The classification of p-local finite groups over the extraspecial group of order p3 and exponent p

Abstract

In this paper we classify the p-local finite groups over p1+2+, the extraspecial group of order p3 and exponent p for odd p. This study reduces to the classification of the saturated fusion systems over p1+2+, which will be characterized by the outer automorphism group, the number of Open image in new window -radical subgroups and the automorphism group of each nontrivial Open image in new window -radical subgroup. As part of this classification, we obtain three new exotic 7-local finite groups.