Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C9 · Schur multiplier (H2) = C24 |
| direct product | Q8×C9×Dic6 |
| Sylow | C3×C9 ⋊ Q82 |
706 conjugacy classes of subgroups.
| transitive degree | μt(G) = 576 |
405 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 18735);