Finite Group DatabasebetaFinite Group Databasebeta| order | 6732 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×C9⋊#595 |
| unambiguous semidirect product | C9⋊(C11×#595) |
| Fitting, Hall | C9×C11×C17 ⋊ C4 |
| derived, Hall | C9×C17 ⋊ C4×C11 |
| Hall | C11×C17 ⋊ Dic9 |
| Hall | C9×C11 ⋊ #595 |
| Sylow | C17 ⋊ C11×Dic9 |
| Sylow | C9 ⋊ C11×#595 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | C9⋊#595 |
| commutator, hypocenter | C9×C17 | C4×C11 |
| Frattini | C3 | C11×C3⋊#595 |
| Fitting | C9×C11×C17 | C4 |
| socle | C3×C11×C17 | Dic3 |
| LCS | G ▷ C9×C17 | |
| UCS | C1 ◁ C11 | |
36 conjugacy classes of subgroups.
528 conjugacy classes — view the full character table.
| maximal subgroup of | C11⋊C5×C9⋊#595, C5×C11×C9⋊#595, C11×C9⋊#66775, … |
| maximal normal subgroup of | C11⋊C5×C9⋊#595, C5×C11×C9⋊#595 |
| maximal quotient of | C5×C11×C9⋊#595, C11×C9⋊#66775, C11×C9⋊#66776, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6732, 13);