Finite Group DatabasebetaFinite Group Databasebeta| order | 32382 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C257 · Schur multiplier (H2) = C3 |
| direct product | C3⋊D21×C257 |
| unambiguous semidirect product | C3⋊(D21×C257) |
| unambiguous semidirect product | C7⋊(C3⋊D3×C257) |
| Fitting, socle, Hall | C32×C7×C257 ⋊ C2 |
| derived, Hall | C32×C7 ⋊ C2×C257 |
| Hall | C32×C257 ⋊ D7 |
| Hall | C7×C257 ⋊ C3⋊D3 |
| Sylow | C32 ⋊ D7×C257 |
| Sylow | C7 ⋊ C3⋊D3×C257 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C257 | C3⋊D21 |
| commutator, cosocle, hypocenter | C32×C7 | C2×C257 |
| Frattini | C1 | G |
| Fitting, socle | C32×C7×C257 | C2 |
| LCS | G ▷ C32×C7 | |
| UCS | C1 ◁ C257 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16191 |
8481 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32382, 31);