Finite Group DatabasebetaFinite Group Databasebeta| order | 8514 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C11⋊(D43⋊C9) |
| unambiguous semidirect product | (C43⋊C9)⋊D11 |
| unambiguous semidirect product | D473⋊C9 |
| derived, Hall | C11×C43 ⋊ C2×C9 |
| Hall | C11×C43⋊C9 ⋊ C2 |
| Hall | D473 ⋊ C9 |
| Hall | C43⋊C9 ⋊ D11 |
| Sylow | C43 ⋊ C9×D11 |
| Sylow | C11 ⋊ D43⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C11⋊(D43⋊C3) |
| commutator, hypocenter | C11×C43 | C2×C9 |
| Fitting, socle | C3×C11×C43 | C2×C3 |
| LCS | G ▷ C11×C43 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,11,43,3|b^3=e,c^a=c^10,d^a=d^42,d^b=d^36294 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, 12);