Finite Group DatabasebetaFinite Group Databasebeta| order | 9009 |
| isoclinism | isoclinic class of C13⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C7×C9×C11 · Schur multiplier (H2) = C1 |
| direct product | C7×C11×C13⋊C9 |
| unambiguous semidirect product | C13⋊(C7×C9×C11) |
| unambiguous semidirect product | (C11×C13)⋊(C7×C9) |
| derived, Sylow | C13 ⋊ C7×C9×C11 |
| Hall | C7×C11×C13 ⋊ C9 |
| Hall | C11×C13 ⋊ C7×C9 |
| Hall | C7×C13 ⋊ C9×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C7×C11 | C13⋊C3 |
| commutator, hypocenter | C13 | C7×C9×C11 |
| Frattini | C3 | C7×C11×C13⋊C3 |
| Fitting, socle | C3×C7×C11×C13 | C3 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C3×C7×C11 | |
24 conjugacy classes of subgroups.
1617 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C7×C11×C13⋊C9, C7×C11×D13⋊C9, C7×D11×C13⋊C9, … |
| maximal normal subgroup of | C2×C7×C11×C13⋊C9, C7×C11×D13⋊C9, C7×D11×C13⋊C9, … |
| maximal quotient of | C2×C7×C11×C13⋊C9, C7×C11×C22⋊(C13⋊C9) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9009, 2);