Finite Group DatabasebetaFinite Group Databasebeta| order | 8514 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×D43⋊C9 |
| unambiguous semidirect product | D43⋊(C9×C11) |
| unambiguous semidirect product | (C43⋊C9)⋊(C2×C11) |
| unambiguous semidirect product | (C11×D43)⋊C9 |
| derived, Sylow | C43 ⋊ C2×C9×C11 |
| Hall | C11×C43⋊C9 ⋊ C2 |
| Hall | C11×D43 ⋊ C9 |
| Hall | C11×C43 ⋊ C2×C9 |
| Hall | C43⋊C9 ⋊ C2×C11 |
| Hall | D43 ⋊ C9×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C11 | D43⋊C3 |
| commutator, hypocenter | C43 | C2×C9×C11 |
| Frattini | C3 | C11×D43⋊C3 |
| Fitting, socle | C3×C11×C43 | C2×C3 |
| LCS | G ▷ C43 | |
| UCS | C1 ◁ C3×C11 | |
24 conjugacy classes of subgroups.
429 conjugacy classes — view the full character table.
| maximal subgroup of | D11×D43⋊C9, C2×C11×D43⋊C9 |
| maximal normal subgroup of | D11×D43⋊C9, C2×C11×D43⋊C9 |
| maximal quotient of | C11×Dic43⋊C9, C2×C11×D43⋊C9 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8514, 10);