Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | D32×#208 |
| Sylow | C33 ⋊ C22×M16 |
1416 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
162 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 36544);