Finite Group DatabasebetaFinite Group Databasebeta| order | 23034 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×D349⋊C3 |
| unambiguous semidirect product | D349⋊(C3×C11) |
| unambiguous semidirect product | (C349⋊C3)⋊(C2×C11) |
| unambiguous semidirect product | (C11×D349)⋊C3 |
| Fitting, socle, Hall | C11×C349 ⋊ C2×C3 |
| derived, Sylow | C349 ⋊ C2×C3×C11 |
| Hall | C11×C349⋊C3 ⋊ C2 |
| Hall | C11×D349 ⋊ C3 |
| Hall | C349⋊C3 ⋊ C2×C11 |
| Hall | D349 ⋊ C3×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D349⋊C3 |
| commutator, cosocle, hypocenter | C349 | C2×C3×C11 |
| Frattini | C1 | G |
| Fitting, socle | C11×C349 | C2×C3 |
| LCS | G ▷ C349 | |
| UCS | C1 ◁ C11 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3839 |
704 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23034, 10);