Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C3 |
No aliases for this group.
| Fitting | C3×C9×#137 ⋊ C2 |
| Sylow | C3×C9 ⋊ #577 |
1290 conjugacy classes of subgroups.
| transitive degree | μt(G) = 432 |
Polycyclic presentation:
2^6,3^3|c^2=f,e^2=f,h^3=i,b^a=bf,g^a=g^2,h^a=h^2i^2,i^a=i^2,d^b=df,d^c=de,e^c=ef,e^d=ef165 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 20450);