Finite Group DatabasebetaFinite Group Databasebeta| order | 9009 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×#11717942 |
| derived, Hall | C7×C13 ⋊ C9×C11 |
| Hall | C7×C11×C13 ⋊ C9 |
| Hall | C11×C13 ⋊ C7⋊C9 |
| Hall | C7×C11 ⋊ C13⋊C9 |
| Sylow | C13 ⋊ C11×C7⋊C9 |
| Sylow | C7 ⋊ C11×C13⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C11 | #63271 |
| commutator, hypocenter | C7×C13 | C9×C11 |
| Frattini | C3 | C11×#63271 |
| Fitting, socle | C3×C7×C11×C13 | C3 |
| LCS | G ▷ C7×C13 | |
| UCS | C1 ◁ C3×C11 | |
24 conjugacy classes of subgroups.
1089 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C11×#11717942, C11×#13109897, D11×#11717942, … |
| maximal normal subgroup of | C2×C11×#11717942, C11×#13109897, D11×#11717942, … |
| maximal quotient of | C2×C11×#11717942, C11×C22⋊#11717942 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9009, 5);