Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C42 · Schur multiplier (H2) = C2×C4 |
| direct product | C3×#10589158 |
| Sylow | C33 ⋊ H(3,ℤ/4) |
650 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
234 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 11517);