Finite Group DatabasebetaFinite Group Databasebeta| order | 32364 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C29×C31 · Schur multiplier (H2) = C2 |
| direct product | D32×C29×C31 |
| unambiguous semidirect product | (C3×D3)⋊(C2×C29×C31) |
| unambiguous semidirect product | (C3⋊D3)⋊(C2×C29×C31) |
| Fitting, socle, Hall | C32×C29×C31 ⋊ C22 |
| derived, Sylow | C32 ⋊ C22×C29×C31 |
| Hall | C32×C31 ⋊ C22×C29 |
| Hall | C32×C29 ⋊ C22×C31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C29×C31 | D32 |
| commutator, cosocle, hypocenter | C32 | C22×C29×C31 |
| Frattini | C1 | G |
| Fitting, socle | C32×C29×C31 | C22 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C29×C31 | |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5394 |
8091 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32364, 98);