Abstract
In this article, we determine the automorphism groups of a family of cubic hypersurfaces generalizing those introduced in part I. Along the way, we determine all algebraic groups which contain PSL 2(Fq) and which lie in PGLn (C), where q=2 n ± 1. This is accomplished using the classification of finite simple groups, information from the ATLAS of finite simple groups, the degrees of some complex representations of reductive groups over a finite field and techniques from Part I of this article needed to prove that the automorphism groups in question are finite.
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