Finite Group DatabasebetaFinite Group Databasebeta| order | 9996 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C17×C49 · Schur multiplier (H2) = C2 |
| direct product | C2×D3×C17×C49 |
| unambiguous semidirect product | C3⋊(C22×C17×C49) |
| unambiguous semidirect product | (C2×C3)⋊(C2×C17×C49) |
| Fitting | C2×C3×C17×C49 ⋊ C2 |
| derived, Sylow | C3 ⋊ C22×C17×C49 |
| Hall | C3×C17×C49 ⋊ C22 |
| Hall | C3×C49 ⋊ C22×C17 |
| Hall | C3×C17 ⋊ C22×C49 |
60 conjugacy classes of subgroups.
4998 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C17×D9×C49, C2×D3×C17×C49⋊C3, D32×C17×C49, … |
| maximal normal subgroup of | C2×D3×C17×C49⋊C3, C2×C3×D3×C17×C49 |
| maximal quotient of | C2×C17×D9×C49, D32×C17×C49, C2×C17×C3⋊D3×C49, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9996, 37);