| order | 3456 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29×C3 |
| direct product | C2×D3×M16×C3⋊D3 |
| Fitting | C2×C33×M16 ⋊ C22 |
| Sylow | C33 ⋊ C23×M16 |
11512 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
360 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.