Finite Group DatabasebetaFinite Group Databasebeta| order | 9996 |
| isoclinism | isoclinic class of A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C17×C49 · Schur multiplier (H2) = C2 |
| direct product | A4×C17×C49 |
| unambiguous semidirect product | C22⋊(C3×C17×C49) |
| unambiguous semidirect product | (C22×C17)⋊(C3×C49) |
| Fitting, Hall | C22×C17×C49 ⋊ C3 |
| derived, Sylow | C22 ⋊ C3×C17×C49 |
| Hall | C22×C49 ⋊ C3×C17 |
| Hall | C22×C17 ⋊ C3×C49 |
30 conjugacy classes of subgroups.
3332 conjugacy classes. The character table is too large to display.
| maximal subgroup of | A4×C17×C49⋊C3, C3×A4×C17×C49 |
| maximal normal subgroup of | A4×C17×C49⋊C3, C3×A4×C17×C49 |
| maximal quotient of | C17×C22⋊C9×C49, C3×A4×C17×C49 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9996, 32);