Finite Group DatabasebetaFinite Group Databasebeta| order | 23826 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C11⋊((C19⋊C3)⋊D19) |
| unambiguous semidirect product | (C19⋊C3)⋊D209 |
| Fitting, socle, derived, Hall | C11×C192 ⋊ C2×C3 |
| Hall | C11×C19×C19⋊C3 ⋊ C2 |
| Hall | C11⋊(C19⋊D19) ⋊ C3 |
| Hall | C19×C19⋊C3 ⋊ D11 |
| Sylow | C192 ⋊ C3×D11 |
| Sylow | C11 ⋊ (C19⋊C3)⋊D19 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C192 | C2×C3 |
| LCS | G ▷ C11×C192 | |
| UCS | C1 | |
56 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 627 |
A minimal faithful permutation representation — 2 generators on 49 points:
(2,3)(4,5)(6,7)(8,9)(10,11)(13,17,18,14,15,19)(16,25,22,20,21,27)(23,28,30,29,26,24)(32,33)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)(48,49);(1,2,4,6,8,10,11,9,7,5,3)(12,13,16,22,28,25,29,15,19,24,30,18,17,23,21,26,27,20,14)(31,32,34,36,38,40,42,44,46,48,49,47,45,43,41,39,37,35,33)Polycyclic presentation:
2,3,11,19^2|c^a=c^10,d^a=d^18,e^a=e^18,d^b=d^7945 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23826, 25);