Finite Group DatabasebetaFinite Group Databasebeta| order | 23826 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×(C19⋊C3)⋊D19 |
| unambiguous semidirect product | (C19⋊C3)⋊(C11×D19) |
| Fitting, socle, Hall | C11×C192 ⋊ C2×C3 |
| derived, Sylow | C192 ⋊ C2×C3×C11 |
| Hall | C11×C19×C19⋊C3 ⋊ C2 |
| Hall | C11×C19⋊D19 ⋊ C3 |
| Hall | C19×C19⋊C3 ⋊ C2×C11 |
| Hall | C19⋊D19 ⋊ C3×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | (C19⋊C3)⋊D19 |
| commutator, cosocle, hypocenter | C192 | C2×C3×C11 |
| Frattini | C1 | G |
| Fitting, socle | C11×C192 | C2×C3 |
| LCS | G ▷ C192 | |
| UCS | C1 ◁ C11 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 627 |
990 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23826, 16);