I have this group of permutations:
And I have this group of complex numbers:
These groups are isomorphic to each other, but it seems I do not understand why. I was looking for similarities in structure and I would have thought because they do not share the same structure, that they were not isomorphic. Like take the diagonal of $g$s in the group of permutations. In the group of complex numbers this same diagonal is made of different elements, $i$ and $1$. It seems
I do not fully understand isomorphism, because I was looking for the same structure. Could someone explain why these groups are isomorphic?