Finite Group DatabasebetaFinite Group Databasebeta| order | 32422 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C29 · Schur multiplier (H2) = C1 |
| direct product | C29×D559 |
| unambiguous semidirect product | C13⋊(C29×D43) |
| unambiguous semidirect product | C43⋊(D13×C29) |
| Fitting, socle, Hall | C13×C29×C43 ⋊ C2 |
| derived, Hall | C13×C43 ⋊ C2×C29 |
| Hall | C29×C43 ⋊ D13 |
| Hall | C13×C29 ⋊ D43 |
| Sylow | C43 ⋊ D13×C29 |
| Sylow | C13 ⋊ C29×D43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C29 | D559 |
| commutator, cosocle, hypocenter | C13×C43 | C2×C29 |
| Frattini | C1 | G |
| Fitting, socle | C13×C29×C43 | C2 |
| LCS | G ▷ C13×C43 | |
| UCS | C1 ◁ C29 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16211 |
8149 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32422, 6);