What is the smallest group $G$ such that $\operatorname{Rep}(G)$ has a non-symmetric braiding (or just an easy example)?

I seem to remember a result classifying all universal $R$-matrices of $\mathbb C[G]$ for finite groups $G$, but cannot find this. But I remember that with this result, I found that the only non-trivial universal $R$-matrix of $C_2$ was

$$R=\frac12(e\otimes e+e\otimes g+g\otimes e-g\otimes g).$$

But this $R$-matrix gives a symmetric braiding on $\operatorname{Rep}(C_2)$. I'm looking for one that will give me a non-symmetric braiding.