Finite Group DatabasebetaFinite Group Databasebeta| order | 9933 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C7×C11 · Schur multiplier (H2) = C1 |
| Fitting, socle, Hall | C11×C43 ⋊ C3×C7 |
| derived, Sylow | C43 ⋊ C3×C7×C11 |
| Hall | C11×C43⋊C7 ⋊ C3 |
| Hall | C11×C43⋊C3 ⋊ C7 |
| Hall | C43⋊C7 ⋊ C3×C11 |
| Hall | C43⋊C3 ⋊ C7×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | (C43⋊C3)⋊C7 |
| commutator, hypocenter | C43 | C3×C7×C11 |
| Frattini | C1 | G |
| Fitting, socle | C11×C43 | C3×C7 |
| LCS | G ▷ C43 | |
| UCS | C1 ◁ C11 | |
16 conjugacy classes of subgroups.
253 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C11×(C43⋊C3)⋊C7 |
| maximal normal subgroup of | C3×C11×(C43⋊C3)⋊C7 |
| maximal quotient of | C11×(C43⋊C7)⋊C9, C3×C11×(C43⋊C3)⋊C7 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9933, 7);