Finite Group DatabasebetaFinite Group Databasebeta| order | 23826 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C361 · Schur multiplier (H2) = C1 |
| direct product | D33×C361 |
| unambiguous semidirect product | C3⋊(D11×C361) |
| unambiguous semidirect product | C11⋊(D3×C361) |
| Fitting, Hall | C3×C11×C361 ⋊ C2 |
| derived, Hall | C3×C11 ⋊ C2×C361 |
| Hall | C11×C361 ⋊ D3 |
| Hall | C3×C361 ⋊ D11 |
| Sylow | C11 ⋊ D3×C361 |
| Sylow | C3 ⋊ D11×C361 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C361 | D33 |
| commutator, hypocenter | C3×C11 | C2×C361 |
| Frattini | C19 | C19×D33 |
| Fitting | C3×C11×C361 | C2 |
| socle, cosocle | C3×C11×C19 | C2×C19 |
| prime radical | C19×D33 | C19 |
| LCS | G ▷ C3×C11 | |
| UCS | C1 ◁ C361 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11913 |
6498 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23826, 11);