Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | D32×Dic12 |
| Sylow | C33 ⋊ C22×Q16 |
1230 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
135 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 33814);