Finite Group DatabasebetaFinite Group Databasebeta| order | 2916 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C9 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×D3×C9×D9 |
| Fitting, Sylow | C32×C92 ⋊ C22 |
| derived | C3×C9 ⋊ C22×C3×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C9 | D3×D9 |
| commutator, hypocenter | C3×C9 | C22×C3×C9 |
| Frattini | C32 | C32×D32 |
| Fitting | C32×C92 | C22 |
| socle | C34 | C2×C3×D3 |
| prime radical | C32×D3×D9 | C3 |
| cosocle | C32×C9 | C22×C32 |
| LCS | G ▷ C3×C9 | |
| UCS | C1 ◁ C3×C9 | |
793 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 793 conjugacy classes of subgroups — too many to draw. Only its 130 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
486 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C9×D9×AGL(1,ℤ/9), C3×D3×#92265, C3×D3×D92, … |
| maximal normal subgroup of | C3×D3×#92265, C3×D3×D92, D32×C9×D9, … |
| maximal quotient of | C9×D9×AGL(1,ℤ/9) |
Past the SmallGroups library coverage — no SmallGroups id.