I have an idea about the solution, I assume that you are the same student who has sent the question asking S5=Aut(A5). I know that its proof is too hard and long and I guess I have seen that long time ago in a book whose name I have forgot. But I believe that the key point to solve this problem is actually the same thing. S5=Aut(A5) and we assume that we already know this. Please read this carefully and book keep the names. Therefore, let's start:
<br><br>Consider an element like x in G/A5. Find its inverse image in G and call it y. Well, because we do not know whether the map has been 1-1 or not, we might have several inverse images for x, for the moment let's choose one of them and call it y. Now any conjugation with this y, will give us a conjugation automorphism (inner ...