Finite Group DatabasebetaFinite Group Databasebeta| order | 5676 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D11×D129 |
| unambiguous semidirect product | (C3×D11)⋊D43 |
| unambiguous semidirect product | (D11×C43)⋊D3 |
| Fitting, socle, derived, Hall | C3×C11×C43 ⋊ C22 |
| Hall | C11×C43 ⋊ C2×D3 |
| Hall | C3×C43 ⋊ C2×D11 |
| Sylow | C43 ⋊ D3×D11 |
| Hall | C3×C11 ⋊ C2×D43 |
| Sylow | C11 ⋊ C2×D129 |
| Sylow | C3 ⋊ D11×D43 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C11×C43 | C22 |
| LCS | G ▷ C3×C11×C43 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
462 conjugacy classes — view the full character table.
| maximal subgroup of | D11×D387, D11×C3⋊(D43⋊C3), C3×D11×D129, … |
| maximal normal subgroup of | D11×C3⋊(D43⋊C3), C3×D11×D129, AGL(1,𝔽11)×D129, … |
| maximal quotient of | D11×D387, C3×D11×D129, D11×C3⋊D129, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5676, 22);