Finite Group DatabasebetaFinite Group Databasebeta| order | 9996 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C7×D17×D21 |
| unambiguous semidirect product | (C3×D17)⋊(C7×D7) |
| unambiguous semidirect product | (C7×D17)⋊(D3×C7) |
| Fitting, socle, Hall | C3×C72×C17 ⋊ C22 |
| derived | C3×C7×C17 ⋊ C22×C7 |
| Hall | C72×C17 ⋊ C2×D3 |
| Hall | C3×C72 ⋊ C2×D17 |
| Hall | C3×C17 ⋊ C2×C7×D7 |
| Sylow | C72 ⋊ D3×D17 |
| Sylow | C17 ⋊ C2×C7×D21 |
| Sylow | C3 ⋊ C7×D7×D17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D17×D21 |
| commutator, cosocle, hypocenter | C3×C7×C17 | C22×C7 |
| Frattini | C1 | G |
| Fitting, socle | C3×C72×C17 | C22 |
| LCS | G ▷ C3×C7×C17 | |
| UCS | C1 ◁ C7 | |
104 conjugacy classes of subgroups.
840 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9996, 147);