Finite Group DatabasebetaFinite Group Databasebeta| order | 9933 |
| isoclinism | isoclinic class of C43⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C7×C11 · Schur multiplier (H2) = C1 |
| direct product | C7×C11×C43⋊C3 |
| Fitting, socle, Hall | C7×C11×C43 ⋊ C3 |
| derived, Sylow | C43 ⋊ C3×C7×C11 |
| Hall | C11×C43 ⋊ C3×C7 |
| Hall | C7×C43 ⋊ C3×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7×C11 | C43⋊C3 |
| commutator, hypocenter | C43 | C3×C7×C11 |
| Frattini | C1 | G |
| Fitting, socle | C7×C11×C43 | C3 |
| LCS | G ▷ C43 | |
| UCS | C1 ◁ C7×C11 | |
16 conjugacy classes of subgroups.
1309 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C11×ΓL(1,𝔽8)×C43⋊C3, C3×C7×C11×C43⋊C3 |
| maximal normal subgroup of | C11×ΓL(1,𝔽8)×C43⋊C3, C3×C7×C11×C43⋊C3 |
| maximal quotient of | C7×C11×C43⋊C9, C3×C7×C11×C43⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9933, 3);