Finite Group DatabasebetaFinite Group Databasebeta| order | 23826 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×#14524212 |
| Fitting, socle, Hall | C11×C192 ⋊ D3 |
| derived, Hall | #11762246 ⋊ C2×C11 |
| Hall | C11×#11762246 ⋊ C2 |
| Sylow | C192 ⋊ D3×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | #14524212 |
| commutator, cosocle, hypocenter | #11762246 | C2×C11 |
| Frattini | C1 | G |
| Fitting, socle | C11×C192 | D3 |
| LCS | G ▷ #11762246 | |
| UCS | C1 ◁ C11 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 418 |
990 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23826, 14);