Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23×C3 |
| direct product | C3×C3⋊D3×#106 |
| Fitting | C33×#106 ⋊ C2 |
| Sylow | C33 ⋊ C2×#106 |
924 conjugacy classes of subgroups.
| transitive degree | μt(G) = 576 |
252 conjugacy classes — view the full character table.
| maximal subgroup of | D3×C3⋊D3×#106, C3×C3⋊D3×#442, C3⋊D3×#4869, … |
| maximal normal subgroup of | D3×C3⋊D3×#106, C3×C3⋊D3×#442, C3⋊D3×#4869 |
| maximal quotient of | #106×C3⋊AGL(1,ℤ/9) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 28960);