Finite Group DatabasebetaFinite Group Databasebeta| order | 22374 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C113 · Schur multiplier (H2) = C1 |
| direct product | C113×D99 |
| unambiguous semidirect product | C9⋊(D11×C113) |
| unambiguous semidirect product | C11⋊(D9×C113) |
| Fitting, Hall | C9×C11×C113 ⋊ C2 |
| derived, Hall | C9×C11 ⋊ C2×C113 |
| Hall | C11×C113 ⋊ D9 |
| Hall | C9×C113 ⋊ D11 |
| Sylow | C11 ⋊ D9×C113 |
| Sylow | C9 ⋊ D11×C113 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C113 | D99 |
| commutator, cosocle, hypocenter | C9×C11 | C2×C113 |
| Frattini | C3 | D33×C113 |
| Fitting | C9×C11×C113 | C2 |
| socle | C3×C11×C113 | D3 |
| LCS | G ▷ C9×C11 | |
| UCS | C1 ◁ C113 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11187 |
5763 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22374, 7);