Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24×C3 |
| direct product | C3⋊D3×(C2×D3)⋊C8 |
| Fitting | C2×C33×C8 ⋊ C22 |
| Sylow | C33 ⋊ C2×C22⋊C8 |
1412 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
216 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 26087);