Finite Group DatabasebetaFinite Group Databasebeta| order | 23826 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | D11×#11762245 |
| unambiguous semidirect product | C11⋊(C2×#11762245) |
| Fitting, socle, derived, Hall | C11×C192 ⋊ C2×C3 |
| Hall | C11×#11762245 ⋊ C2 |
| Hall | C192×D11 ⋊ C3 |
| Sylow | C192 ⋊ C3×D11 |
| Sylow | C11 ⋊ C2×#11762245 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C192 | C2×C3 |
| LCS | G ▷ C11×C192 | |
| UCS | C1 | |
176 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3971 |
861 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23826, 27);