Finite Group DatabasebetaFinite Group Databasebeta| order | 6732 |
| isoclinism | isoclinic class of D17 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4×C11 · Schur multiplier (H2) = C3 |
| direct product | C32×C11×Dic17 |
| derived, Sylow | C17 ⋊ C32×C4×C11 |
| Hall | C32×C11×C17 ⋊ C4 |
| Hall | C11×C17 ⋊ C32×C4 |
| Hall | C32×C17 ⋊ C4×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32×C11 | D17 |
| commutator, hypocenter | C17 | C32×C4×C11 |
| Frattini | C2 | C32×C11×D17 |
| Fitting, socle | C2×C32×C11×C17 | C2 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C2×C32×C11 | |
72 conjugacy classes of subgroups.
1980 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×C11⋊C5×Dic17, C32×C11×Dic85, C32×C5×C11×Dic17, … |
| maximal normal subgroup of | C32×C11⋊C5×Dic17, C32×C5×C11×Dic17 |
| maximal quotient of | C32×C11×Dic85, C32×C5×C11×Dic17, C32×C11×#66774 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6732, 30);