Let $H,K$ be two non-isomorphic groups such that $H\cong Aut(K)$ and $K\cong Aut(H)$.

Is there any example of such groups ?

**Note:** I had asked the question there.

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Let $H,K$ be two non-isomorphic groups such that $H\cong Aut(K)$ and $K\cong Aut(H)$.

Is there any example of such groups ?

**Note:** I had asked the question there.

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Computer search in sage/gap didn't found any solutions for orders up to $120$.

It didn't assume the orders are equal.

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