Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27×C3 |
| direct product | C2×D3×C22⋊#157 |
| Fitting | C23×C33 ⋊ C2×C4 |
| Sylow | C33 ⋊ C22×C22⋊C4 |
3112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
108 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 47071);