Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of D3×AGL(1,ℤ/9) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C4 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×D3×3−1+2⋊C4 |
| unambiguous semidirect product | (D3×Dic9)⋊C32 |
| unambiguous semidirect product | (C3×D3×Dic9)⋊C3 |
| derived | C3×C9 ⋊ C2×C32×C4 |
| Sylow | C32×3−1+2 ⋊ C2×C4 |
566 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 122 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.
| maximal subgroup of | D3×#11757569, D3×(C3⋊AGL(1,ℤ/9))⋊C4, C3×D3×#611⋊C3, … |
| maximal normal subgroup of | D3×#11757569, D3×(C3⋊AGL(1,ℤ/9))⋊C4, C3×D3×#611⋊C3, … |
| maximal quotient of | D3×#11757569 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3030);