Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C25 |
| direct product | C3×D32×SD16 |
| Fitting | C33×SD16 ⋊ C22 |
| Sylow | C33 ⋊ C22×SD16 |
1416 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
189 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 40398);