Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C3×C9×SD16 ⋊ C22 |
| Sylow | C3×C9 ⋊ #577 |
834 conjugacy classes of subgroups.
| minimal degree | μ(G) = 28 |
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^6,3^3|d^2=f,e^2=f,g^3=i,b^a=bf,g^a=g^2i^2,i^a=i^2,d^b=df,h^b=h^2,d^c=de,e^c=ef,e^d=ef108 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 16008);