Find isomorphism of graph with maximal number $x$ such that $f(x)\neq x$ - assuming $NP=P$
Consider the decision version of computing $\#G$:

$L=\{(G,k) | \text{$G$ has an automorphism $f$ with $\#f\ge k$}\}$

$L$ is obviously in NP (an automorphism $f$ with $\#f\ge k$ is a witness). If $\mathsf{P=NP}$ then $L\in P$, and you can compute $\#G$ in polynomial time using binary search.