Finite Group DatabasebetaFinite Group Databasebeta| order | 32382 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C7⋊C9)⋊D257 |
| unambiguous semidirect product | C257⋊(D7⋊C9) |
| unambiguous semidirect product | D1799⋊C9 |
| derived, Hall | C7×C257 ⋊ C2×C9 |
| Hall | C7⋊C9×C257 ⋊ C2 |
| Hall | D1799 ⋊ C9 |
| Sylow | C257 ⋊ D7⋊C9 |
| Hall | C7⋊C9 ⋊ D257 |
| Sylow | C7 ⋊ C9×D257 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | ΓL(1,𝔽8)⋊D257 |
| commutator, hypocenter | C7×C257 | C2×C9 |
| Fitting, socle, cosocle | C3×C7×C257 | C2×C3 |
| prime radical | C3×D1799 | C3 |
| LCS | G ▷ C7×C257 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16191 |
Polycyclic presentation:
2,3,7,257,3|b^3=e,c^a=c^6,d^a=d^256,c^b=c^21941 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32382, 12);