Finite Group DatabasebetaFinite Group Databasebeta| order | 9996 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C17 · Schur multiplier (H2) = C2 |
| direct product | D3×C17×D49 |
| unambiguous semidirect product | (D3×C49)⋊(C2×C17) |
| unambiguous semidirect product | (C3×D49)⋊(C2×C17) |
| unambiguous semidirect product | D147⋊(C2×C17) |
| Fitting, Hall | C3×C17×C49 ⋊ C22 |
| derived, Hall | C3×C49 ⋊ C22×C17 |
| Hall | C17×C49 ⋊ C2×D3 |
| Hall | C3×C17 ⋊ C2×D49 |
| Sylow | C49 ⋊ C2×D3×C17 |
| Sylow | C3 ⋊ C2×C17×D49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | D3×D49 |
| commutator, cosocle, hypocenter | C3×C49 | C22×C17 |
| Frattini | C7 | D3×D7×C17 |
| Fitting | C3×C17×C49 | C22 |
| socle | C3×C7×C17 | C2×D7 |
| LCS | G ▷ C3×C49 | |
| UCS | C1 ◁ C17 | |
60 conjugacy classes of subgroups.
1326 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C17×D9×D49, D3×C17×D49⋊C3, C3×D3×C17×D49, … |
| maximal normal subgroup of | D3×C17×D49⋊C3, C3×D3×C17×D49 |
| maximal quotient of | C17×D9×D49, C3×D3×C17×D49, C17×C3⋊D3×D49, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9996, 27);