Finite Group DatabasebetaFinite Group Databasebeta| order | 19834 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D9917 |
| unambiguous semidirect product | C47⋊D211 |
| unambiguous semidirect product | C211⋊D47 |
| Fitting, socle, derived, Hall | C47×C211 ⋊ C2 |
| Sylow | C211 ⋊ D47 |
| Sylow | C47 ⋊ D211 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C47×C211 | C2 |
| LCS | G ▷ C47×C211 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 258 |
| transitive degree | μt(G) = 9917 |
A minimal faithful permutation representation — 2 generators on 258 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);(2,47)(3,46)(4,45)(5,44)(6,43)(7,42)(8,41)(9,40)(10,39)(11,38)(12,37)(13,36)(14,35)(15,34)(16,33)(17,32)(18,31)(19,30)(20,29)(21,28)(22,27)(23,26)(24,25)(49,258)(50,257)(51,256)(52,255)(53,254)(54,253)(55,252)(56,251)(57,250)(58,249)(59,248)(60,247)(61,246)(62,245)(63,244)(64,243)(65,242)(66,241)(67,240)(68,239)(69,238)(70,237)(71,236)(72,235)(73,234)(74,233)(75,232)(76,231)(77,230)(78,229)(79,228)(80,227)(81,226)(82,225)(83,224)(84,223)(85,222)(86,221)(87,220)(88,219)(89,218)(90,217)(91,216)(92,215)(93,214)(94,213)(95,212)(96,211)(97,210)(98,209)(99,208)(100,207)(101,206)(102,205)(103,204)(104,203)(105,202)(106,201)(107,200)(108,199)(109,198)(110,197)(111,196)(112,195)(113,194)(114,193)(115,192)(116,191)(117,190)(118,189)(119,188)(120,187)(121,186)(122,185)(123,184)(124,183)(125,182)(126,181)(127,180)(128,179)(129,178)(130,177)(131,176)(132,175)(133,174)(134,173)(135,172)(136,171)(137,170)(138,169)(139,168)(140,167)(141,166)(142,165)(143,164)(144,163)(145,162)(146,161)(147,160)(148,159)(149,158)(150,157)(151,156)(152,155)(153,154)Polycyclic presentation:
2,47,211|b^a=b^46,c^a=c^2104960 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19834, 3);