Finite Group DatabasebetaFinite Group Databasebeta| order | 6732 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| direct product | C9×C11⋊#595 |
| unambiguous semidirect product | C11⋊(C9×#595) |
| Fitting, Hall | C9×C11×C17 ⋊ C4 |
| derived, Hall | C11×C17 ⋊ C4×C9 |
| Hall | C9×C17 ⋊ Dic11 |
| Hall | C9×C11 ⋊ #595 |
| Sylow | C17 ⋊ C9×Dic11 |
| Sylow | C11 ⋊ C9×#595 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | C11⋊#595 |
| commutator, hypocenter | C11×C17 | C4×C9 |
| Frattini | C3 | C3×C11⋊#595 |
| Fitting | C9×C11×C17 | C4 |
| socle | C3×C11×C17 | C3×C4 |
| LCS | G ▷ C11×C17 | |
| UCS | C1 ◁ C9 | |
36 conjugacy classes of subgroups.
522 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, 11);