{{\operatorname{Aut}}}(A)$ be an action of $G$ on $A$. We say that ${\alpha}$ is [*approximately representable*]{} if for every finite set $F {\subset}A$ and every ${\varepsilon}> 0$, there are $z_g \in {{\operatorname{U}}}(A)$ for $g \in G$ such that:

1.  \[D\_9719\_AppRep.1\] $\| {\alpha}_g (a) - z_g a z_g^* \| < {\varepsilon}$ for all $g \in G$ and all $a \in F$.

2.  \[D\_9719\_AppRep.2\] $\| z_g z_h - z_{gh}\| < {\varepsilon}$ for all $g, h \in G$.

3.  \[D\_9719\_AppRep.3\] $\| {\alpha}_g (z_h) - z_{g h g^{-1}}\| < {\varepsilon}$ for all $g, h \in G$.

Obviously, in the abelian case, Condition (\[D\_9719\_AppRep.3\]) reduces to $\| {\alpha}_g (z_h) - z_{h}\| < {\varepsilon}$. The following lemma is a generalization of Lemma 3.1 of [@Ph11] to nonabelian groups.

\[Lem.PZ.20200623\] Let $A$ be a separable unital C\*-algebra and let $G$ be a finite group (not necessarily abelian). Let $\alpha \colon G \to {{\operatorname{Aut}}}(A)$ be an action. Then $\alpha$ is approximately representable in the sense of Izumi (Definition \[Izum\_Def\_app\_Rep\]) if and only if $\alpha$ is approximately representable in the sense of Phillips (Definition \[D\_9719\_AppRep\_Phi\]).

We first prove the backwards implication. Since $A$ is separable, we can choose finite sets $F_n \subset A$ such that $F_1 \subseteq F_2 \subseteq \ldots$ 