Finite Group DatabasebetaFinite Group Databasebeta| order | 5742 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×D261 |
| unambiguous semidirect product | C9⋊(C11×D29) |
| unambiguous semidirect product | C29⋊(C11×D9) |
| Fitting, Hall | C9×C11×C29 ⋊ C2 |
| derived, Hall | C9×C29 ⋊ C2×C11 |
| Hall | C11×C29 ⋊ D9 |
| Hall | C9×C11 ⋊ D29 |
| Sylow | C29 ⋊ C11×D9 |
| Sylow | C9 ⋊ C11×D29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D261 |
| commutator, hypocenter | C9×C29 | C2×C11 |
| Frattini | C3 | C11×D87 |
| Fitting | C9×C11×C29 | C2 |
| socle | C3×C11×C29 | D3 |
| LCS | G ▷ C9×C29 | |
| UCS | C1 ◁ C11 | |
24 conjugacy classes of subgroups.
1452 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C11×D9×D29, D11×D261, D99⋊D29, … |
| maximal normal subgroup of | C11×D9×D29, D11×D261, D99⋊D29, … |
| maximal quotient of | C11×Dic261, C2×C11×D261, C5×C11×D261, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5742, 6);