Finite Group DatabasebetaFinite Group Databasebeta| order | 19598 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D9799 |
| unambiguous semidirect product | C41⋊D239 |
| unambiguous semidirect product | C239⋊D41 |
| Fitting, socle, derived, Hall | C41×C239 ⋊ C2 |
| Sylow | C239 ⋊ D41 |
| Sylow | C41 ⋊ D239 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C41×C239 | C2 |
| LCS | G ▷ C41×C239 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 280 |
| transitive degree | μt(G) = 9799 |
A minimal faithful permutation representation — 2 generators on 280 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);(2,41)(3,40)(4,39)(5,38)(6,37)(7,36)(8,35)(9,34)(10,33)(11,32)(12,31)(13,30)(14,29)(15,28)(16,27)(17,26)(18,25)(19,24)(20,23)(21,22)(43,280)(44,279)(45,278)(46,277)(47,276)(48,275)(49,274)(50,273)(51,272)(52,271)(53,270)(54,269)(55,268)(56,267)(57,266)(58,265)(59,264)(60,263)(61,262)(62,261)(63,260)(64,259)(65,258)(66,257)(67,256)(68,255)(69,254)(70,253)(71,252)(72,251)(73,250)(74,249)(75,248)(76,247)(77,246)(78,245)(79,244)(80,243)(81,242)(82,241)(83,240)(84,239)(85,238)(86,237)(87,236)(88,235)(89,234)(90,233)(91,232)(92,231)(93,230)(94,229)(95,228)(96,227)(97,226)(98,225)(99,224)(100,223)(101,222)(102,221)(103,220)(104,219)(105,218)(106,217)(107,216)(108,215)(109,214)(110,213)(111,212)(112,211)(113,210)(114,209)(115,208)(116,207)(117,206)(118,205)(119,204)(120,203)(121,202)(122,201)(123,200)(124,199)(125,198)(126,197)(127,196)(128,195)(129,194)(130,193)(131,192)(132,191)(133,190)(134,189)(135,188)(136,187)(137,186)(138,185)(139,184)(140,183)(141,182)(142,181)(143,180)(144,179)(145,178)(146,177)(147,176)(148,175)(149,174)(150,173)(151,172)(152,171)(153,170)(154,169)(155,168)(156,167)(157,166)(158,165)(159,164)(160,163)(161,162)Polycyclic presentation:
2,41,239|b^a=b^40,c^a=c^2384901 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19598, 3);