Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of D32×D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C3×D32×D9 |
| Fitting, Sylow | C33×C9 ⋊ C23 |
| derived | C32×C9 ⋊ C23×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D32×D9 |
| commutator, cosocle, hypocenter | C32×C9 | C23×C3 |
| Frattini | C3 | C3×D33 |
| Fitting | C33×C9 | C23 |
| socle | C34 | C22×D3 |
| LCS | G ▷ C32×C9 | |
| UCS | C1 ◁ C3 | |
684 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 96 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
162 conjugacy classes — view the full character table.
| maximal subgroup of | D3×D9×AGL(1,ℤ/9), C3×D3×D92, C3×D32×AGL(1,ℤ/9), … |
| maximal normal subgroup of | C3×D32×AGL(1,ℤ/9), D32×D9⋊C9, D32×C9×D9, … |
| maximal quotient of | D3×D9×AGL(1,ℤ/9), C3×D3×D92, D32×D27⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3562);