Finite Group DatabasebetaFinite Group Databasebeta| order | 9996 |
| isoclinism | isoclinic class of D17 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C49 · Schur multiplier (H2) = C1 |
| direct product | C3×C49×Dic17 |
| derived, Sylow | C17 ⋊ C3×C4×C49 |
| Hall | C3×C17×C49 ⋊ C4 |
| Hall | C17×C49 ⋊ C3×C4 |
| Hall | C3×C17 ⋊ C4×C49 |
36 conjugacy classes of subgroups.
2940 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Dic17×C49⋊C9, C9×C49×Dic17, C3×Dic17×C49⋊C3, … |
| maximal normal subgroup of | Dic17×C49⋊C9, C9×C49×Dic17, C3×Dic17×C49⋊C3, … |
| maximal quotient of | C9×C49×Dic17, C32×C49×Dic17, C3×C49×Dic51 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9996, 6);