Finite Group DatabasebetaFinite Group Databasebeta| order | 5082 |
| isoclinism | isoclinic class of AGL(1,𝔽7) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C121 · Schur multiplier (H2) = C1 |
| direct product | AGL(1,𝔽7)×C121 |
| unambiguous semidirect product | D7⋊(C3×C121) |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊(C2×C121) |
| unambiguous semidirect product | (D7×C121)⋊C3 |
| Fitting, Hall | C7×C121 ⋊ C2×C3 |
| derived, Sylow | C7 ⋊ C2×C3×C121 |
| Hall | ΓL(1,𝔽8)×C121 ⋊ C2 |
| Hall | D7×C121 ⋊ C3 |
| Hall | ΓL(1,𝔽8) ⋊ C2×C121 |
| Hall | D7 ⋊ C3×C121 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C121 | AGL(1,𝔽7) |
| commutator, hypocenter | C7 | C2×C3×C121 |
| Frattini | C11 | C11×AGL(1,𝔽7) |
| Fitting | C7×C121 | C2×C3 |
| socle | C7×C11 | C2×C3×C11 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C121 | |
24 conjugacy classes of subgroups.
847 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5082, 3);