Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C25×C3 |
| direct product | C2×C3×SD16×C3⋊D3 |
| Fitting | C2×C33×SD16 ⋊ C2 |
| Sylow | C33 ⋊ C22×SD16 |
2060 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
252 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×SD16×C3⋊D3, C2×C3×C3⋊D3×AGL(1,ℤ/8), C2×C3⋊D3×#914 |
| maximal normal subgroup of | C2×D3×SD16×C3⋊D3, C2×C3×C3⋊D3×AGL(1,ℤ/8), C2×C3⋊D3×#914 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 45572);