Finite Group DatabasebetaFinite Group Databasebeta| order | 5742 |
| isoclinism | isoclinic class of D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9×C29 · Schur multiplier (H2) = C1 |
| direct product | C9×D11×C29 |
| unambiguous semidirect product | C11⋊(C2×C9×C29) |
| Fitting, Hall | C9×C11×C29 ⋊ C2 |
| derived, Sylow | C11 ⋊ C2×C9×C29 |
| Hall | C11×C29 ⋊ C2×C9 |
| Hall | C9×C11 ⋊ C2×C29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9×C29 | D11 |
| commutator, hypocenter | C11 | C2×C9×C29 |
| Frattini | C3 | C3×D11×C29 |
| Fitting | C9×C11×C29 | C2 |
| socle | C3×C11×C29 | C2×C3 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C9×C29 | |
24 conjugacy classes of subgroups.
1827 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C9×D11×D29, D9×D11×C29, D11×D261, … |
| maximal normal subgroup of | C9×D11×D29, D9×D11×C29, D11×D261, … |
| maximal quotient of | C9×C29×Dic11, C2×C9×D11×C29, C5×C9×D11×C29, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5742, 3);