Finite Group DatabasebetaFinite Group Databasebeta| order | 3456 |
| isoclinism | isoclinic class of AGL(1,𝔽9) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C8×C16 · Schur multiplier (H2) = C8 |
| direct product | C3×C16×AGL(1,𝔽9) |
| Fitting | C33×C16 ⋊ C8 |
| derived | C32 ⋊ C3×C8×C16 |
| Sylow | C33 ⋊ C8×C16 |
246 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 114 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×C16×AΓL(1,𝔽9), C3×C32×AGL(1,𝔽9), C3×#72219115 |
| maximal normal subgroup of | C3×C16×AΓL(1,𝔽9), C3×C32×AGL(1,𝔽9), C3×#72219115 |
| maximal quotient of | C3×C32×AGL(1,𝔽9) |
Past the SmallGroups library coverage — no SmallGroups id.