Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of D3×AGL(1,ℤ/9) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C8 · Schur multiplier (H2) = C2 |
| direct product | D3×3−1+2⋊C8 |
| unambiguous semidirect product | (D3×3−1+2)⋊C8 |
| unambiguous semidirect product | (D3×C9⋊C8)⋊C3 |
| derived | C3×C9 ⋊ C2×C3×C8 |
| Sylow | C3×3−1+2 ⋊ C2×C8 |
182 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 1308);