Finite Group DatabasebetaFinite Group Databasebeta| order | 6732 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C32×Dic187 |
| unambiguous semidirect product | C11⋊(C32×Dic17) |
| derived, Hall | C11×C17 ⋊ C32×C4 |
| Hall | C32×C11×C17 ⋊ C4 |
| Hall | C32×C17 ⋊ Dic11 |
| Hall | C32×C11 ⋊ Dic17 |
| Sylow | C17 ⋊ C32×Dic11 |
| Sylow | C11 ⋊ C32×Dic17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32 | D187 |
| commutator, hypocenter | C11×C17 | C32×C4 |
| Frattini | C2 | C32×D187 |
| Fitting, socle | C2×C32×C11×C17 | C2 |
| LCS | G ▷ C11×C17 | |
| UCS | C1 ◁ C2×C32 | |
72 conjugacy classes of subgroups.
1710 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×(C11⋊C5)⋊Dic17, C32×Dic935, C32×C5×Dic187, … |
| maximal normal subgroup of | C32×(C11⋊C5)⋊Dic17, C32×C5×Dic187 |
| maximal quotient of | C32×Dic935, C32×C5×Dic187, C32×C11⋊#66774 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6732, 32);