Finite Group DatabasebetaFinite Group Databasebeta| order | 8514 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | D33×C43⋊C3 |
| unambiguous semidirect product | C3⋊(D11×C43⋊C3) |
| unambiguous semidirect product | C11⋊(D3×C43⋊C3) |
| unambiguous semidirect product | (C43×D33)⋊C3 |
| Fitting, socle, derived | C3×C11×C43 ⋊ C2×C3 |
| Hall | C3×C11×C43⋊C3 ⋊ C2 |
| Hall | C11×C43 ⋊ C3×D3 |
| Hall | C3×C43⋊C3 ⋊ D11 |
| Sylow | C43 ⋊ C3×D33 |
| Sylow | C11 ⋊ D3×C43⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C11×C43 | C2×C3 |
| LCS | G ▷ C3×C11×C43 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
306 conjugacy classes — view the full character table.
| maximal subgroup of | D33×D43⋊C3, D33⋊(D43⋊C3), D3×D11×C43⋊C3, … |
| maximal normal subgroup of | D33×D43⋊C3, D33⋊(D43⋊C3), D3×D11×C43⋊C3, … |
| maximal quotient of | C43⋊C3×Dic33, C2×D33×C43⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8514, 20);