Finite Group DatabasebetaFinite Group Databasebeta| order | 22374 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C32×D1243 |
| unambiguous semidirect product | C11⋊(C32×D113) |
| unambiguous semidirect product | C113⋊(C32×D11) |
| Fitting, socle, Hall | C32×C11×C113 ⋊ C2 |
| derived, Hall | C11×C113 ⋊ C2×C32 |
| Hall | C32×C113 ⋊ D11 |
| Sylow | C113 ⋊ C32×D11 |
| Hall | C32×C11 ⋊ D113 |
| Sylow | C11 ⋊ C32×D113 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | D1243 |
| commutator, cosocle, hypocenter | C11×C113 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C32×C11×C113 | C2 |
| LCS | G ▷ C11×C113 | |
| UCS | C1 ◁ C32 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11187 |
5607 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22374, 12);