  Let $(M, g, J, f)$ be an irreducible non-trivial K\"{a}hler gradient Ricci
soliton of real dimension $2n$. We show that its group of isometries is of
dimension at most $n^2$ and the case of equality is characterized. As a
consequence, our framework shows the uniqueness of $U(n)$-invariant K\"{a}hler
gradient Ricci solitons constructed earlier. There are corollaries regarding
the groups of automorphisms or affine transformations and a general version for
almost Hermitian GRS. The approach is based on a connection to the geometry of
an almost contact metric structure.
