Minimal characteristic bisets and finite groups realizing Ruiz–Viruel exotic fusion systems

Continuing our previous work (Park, 2010) [2], , we determine a minimal left characteristic biset X for every exotic fusion system F on the extraspecial group S of order 73 and exponent 7 discovered by Ruiz and Viruel (2004) [6], , and analyze the finite group G obtained from X by the method of Park (2010) [2] which realizes F as the full subcategory of the 7-fusion system of G. In particular, we obtain an upper bound for the exoticity index for F.