Finite Group DatabasebetaFinite Group Databasebeta| order | 5676 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×D11×C43⋊C3 |
| unambiguous semidirect product | C11⋊(C22×C43⋊C3) |
| unambiguous semidirect product | (C2×C11)⋊(C2×C43⋊C3) |
| unambiguous semidirect product | (C2×D11×C43)⋊C3 |
| Fitting, socle | C2×C11×C43 ⋊ C2×C3 |
| derived, Hall | C11×C43 ⋊ C22×C3 |
| Hall | C2×D11×C43 ⋊ C3 |
| Hall | C11×C43⋊C3 ⋊ C22 |
| Sylow | C43 ⋊ C2×C3×D11 |
| Sylow | C11 ⋊ C22×C43⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D11×C43⋊C3 |
| commutator, hypocenter | C11×C43 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C11×C43 | C2×C3 |
| LCS | G ▷ C11×C43 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
238 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5676, 17);