Finite Group DatabasebetaFinite Group Databasebeta| order | 23826 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×D361⋊C3 |
| unambiguous semidirect product | D361⋊(C3×C11) |
| unambiguous semidirect product | (C361⋊C3)⋊(C2×C11) |
| unambiguous semidirect product | (C11×D361)⋊C3 |
| Fitting, Hall | C11×C361 ⋊ C2×C3 |
| derived, Sylow | C361 ⋊ C2×C3×C11 |
| Hall | C11×C361⋊C3 ⋊ C2 |
| Hall | C11×D361 ⋊ C3 |
| Hall | C361⋊C3 ⋊ C2×C11 |
| Hall | D361 ⋊ C3×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D361⋊C3 |
| commutator, cosocle, hypocenter | C361 | C2×C3×C11 |
| Frattini | C19 | C11×D19⋊C3 |
| Fitting | C11×C361 | C2×C3 |
| socle | C11×C19 | D19⋊C3 |
| LCS | G ▷ C361 | |
| UCS | C1 ◁ C11 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3971 |
726 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23826, 2);