Finite Group DatabasebetaFinite Group Databasebeta| order | 6732 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C11 · Schur multiplier (H2) = C3 |
| direct product | C11×#10597479 |
| Fitting, socle, Hall | C32×C11×C17 ⋊ C4 |
| derived, Hall | C32×C17 ⋊ C4×C11 |
| Hall | C11×C17 ⋊ #157 |
| Hall | C32×C11 ⋊ #595 |
| Sylow | C17 ⋊ C11×#157 |
| Sylow | C32 ⋊ C11×#595 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | #10597479 |
| commutator, hypocenter | C32×C17 | C4×C11 |
| Frattini | C1 | G |
| Fitting, socle | C32×C11×C17 | C4 |
| LCS | G ▷ C32×C17 | |
| UCS | C1 ◁ C11 | |
40 conjugacy classes of subgroups.
462 conjugacy classes — view the full character table.
| maximal subgroup of | C11⋊C5×#10597479, C5×C11×#10597479, C11×#15690390, … |
| maximal normal subgroup of | C11⋊C5×#10597479, C5×C11×#10597479 |
| maximal quotient of | C5×C11×#10597479, C11×#15690390, C11×#15690391, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6732, 72);