Finite Group DatabasebetaFinite Group Databasebeta| order | 5742 |
| isoclinism | isoclinic class of D29 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9×C11 · Schur multiplier (H2) = C1 |
| direct product | C9×C11×D29 |
| unambiguous semidirect product | C29⋊(C2×C9×C11) |
| Fitting, Hall | C9×C11×C29 ⋊ C2 |
| derived, Sylow | C29 ⋊ C2×C9×C11 |
| Hall | C11×C29 ⋊ C2×C9 |
| Hall | C9×C29 ⋊ C2×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9×C11 | D29 |
| commutator, hypocenter | C29 | C2×C9×C11 |
| Frattini | C3 | C3×C11×D29 |
| Fitting | C9×C11×C29 | C2 |
| socle | C3×C11×C29 | C2×C3 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C9×C11 | |
24 conjugacy classes of subgroups.
1584 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C9×C11×#1181, C9×C11⋊#1181, C9×D11×D29, … |
| maximal normal subgroup of | C9×C11×#1181, C9×C11⋊#1181, C9×D11×D29, … |
| maximal quotient of | C9×C11×Dic29, C2×C9×C11×D29, C5×C9×C11×D29, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5742, 2);