Finite Group DatabasebetaFinite Group Databasebeta| order | 24418 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D12209 |
| unambiguous semidirect product | C29⋊D421 |
| unambiguous semidirect product | C421⋊D29 |
| Fitting, socle, derived, Hall | C29×C421 ⋊ C2 |
| Sylow | C421 ⋊ D29 |
| Sylow | C29 ⋊ D421 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C29×C421 | C2 |
| LCS | G ▷ C29×C421 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 450 |
| transitive degree | μt(G) = 12209 |
A minimal faithful permutation representation — 2 generators on 450 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);(2,29)(3,28)(4,27)(5,26)(6,25)(7,24)(8,23)(9,22)(10,21)(11,20)(12,19)(13,18)(14,17)(15,16)(31,450)(32,449)(33,448)(34,447)(35,446)(36,445)(37,444)(38,443)(39,442)(40,441)(41,440)(42,439)(43,438)(44,437)(45,436)(46,435)(47,434)(48,433)(49,432)(50,431)(51,430)(52,429)(53,428)(54,427)(55,426)(56,425)(57,424)(58,423)(59,422)(60,421)(61,420)(62,419)(63,418)(64,417)(65,416)(66,415)(67,414)(68,413)(69,412)(70,411)(71,410)(72,409)(73,408)(74,407)(75,406)(76,405)(77,404)(78,403)(79,402)(80,401)(81,400)(82,399)(83,398)(84,397)(85,396)(86,395)(87,394)(88,393)(89,392)(90,391)(91,390)(92,389)(93,388)(94,387)(95,386)(96,385)(97,384)(98,383)(99,382)(100,381)(101,380)(102,379)(103,378)(104,377)(105,376)(106,375)(107,374)(108,373)(109,372)(110,371)(111,370)(112,369)(113,368)(114,367)(115,366)(116,365)(117,364)(118,363)(119,362)(120,361)(121,360)(122,359)(123,358)(124,357)(125,356)(126,355)(127,354)(128,353)(129,352)(130,351)(131,350)(132,349)(133,348)(134,347)(135,346)(136,345)(137,344)(138,343)(139,342)(140,341)(141,340)(142,339)(143,338)(144,337)(145,336)(146,335)(147,334)(148,333)(149,332)(150,331)(151,330)(152,329)(153,328)(154,327)(155,326)(156,325)(157,324)(158,323)(159,322)(160,321)(161,320)(162,319)(163,318)(164,317)(165,316)(166,315)(167,314)(168,313)(169,312)(170,311)(171,310)(172,309)(173,308)(174,307)(175,306)(176,305)(177,304)(178,303)(179,302)(180,301)(181,300)(182,299)(183,298)(184,297)(185,296)(186,295)(187,294)(188,293)(189,292)(190,291)(191,290)(192,289)(193,288)(194,287)(195,286)(196,285)(197,284)(198,283)(199,282)(200,281)(201,280)(202,279)(203,278)(204,277)(205,276)(206,275)(207,274)(208,273)(209,272)(210,271)(211,270)(212,269)(213,268)(214,267)(215,266)(216,265)(217,264)(218,263)(219,262)(220,261)(221,260)(222,259)(223,258)(224,257)(225,256)(226,255)(227,254)(228,253)(229,252)(230,251)(231,250)(232,249)(233,248)(234,247)(235,246)(236,245)(237,244)(238,243)(239,242)(240,241)Polycyclic presentation:
2,29,421|b^a=b^28,c^a=c^4206106 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24418, 3);