However, when trying to find an isomorphism there are a few things to note,
If you map to the generators then your homomorphism will be surjective,
If the kernel is trivial then your homomorphism will be injective,
Try to find a `common' group which both groups are isomorphic to (as in the example),
Often there exists some well-known function which actually turns out to be an isomorphism of groups (for example, , and the isomorphism is given by ).
A homomorphism is an isomorphism if and only if there exists an inverse function. Sometimes this can be easily found.