Finite Group DatabasebetaFinite Group Databasebeta| order | 32868 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C83 · Schur multiplier (H2) = C2 |
| direct product | D3×D33×C83 |
| unambiguous semidirect product | (C3×D3)⋊(D11×C83) |
| unambiguous semidirect product | (D3×C11)⋊(D3×C83) |
| Fitting, socle, Hall | C32×C11×C83 ⋊ C22 |
| derived, Hall | C32×C11 ⋊ C22×C83 |
| Hall | C11×C83 ⋊ D32 |
| Hall | C32×C83 ⋊ C2×D11 |
| Sylow | C11 ⋊ D32×C83 |
| Sylow | C32 ⋊ C2×D11×C83 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C83 | D3×D33 |
| commutator, cosocle, hypocenter | C32×C11 | C22×C83 |
| Frattini | C1 | G |
| Fitting, socle | C32×C11×C83 | C22 |
| LCS | G ▷ C32×C11 | |
| UCS | C1 ◁ C83 | |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5478 |
4482 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32868, 52);