Finite Group DatabasebetaFinite Group Databasebeta| order | 32422 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C43 · Schur multiplier (H2) = C1 |
| direct product | C43×D377 |
| unambiguous semidirect product | C13⋊(C43×D29) |
| unambiguous semidirect product | C29⋊(D13×C43) |
| Fitting, socle, Hall | C13×C29×C43 ⋊ C2 |
| derived, Hall | C13×C29 ⋊ C2×C43 |
| Hall | C29×C43 ⋊ D13 |
| Hall | C13×C43 ⋊ D29 |
| Sylow | C29 ⋊ D13×C43 |
| Sylow | C13 ⋊ C43×D29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C43 | D377 |
| commutator, cosocle, hypocenter | C13×C29 | C2×C43 |
| Frattini | C1 | G |
| Fitting, socle | C13×C29×C43 | C2 |
| LCS | G ▷ C13×C29 | |
| UCS | C1 ◁ C43 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16211 |
8170 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32422, 7);