Finite Group DatabasebetaFinite Group Databasebeta| order | 32382 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | C9×D1799 |
| unambiguous semidirect product | C257⋊(C9×D7) |
| Fitting, Hall | C7×C9×C257 ⋊ C2 |
| derived, Hall | C7×C257 ⋊ C2×C9 |
| Hall | C9×C257 ⋊ D7 |
| Sylow | C257 ⋊ C9×D7 |
| Hall | C7×C9 ⋊ D257 |
| Sylow | C7 ⋊ C9×D257 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | D1799 |
| commutator, hypocenter | C7×C257 | C2×C9 |
| Frattini | C3 | C3×D1799 |
| Fitting | C7×C9×C257 | C2 |
| socle, cosocle | C3×C7×C257 | C2×C3 |
| prime radical | C3×D1799 | C3 |
| LCS | G ▷ C7×C257 | |
| UCS | C1 ◁ C9 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16191 |
8109 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32382, 5);