  Let $X$ be a compact complex manifold in Fujiki's class $\mathcal{C}$, i.e.,
admitting a big $(1,1)$-class $[\alpha]$. Consider $\text{Aut}(X)$ the group of
biholomorphic automorphisms and $\text{Aut}_{[\alpha]}(X)$ the subgroup of
automorphisms preserving the class $[\alpha]$ via pullback. We show that $X$
admits an $\text{Aut}_{[\alpha]}(X)$-equivariant K\"{a}hler model: there is a
bimeromorphic holomorphic map $\sigma \colon \widetilde{X}\to X$ from a
K\"{a}hler manifold $\widetilde{X}$ such that $\text{Aut}_{[\alpha]}(X)$ lifts
holomorphically via $\sigma$.
  There are several applications. We show that $\text{Aut}_{[\alpha]}(X)$ is a
Lie group with only finitely many components. This generalizes an early result
of Lieberman and Fujiki on the K\"{a}hler case. We also show that every torsion
subgroup of $\text{Aut}(X)$ is almost abelian, and $\text{Aut}(X)$ is finite if
it is a torsion group.
