Finite Group DatabasebetaFinite Group Databasebeta| order | 32364 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×C32×D899 |
| unambiguous semidirect product | (C2×C29)⋊(C32×D31) |
| Fitting, socle | C2×C32×C29×C31 ⋊ C2 |
| derived, Hall | C29×C31 ⋊ C22×C32 |
| Hall | C32×C29×C31 ⋊ C22 |
| Hall | C32×C31 ⋊ C2×D29 |
| Hall | C32×C29 ⋊ C2×D31 |
| Sylow | C31 ⋊ C2×C32×D29 |
| Sylow | C29 ⋊ C2×C32×D31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32 | D899 |
| commutator, cosocle, hypocenter | C29×C31 | C22×C32 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C29×C31 | C2 |
| LCS | G ▷ C29×C31 | |
| UCS | C1 ◁ C2×C32 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16182 |
8118 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32364, 121);