Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | D3×#611⋊C4 |
| Fitting | C3×C9×C22⋊C4 ⋊ C22 |
| Sylow | C3×C9 ⋊ C2×C4×D4 |
1372 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
180 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 14455);