Finite Group DatabasebetaFinite Group Databasebeta| order | 8514 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C3×D11×C43⋊C3 |
| unambiguous semidirect product | C11⋊(C2×C3×C43⋊C3) |
| unambiguous semidirect product | (D11×C43)⋊C32 |
| unambiguous semidirect product | (C3×D11×C43)⋊C3 |
| Fitting, socle | C3×C11×C43 ⋊ C2×C3 |
| derived, Hall | C11×C43 ⋊ C2×C32 |
| Hall | C3×C11×C43⋊C3 ⋊ C2 |
| Hall | D11×C43 ⋊ C32 |
| Sylow | C43 ⋊ C32×D11 |
| Sylow | C11 ⋊ C2×C3×C43⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D11×C43⋊C3 |
| commutator, hypocenter | C11×C43 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C11×C43 | C2×C3 |
| LCS | G ▷ C11×C43 | |
| UCS | C1 ◁ C3 | |
48 conjugacy classes of subgroups.
357 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D11×D43⋊C3, D11×C3⋊(D43⋊C3), D3×D11×C43⋊C3, … |
| maximal normal subgroup of | C3×D11×D43⋊C3, D11×C3⋊(D43⋊C3), D3×D11×C43⋊C3, … |
| maximal quotient of | C3×Dic11×C43⋊C3, C2×C3×D11×C43⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8514, 16);