Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C9 · Schur multiplier (H2) = C22 |
| direct product | C9×#4749 |
| Fitting | C3×C9×#100 ⋊ C2 |
| Sylow | C3×C9 ⋊ #472 |
370 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
243 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 7734);