Finite Group DatabasebetaFinite Group Databasebeta| order | 32364 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C29 · Schur multiplier (H2) = C2 |
| direct product | D3×C29×D93 |
| unambiguous semidirect product | (C3×D3)⋊(C29×D31) |
| unambiguous semidirect product | (D3×C31)⋊(D3×C29) |
| Fitting, socle, Hall | C32×C29×C31 ⋊ C22 |
| derived, Hall | C32×C31 ⋊ C22×C29 |
| Hall | C29×C31 ⋊ D32 |
| Hall | C32×C29 ⋊ C2×D31 |
| Sylow | C31 ⋊ D32×C29 |
| Sylow | C32 ⋊ C2×C29×D31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C29 | D3×D93 |
| commutator, cosocle, hypocenter | C32×C31 | C22×C29 |
| Frattini | C1 | G |
| Fitting, socle | C32×C29×C31 | C22 |
| LCS | G ▷ C32×C31 | |
| UCS | C1 ◁ C29 | |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5394 |
4176 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32364, 99);