I have two group tables, both with order $24$. Now I have to write the images of the first generator as the second generator. The group elements are all letters, thus $G=\{A,B,C,...,V,W,X\}$ and the same holds for $H$, but the permutations of these elements are different.
In $G$, I have two generators, namely $L$ and $M$. Thus I can compute all other elements by these two. Now how do I find the images of these generators!? Are they, by definition, mapped into the generators of $H$ or does this not hold?
If this question is too vague, let me know, I find it hard to word it in an understanding way.