Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#11720820 |
| Fitting | C2×C3×C8×C9 ⋊ C22 |
| Sylow | C3×C9 ⋊ C2×AGL(1,ℤ/8) |
962 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
156 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 15841);