Finite Group DatabasebetaFinite Group Databasebeta| order | 18612 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C47 · Schur multiplier (H2) = C2 |
| direct product | D3×C47×D33 |
| unambiguous semidirect product | (C3×D3)⋊(D11×C47) |
| unambiguous semidirect product | (D3×C11)⋊(D3×C47) |
| Fitting, socle, Hall | C32×C11×C47 ⋊ C22 |
| derived, Hall | C32×C11 ⋊ C22×C47 |
| Hall | C11×C47 ⋊ D32 |
| Hall | C32×C47 ⋊ C2×D11 |
| Sylow | C11 ⋊ D32×C47 |
| Sylow | C32 ⋊ C2×D11×C47 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C47 | D3×D33 |
| commutator, cosocle, hypocenter | C32×C11 | C22×C47 |
| Frattini | C1 | G |
| Fitting, socle | C32×C11×C47 | C22 |
| LCS | G ▷ C32×C11 | |
| UCS | C1 ◁ C47 | |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3102 |
2538 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18612, 54);