Finite Group DatabasebetaFinite Group Databasebeta| order | 23406 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D11703 |
| unambiguous semidirect product | C3⋊D3901 |
| unambiguous semidirect product | C47⋊D249 |
| unambiguous semidirect product | C83⋊D141 |
| Fitting, socle, derived, Hall | C3×C47×C83 ⋊ C2 |
| Hall | C47×C83 ⋊ D3 |
| Hall | C3×C83 ⋊ D47 |
| Hall | C3×C47 ⋊ D83 |
| Sylow | C83 ⋊ D141 |
| Sylow | C47 ⋊ D249 |
| Sylow | C3 ⋊ D3901 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C47×C83 | C2 |
| LCS | G ▷ C3×C47×C83 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 133 |
| transitive degree | μt(G) = 11703 |
A minimal faithful permutation representation — 2 generators on 133 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);(2,3)(5,50)(6,49)(7,48)(8,47)(9,46)(10,45)(11,44)(12,43)(13,42)(14,41)(15,40)(16,39)(17,38)(18,37)(19,36)(20,35)(21,34)(22,33)(23,32)(24,31)(25,30)(26,29)(27,28)(52,133)(53,132)(54,131)(55,130)(56,129)(57,128)(58,127)(59,126)(60,125)(61,124)(62,123)(63,122)(64,121)(65,120)(66,119)(67,118)(68,117)(69,116)(70,115)(71,114)(72,113)(73,112)(74,111)(75,110)(76,109)(77,108)(78,107)(79,106)(80,105)(81,104)(82,103)(83,102)(84,101)(85,100)(86,99)(87,98)(88,97)(89,96)(90,95)(91,94)(92,93)Polycyclic presentation:
2,3,47,83|b^a=b^2,c^a=c^46,d^a=d^825853 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23406, 8);