How to use GAP to cumpute $S=\{s|s=h^2, h\in H\}$ for every subgroup $H$ of $G$?

Question

Let $G$ be a finite group, then how to use GAP to cumpute $S=\{s|s=h^2, h\in H\}$ for every subgroup $H$ of $G$?

Answer 1

Since every element lies in a subgroup, this is just the set $\{h^2| h\in G\}$. So calculate the conjugacy classes, check which classes are squares (the classes of elements of odd order and those of even order into which other classes square) and take the elements of these classes.