Finite Group DatabasebetaFinite Group Databasebeta| order | 32364 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | C9×D29×D31 |
| Fitting, Hall | C9×C29×C31 ⋊ C22 |
| derived, Hall | C29×C31 ⋊ C22×C9 |
| Hall | C9×C31 ⋊ C2×D29 |
| Hall | C9×C29 ⋊ C2×D31 |
| Sylow | C31 ⋊ C2×C9×D29 |
| Sylow | C29 ⋊ C2×C9×D31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | D29×D31 |
| commutator, hypocenter | C29×C31 | C22×C9 |
| Frattini | C3 | C3×D29×D31 |
| Fitting | C9×C29×C31 | C22 |
| socle, cosocle | C3×C29×C31 | C22×C3 |
| prime radical | C3×D29×D31 | C3 |
| LCS | G ▷ C29×C31 | |
| UCS | C1 ◁ C9 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8091 |
2448 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32364, 22);