Finite Group DatabasebetaFinite Group Databasebeta| order | 22374 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C3 |
| direct product | C11×C3⋊D339 |
| unambiguous semidirect product | C3⋊(C11×D339) |
| unambiguous semidirect product | C113⋊(C11×C3⋊D3) |
| Fitting, socle, Hall | C32×C11×C113 ⋊ C2 |
| derived, Hall | C32×C113 ⋊ C2×C11 |
| Hall | C11×C113 ⋊ C3⋊D3 |
| Sylow | C113 ⋊ C11×C3⋊D3 |
| Hall | C32×C11 ⋊ D113 |
| Sylow | C32 ⋊ C11×D113 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | C3⋊D339 |
| commutator, cosocle, hypocenter | C32×C113 | C2×C11 |
| Frattini | C1 | G |
| Fitting, socle | C32×C11×C113 | C2 |
| LCS | G ▷ C32×C113 | |
| UCS | C1 ◁ C11 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11187 |
5610 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22374, 18);