[Dolphinsiu]

For the products of two symmetry operations,

sigma v' = (sigma v) (C3), Right?

But what is the difference between sigma v' and sigma v'' (what is the difference in the product of the two operations)?

Then, again, what is C3' and C3''(what is the difference in the product of the two operations)

Thank you!

[Alpha-Omega]

You have to define which point group you are referring to in order for that question to have meaning/significance/relevance.  The operations, order of operations, commutation properties of compound/multiplicative operations all depend on which symmetry point group you are dealing with.

Please keep in mind that there are times when the order of operations is important.  They do not necessarily commute.  Two operations only commute if the result of successive application of the two operators is the same.


Please see the attached word document