Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of D3×AGL(1,ℤ/9) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C9 · Schur multiplier (H2) = C2 |
| direct product | Dic3×D9⋊C9 |
| unambiguous semidirect product | D9⋊(C9×Dic3) |
| unambiguous semidirect product | (Dic3×D9)⋊C9 |
| unambiguous semidirect product | (C3×D9⋊C9)⋊C4 |
| derived | C3×C9 ⋊ C2×C4×C9 |
| Sylow | C3×C9⋊C9 ⋊ C2×C4 |
232 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
180 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 1164);