Finite Group DatabasebetaFinite Group Databasebeta| order | 9009 |
| isoclinism | isoclinic class of #63270 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C11 · Schur multiplier (H2) = C3 |
| direct product | C3×C11×#63270 |
| Fitting, socle | C3×C7×C11×C13 ⋊ C3 |
| derived, Hall | C7×C13 ⋊ C32×C11 |
| Hall | C7×C11×C13 ⋊ C32 |
| Hall | C11×C13 ⋊ C3×ΓL(1,𝔽8) |
| Hall | C7×C11 ⋊ C3×C13⋊C3 |
| Sylow | C13 ⋊ C3×C11×ΓL(1,𝔽8) |
| Sylow | C7 ⋊ C3×C11×C13⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C11 | #63270 |
| commutator, hypocenter | C7×C13 | C32×C11 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C11×C13 | C3 |
| LCS | G ▷ C7×C13 | |
| UCS | C1 ◁ C3×C11 | |
48 conjugacy classes of subgroups.
1089 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9009, 8);