Finite Group DatabasebetaFinite Group Databasebeta| order | 9996 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×D17×D49 |
| Fitting, Hall | C3×C17×C49 ⋊ C22 |
| derived, Hall | C17×C49 ⋊ C22×C3 |
| Hall | C3×C49 ⋊ C2×D17 |
| Hall | C3×C17 ⋊ C2×D49 |
| Sylow | C49 ⋊ C2×C3×D17 |
| Sylow | C17 ⋊ C2×C3×D49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D17×D49 |
| commutator, cosocle, hypocenter | C17×C49 | C22×C3 |
| Frattini | C7 | C3×D7×D17 |
| Fitting | C3×C17×C49 | C22 |
| socle | C3×C7×C17 | C2×D7 |
| LCS | G ▷ C17×C49 | |
| UCS | C1 ◁ C3 | |
60 conjugacy classes of subgroups.
780 conjugacy classes — view the full character table.
| maximal subgroup of | D17×D49⋊C9, C9×D17×D49, C3×D17×D49⋊C3, … |
| maximal normal subgroup of | D17×D49⋊C9, C9×D17×D49, C3×D17×D49⋊C3, … |
| maximal quotient of | C9×D17×D49, C32×D17×D49, C3×D17×D147, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9996, 24);