Finite Group DatabasebetaFinite Group Databasebeta| order | 2916 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C9 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×D3×D9⋊C9 |
| Fitting, Sylow | C32×C9⋊C9 ⋊ C22 |
| derived | C3×C9 ⋊ C22×C3×C9 |
658 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 658 conjugacy classes of subgroups — too many to draw. Only its 118 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
270 conjugacy classes. The character table is too large to display.
| maximal subgroup of | AGL(1,ℤ/9)×D9⋊C9, C3×D3×#92265, D32×D9⋊C9, … |
| maximal normal subgroup of | C3×D3×#92265, D32×D9⋊C9 |
| maximal quotient of | AGL(1,ℤ/9)×D9⋊C9, C3×D3×AGL(1,ℤ/27) |
Past the SmallGroups library coverage — no SmallGroups id.