Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C26×C3 |
| direct product | C2×C3×D8×C3⋊D3 |
| Fitting | C2×C33×D8 ⋊ C2 |
| Sylow | C33 ⋊ C22×D8 |
2332 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
252 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×D8×C3⋊D3, C3×C3⋊D3×#442, C3⋊D3×#5152, … |
| maximal normal subgroup of | C2×D3×D8×C3⋊D3, C3×C3⋊D3×#442, C3⋊D3×#5152, … |
| maximal quotient of | C2×D8×C3⋊AGL(1,ℤ/9) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 45568);