Finite Group DatabasebetaFinite Group Databasebeta| order | 5082 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×ΓL(1,𝔽8)×D11 |
| unambiguous semidirect product | C11⋊(C2×C11×ΓL(1,𝔽8)) |
| unambiguous semidirect product | (C7×D11)⋊(C3×C11) |
| unambiguous semidirect product | (C7×C11×D11)⋊C3 |
| Fitting, socle, Hall | C7×C112 ⋊ C2×C3 |
| derived | C7×C11 ⋊ C2×C3×C11 |
| Hall | C112×ΓL(1,𝔽8) ⋊ C2 |
| Hall | C7×C11×D11 ⋊ C3 |
| Sylow | C112 ⋊ C2×ΓL(1,𝔽8) |
| Sylow | C7 ⋊ C3×C11×D11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | ΓL(1,𝔽8)×D11 |
| commutator, hypocenter | C7×C11 | C2×C3×C11 |
| Frattini | C1 | G |
| Fitting, socle | C7×C112 | C2×C3 |
| LCS | G ▷ C7×C11 | |
| UCS | C1 ◁ C11 | |
52 conjugacy classes of subgroups.
385 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5082, 21);