Finite Group DatabasebetaFinite Group Databasebeta| order | 5742 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C3 |
| direct product | C11×C3⋊D87 |
| unambiguous semidirect product | C3⋊(C11×D87) |
| unambiguous semidirect product | C29⋊(C11×C3⋊D3) |
| Fitting, socle, Hall | C32×C11×C29 ⋊ C2 |
| derived, Hall | C32×C29 ⋊ C2×C11 |
| Hall | C11×C29 ⋊ C3⋊D3 |
| Hall | C32×C11 ⋊ D29 |
| Sylow | C29 ⋊ C11×C3⋊D3 |
| Sylow | C32 ⋊ C11×D29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | C3⋊D87 |
| commutator, hypocenter | C32×C29 | C2×C11 |
| Frattini | C1 | G |
| Fitting, socle | C32×C11×C29 | C2 |
| LCS | G ▷ C32×C29 | |
| UCS | C1 ◁ C11 | |
48 conjugacy classes of subgroups.
1452 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C11×C3⋊D3×D29, D11×C3⋊D87, D319⋊(C3⋊D3), … |
| maximal normal subgroup of | C11×C3⋊D3×D29, D11×C3⋊D87, D319⋊(C3⋊D3), … |
| maximal quotient of | C11×C3⋊Dic87, C2×C11×C3⋊D87, C5×C11×C3⋊D87, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5742, 18);