Finite Group DatabasebetaFinite Group Databasebeta| order | 32364 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C31 · Schur multiplier (H2) = C2 |
| direct product | D9×C31×D29 |
| unambiguous semidirect product | (D9×C29)⋊(C2×C31) |
| unambiguous semidirect product | (C9×D29)⋊(C2×C31) |
| unambiguous semidirect product | D261⋊(C2×C31) |
| Fitting, Hall | C9×C29×C31 ⋊ C22 |
| derived, Hall | C9×C29 ⋊ C22×C31 |
| Hall | C29×C31 ⋊ C2×D9 |
| Hall | C9×C31 ⋊ C2×D29 |
| Sylow | C29 ⋊ C2×D9×C31 |
| Sylow | C9 ⋊ C2×C31×D29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C31 | D9×D29 |
| commutator, cosocle, hypocenter | C9×C29 | C22×C31 |
| Frattini | C3 | D3×C31×D29 |
| Fitting | C9×C29×C31 | C22 |
| socle | C3×C29×C31 | C2×D3 |
| LCS | G ▷ C9×C29 | |
| UCS | C1 ◁ C31 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8091 |
2976 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32364, 27);