,458)(48,457)(49,456)(50,455)(51,454)(52,453)(53,452)(54,451)(55,450)(56,449)(57,448)(58,447)(59,446)(60,445)(61,444)(62,443)(63,442)(64,441)(65,440)(66,439)(67,438)(68,437)(69,436)(70,435)(71,434)(72,433)(73,432)(74,431)(75,430)(76,429)(77,428)(78,427)(79,426)(80,425)(81,424)(82,423)(83,422)(84,421)(85,420)(86,419)(87,418)(88,417)(89,416)(90,415)(91,414)(92,413)(93,412)(94,411)(95,410)(96,409)(97,408)(98,407)(99,406)(100,405)(101,404)(102,403)(103,402)(104,401)(105,400)(106,399)(107,398)(108,397)(109,396)(110,395)(111,394)(112,393)(113,392)(114,391)(115,390)(116,389)(117,388)(118,387)(119,386)(120,385)(121,384)(122,383)(123,382)(124,381)(125,380)(126,379)(127,378)(128,377)(129,376)(130,375)(131,374)(132,373)(133,372)(134,371)(135,370)(136,369)(137,368)(138,367)(139,366)(140,365)(141,364)(142,363)(143,362)(144,361)(145,360)(146,359)(147,358)(148,357)(149,356)(150,355)(151,354)(152,353)(153,352)(154,351)(155,350)(156,349)(157,348)(158,347)(159,346)(160,345)(161,344)(162,343)(163,342)(164,341)(165,340)(166,339)(167,338)(168,337)(169,336)(170,335)(171,334)(172,333)(173,332)(174,331)(175,330)(176,329)(177,328)(178,327)(179,326)(180,325)(181,324)(182,323)(183,322)(184,321)(185,320)(186,319)(187,318)(188,317)(189,316)(190,315)(191,314)(192,313)(193,312)(194,311)(195,310)(196,309)(197,308)(198,307)(199,306)(200,305)(201,304)(202,303)(203,302)(204,301)(205,300)(206,299)(207,298)(208,297)(209,296)(210,295)(211,294)(212,293)(213,292)(214,291)(215,290)(216,289)(217,288)(218,287)(219,286)(220,285)(221,284)(222,283)(223,282)(224,281)(225,280)(226,279)(227,278)(228,277)(229,276)(230,275)(231,274)(232,273)(233,272)(234,271)(235,270)(236,269)(237,268)(238,267)(239,266)(240,265)(241,264)(242,263)(243,262)(244,261)(245,260)(246,259)(247,258)(248,257)(249,256)(250,255)(251,254)(252,253)Polycyclic presentation:
2,23,457|b^a=b^22,c^a=c^4565257 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21022, 3);