Finite Group DatabasebetaFinite Group Databasebeta| order | 5094 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C3×D283⋊C3 |
| unambiguous semidirect product | D283⋊C32 |
| unambiguous semidirect product | (C283⋊C3)⋊(C2×C3) |
| unambiguous semidirect product | (C3×D283)⋊C3 |
| Fitting, socle | C3×C283 ⋊ C2×C3 |
| derived, Sylow | C283 ⋊ C2×C32 |
| Hall | C3×C283⋊C3 ⋊ C2 |
| Hall | D283 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D283⋊C3 |
| commutator, hypocenter | C283 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C283 | C2×C3 |
| LCS | G ▷ C283 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
159 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C5×D283⋊C3, C3×C5⋊(D283⋊C3), ΓL(1,𝔽8)⋊(D283⋊C3), … |
| maximal normal subgroup of | C3×C5×D283⋊C3, C3×C7×D283⋊C3 |
| maximal quotient of | C3×C5×D283⋊C3, C3×C5⋊(D283⋊C3), ΓL(1,𝔽8)⋊(D283⋊C3), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5094, 8);