  We study the automorphism group of an idempotent evolution algebra, show that
any finite group can be the automorphism group of an evolution algebra, and
describe certain evolution algebras with given automorphism groups. In
particular, we classify $n$-dimensional idempotent evolution algebras whose
automorphism group is isomorphic to the symmetric group $S_n$, and classify
idempotent evolution algebras with maximal diagonal automorphism subgroups.
