Finite Group DatabasebetaFinite Group Databasebeta| order | 23350 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D11675 |
| unambiguous semidirect product | C25⋊D467 |
| unambiguous semidirect product | C467⋊D25 |
| Fitting, derived, Hall | C25×C467 ⋊ C2 |
| Sylow | C467 ⋊ D25 |
| Sylow | C25 ⋊ D467 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C25×C467 | C2 |
| Frattini | C5 | D2335 |
| socle | C5×C467 | D5 |
| LCS | G ▷ C25×C467 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 492 |
| transitive degree | μt(G) = 11675 |
A minimal faithful permutation representation — 2 generators on 492 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);(2,25)(3,24)(4,23)(5,22)(6,21)(7,20)(8,19)(9,18)(10,17)(11,16)(12,15)(13,14)(27,492)(28,491)(29,490)(30,489)(31,488)(32,487)(33,486)(34,485)(35,484)(36,483)(37,482)(38,481)(39,480)(40,479)(41,478)(42,477)(43,476)(44,475)(45,474)(46,473)(47,472)(48,471)(49,470)(50,469)(51,468)(52,467)(53,466)(54,465)(55,464)(56,463)(57,462)(58,461)(59,460)(60,459)(61,458)(62,457)(63,456)(64,455)(65,454)(66,453)(67,452)(68,451)(69,450)(70,449)(71,448)(72,447)(73,446)(74,445)(75,444)(76,443)(77,442)(78,441)(79,440)(80,439)(81,438)(82,437)(83,436)(84,435)(85,434)(86,433)(87,432)(88,431)(89,430)(90,429)(91,428)(92,427)(93,426)(94,425)(95,424)(96,423)(97,422)(98,421)(99,420)(100,419)(101,418)(102,417)(103,416)(104,415)(105,414)(106,413)(107,412)(108,411)(109,410)(110,409)(111,408)(112,407)(113,406)(114,405)(115,404)(116,403)(117,402)(118,401)(119,400)(120,399)(121,398)(122,397)(123,396)(124,395)(125,394)(126,393)(127,392)(128,391)(129,390)(130,389)(131,388)(132,387)(133,386)(134,385)(135,384)(136,383)(137,382)(138,381)(139,380)(140,379)(141,378)(142,377)(143,376)(144,375)(145,374)(146,373)(147,372)(148,371)(149,370)(150,369)(151,368)(152,367)(153,366)(154,365)(155,364)(156,363)(157,362)(158,361)(159,360)(160,359)(161,358)(162,357)(163,356)(164,355)(165,354)(166,353)(167,352)(168,351)(169,350)(170,349)(171,348)(172,347)(173,346)(174,345)(175,344)(176,343)(177,342)(178,341)(179,340)(180,339)(181,338)(182,337)(183,336)(184,335)(185,334)(186,333)(187,332)(188,331)(189,330)(190,329)(191,328)(192,327)(193,326)(194,325)(195,324)(196,323)(197,322)(198,321)(199,320)(200,319)(201,318)(202,317)(203,316)(204,315)(205,314)(206,313)(207,312)(208,311)(209,310)(210,309)(211,308)(212,307)(213,306)(214,305)(215,304)(216,303)(217,302)(218,301)(219,300)(220,299)(221,298)(222,297)(223,296)(224,295)(225,294)(226,293)(227,292)(228,291)(229,290)(230,289)(231,288)(232,287)(233,286)(234,285)(235,284)(236,283)(237,282)(238,281)(239,280)(240,279)(241,278)(242,277)(243,276)(244,275)(245,274)(246,273)(247,272)(248,271)(249,270)(250,269)(251,268)(252,267)(253,266)(254,265)(255,264)(256,263)(257,262)(258,261)(259,260)Polycyclic presentation:
2,5,467,5|b^5=d^4,b^a=b^4d,c^a=c^466,d^a=d^45839 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23350, 4);