Finite Group DatabasebetaFinite Group Databasebeta| order | 2916 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2 |
| direct product | D3×#6894⋊C2 |
| Fitting, Sylow | C3×#6894 ⋊ C22 |
475 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 475 conjugacy classes of subgroups — too many to draw. Only its 79 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
126 conjugacy classes — view the full character table.
| maximal subgroup of | #72243315, D3×3−1+2×AGL(1,ℤ/9), #72243339, … |
| maximal normal subgroup of | D3×3−1+2×AGL(1,ℤ/9) |
| maximal quotient of | #72243315, #72243339, D9×#6894⋊C2, … |
Past the SmallGroups library coverage — no SmallGroups id.