Finite Group DatabasebetaFinite Group Databasebeta| order | 2592 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C8 · Schur multiplier (H2) = C4 |
| direct product | C3×Dic3×AGL(1,𝔽9) |
| derived | C33 ⋊ C3×C4×C8 |
| Sylow | C34 ⋊ C4×C8 |
273 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 273 conjugacy classes of subgroups — too many to draw. Only its 76 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
162 conjugacy classes — view the full character table.
| maximal subgroup of | C3×Dic3×AΓL(1,𝔽9) |
| maximal normal subgroup of | C3×Dic3×AΓL(1,𝔽9) |
Past the SmallGroups library coverage — no SmallGroups id.