Finite Group DatabasebetaFinite Group Databasebeta| order | 32364 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C31 · Schur multiplier (H2) = C2 |
| direct product | D3×C31×D87 |
| unambiguous semidirect product | (C3×D3)⋊(C31×D29) |
| unambiguous semidirect product | (D3×C29)⋊(D3×C31) |
| Fitting, socle, Hall | C32×C29×C31 ⋊ C22 |
| derived, Hall | C32×C29 ⋊ C22×C31 |
| Hall | C29×C31 ⋊ D32 |
| Hall | C32×C31 ⋊ C2×D29 |
| Sylow | C29 ⋊ D32×C31 |
| Sylow | C32 ⋊ C2×C31×D29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C31 | D3×D87 |
| commutator, cosocle, hypocenter | C32×C29 | C22×C31 |
| Frattini | C1 | G |
| Fitting, socle | C32×C29×C31 | C22 |
| LCS | G ▷ C32×C29 | |
| UCS | C1 ◁ C31 | |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5394 |
4185 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32364, 101);