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I'm trying to understand outer automorphisms better. A question that popped in my head was- What do outer automorphisms of most alternating groups of order n mean intuitively? I think that there are automorphisms generated in the alternating group due to conjugation with the elements of symmetric group of order n. I'm looking for an inuitive understanding. To put it differently, what are the automorphisms of alternating group that inner automorphisms can't produce in an alternating group?

ilawid
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    Is this what you are looking for? https://math.stackexchange.com/questions/543691/why-is-conjugation-by-an-odd-permutation-in-s-n-not-an-inner-automorphism-on – Marcos Aug 30 '21 at 13:44
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    Does this duplicate answer your question? "The inner automorphisms are the easy automorphisms to construct. Conjugating by an element is a way to produce an automorphism in any group. Now these are inner ones. So what else is possible? – Dietrich Burde Aug 30 '21 at 13:56

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