Finite Group DatabasebetaFinite Group Databasebeta| order | 20554 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D10277 |
| unambiguous semidirect product | C43⋊D239 |
| unambiguous semidirect product | C239⋊D43 |
| Fitting, socle, derived, Hall | C43×C239 ⋊ C2 |
| Sylow | C239 ⋊ D43 |
| Sylow | C43 ⋊ D239 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C43×C239 | C2 |
| LCS | G ▷ C43×C239 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 282 |
| transitive degree | μt(G) = 10277 |
A minimal faithful permutation representation — 2 generators on 282 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);(2,43)(3,42)(4,41)(5,40)(6,39)(7,38)(8,37)(9,36)(10,35)(11,34)(12,33)(13,32)(14,31)(15,30)(16,29)(17,28)(18,27)(19,26)(20,25)(21,24)(22,23)(45,282)(46,281)(47,280)(48,279)(49,278)(50,277)(51,276)(52,275)(53,274)(54,273)(55,272)(56,271)(57,270)(58,269)(59,268)(60,267)(61,266)(62,265)(63,264)(64,263)(65,262)(66,261)(67,260)(68,259)(69,258)(70,257)(71,256)(72,255)(73,254)(74,253)(75,252)(76,251)(77,250)(78,249)(79,248)(80,247)(81,246)(82,245)(83,244)(84,243)(85,242)(86,241)(87,240)(88,239)(89,238)(90,237)(91,236)(92,235)(93,234)(94,233)(95,232)(96,231)(97,230)(98,229)(99,228)(100,227)(101,226)(102,225)(103,224)(104,223)(105,222)(106,221)(107,220)(108,219)(109,218)(110,217)(111,216)(112,215)(113,214)(114,213)(115,212)(116,211)(117,210)(118,209)(119,208)(120,207)(121,206)(122,205)(123,204)(124,203)(125,202)(126,201)(127,200)(128,199)(129,198)(130,197)(131,196)(132,195)(133,194)(134,193)(135,192)(136,191)(137,190)(138,189)(139,188)(140,187)(141,186)(142,185)(143,184)(144,183)(145,182)(146,181)(147,180)(148,179)(149,178)(150,177)(151,176)(152,175)(153,174)(154,173)(155,172)(156,171)(157,170)(158,169)(159,168)(160,167)(161,166)(162,165)(163,164)Polycyclic presentation:
2,43,239|b^a=b^42,c^a=c^2385140 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20554, 3);