Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | D3×#63476 |
| Fitting | C3×C9×SD16 ⋊ C22 |
| Sylow | C3×C9 ⋊ C2×AGL(1,ℤ/8) |
962 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
117 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 15993);