\author{Sejong Park}
\title{Minimal characteristic bisets and finite groups realizing Ruiz-Viruel exotic fusion systems} 

\begin{abstract}
Continuing our previous work, we determine a minimal left characteristic biset $X$ for every exotic fusion system $\mathcal{F}$ on the extraspecial group $S$ of order $7^3$ and exponent $7$ discovered by Ruiz and Viruel, and analyze the finite group $G$ obtained from $X$ which realizes $\mathcal{F}$ as the full subcategory of the $7$-fusion system of $G$.  In particular, we obtain an upper bound for the exoticity index for $\mathcal{F}$.
\end{abstract}