Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | D3×SD16×D9 |
| Fitting | C3×C9×SD16 ⋊ C22 |
| Sylow | C3×C9 ⋊ C22×SD16 |
962 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
126 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 15991);