Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C25×C3 |
| direct product | C3×#10596233 |
| Fitting | C2×C33×SD16 ⋊ C2 |
| Sylow | C33 ⋊ #577 |
1820 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
234 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 45576);