Finite Group DatabasebetaFinite Group Databasebeta| order | 32382 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×D2313 |
| unambiguous semidirect product | C9⋊(C7×D257) |
| unambiguous semidirect product | C257⋊(C7×D9) |
| Fitting, Hall | C7×C9×C257 ⋊ C2 |
| derived, Hall | C9×C257 ⋊ C2×C7 |
| Hall | C7×C257 ⋊ D9 |
| Sylow | C257 ⋊ C7×D9 |
| Hall | C7×C9 ⋊ D257 |
| Sylow | C9 ⋊ C7×D257 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D2313 |
| commutator, cosocle, hypocenter | C9×C257 | C2×C7 |
| Frattini | C3 | C7×D771 |
| Fitting | C7×C9×C257 | C2 |
| socle | C3×C7×C257 | D3 |
| LCS | G ▷ C9×C257 | |
| UCS | C1 ◁ C7 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16191 |
8106 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32382, 7);