Finite Group DatabasebetaFinite Group Databasebeta| order | 6732 |
| isoclinism | isoclinic class of #595 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9×C11 · Schur multiplier (H2) = C1 |
| direct product | C9×C11×#595 |
| Fitting, Hall | C9×C11×C17 ⋊ C4 |
| derived, Sylow | C17 ⋊ C4×C9×C11 |
| Hall | C11×C17 ⋊ C4×C9 |
| Hall | C9×C17 ⋊ C4×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9×C11 | #595 |
| commutator, hypocenter | C17 | C4×C9×C11 |
| Frattini | C3 | C3×C11×#595 |
| Fitting | C9×C11×C17 | C4 |
| socle | C3×C11×C17 | C3×C4 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C9×C11 | |
36 conjugacy classes of subgroups.
792 conjugacy classes — view the full character table.
| maximal subgroup of | C9×C11⋊C5×#595, C5×C9×C11×#595, C9×C11×#66775, … |
| maximal normal subgroup of | C9×C11⋊C5×#595, C5×C9×C11×#595 |
| maximal quotient of | C5×C9×C11×#595, C9×C11×#66775, C9×C11×#66776, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6732, 10);