Finite Group DatabasebetaFinite Group Databasebeta| order | 3456 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C32 · Schur multiplier (H2) = C4 |
| direct product | C3×#11772656 |
| derived | C32 ⋊ C3×C4×C32 |
| Sylow | C33 ⋊ C4×C32 |
182 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 82 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
432 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×#72219099, C3×C32×AGL(1,𝔽9), C3×#72219114 |
| maximal normal subgroup of | C3×#72219099, C3×C32×AGL(1,𝔽9), C3×#72219114 |
Past the SmallGroups library coverage — no SmallGroups id.