Finite Group DatabasebetaFinite Group Databasebeta| order | 32770 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D3277 |
| unambiguous semidirect product | C29⋊(C5×D113) |
| unambiguous semidirect product | C113⋊(C5×D29) |
| Fitting, socle, Hall | C5×C29×C113 ⋊ C2 |
| derived, Hall | C29×C113 ⋊ C2×C5 |
| Hall | C5×C113 ⋊ D29 |
| Hall | C5×C29 ⋊ D113 |
| Sylow | C113 ⋊ C5×D29 |
| Sylow | C29 ⋊ C5×D113 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D3277 |
| commutator, cosocle, hypocenter | C29×C113 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C29×C113 | C2 |
| LCS | G ▷ C29×C113 | |
| UCS | C1 ◁ C5 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16385 |
8200 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32770, 4);