Finite Group DatabasebetaFinite Group Databasebeta| order | 32382 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | ΓL(1,𝔽8)×D771 |
| unambiguous semidirect product | C3⋊(ΓL(1,𝔽8)×D257) |
| unambiguous semidirect product | C257⋊(D3×ΓL(1,𝔽8)) |
| unambiguous semidirect product | (C7×D771)⋊C3 |
| Fitting, socle, derived | C3×C7×C257 ⋊ C2×C3 |
| Hall | C3×ΓL(1,𝔽8)×C257 ⋊ C2 |
| Hall | C7×C257 ⋊ C3×D3 |
| Sylow | C257 ⋊ D3×ΓL(1,𝔽8) |
| Hall | C3×ΓL(1,𝔽8) ⋊ D257 |
| Sylow | C7 ⋊ C3×D771 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C7×C257 | C2×C3 |
| LCS | G ▷ C3×C7×C257 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5397 |
1935 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32382, 20);