Finite Group DatabasebetaFinite Group Databasebeta| order | 32382 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(ΓL(1,𝔽8)⋊D257) |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊D771 |
| unambiguous semidirect product | C257⋊(C3⋊AGL(1,𝔽7)) |
| unambiguous semidirect product | D5397⋊C3 |
| Fitting, socle, derived | C3×C7×C257 ⋊ C2×C3 |
| Hall | C3×ΓL(1,𝔽8)×C257 ⋊ C2 |
| Hall | C7×C257 ⋊ C3×D3 |
| Sylow | C257 ⋊ C3⋊AGL(1,𝔽7) |
| 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 |
Polycyclic presentation:
2,3^2,7,257|c^a=c^2,d^a=d^6,e^a=e^256,d^b=d^21932 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32382, 18);