[@luukvandenakker7838]

In the case of the C2v, the multiplication table is symmetric, hence the group is abelian right? But is that true for any pointgroup in general?

[@PhysicalChemistry]

No, not all point groups are Abelian.
Some pairs of symmetry operations commute. All of the symmetry operations in C2v are commutative, as you point out. But if there is a Cn axis with n>2 there will be some noncommuting symmetry operations

[@luukvandenakker7838]

@@PhysicalChemistry I see, many thanks 👍

[@khushipokhrel4144]

Thank you sir

[@PhysicalChemistry]

You're very welcome