Sporadic simple groups as flag‐transitive automorphism groups of symmetric designs

Abstract

In this article, we study symmetric designs admitting flag‐transitive, point‐imprimitive almost simple automorphism groups with socle sporadic simple groups. As a corollary, we present a classification of symmetric designs admitting flag‐transitive automorphism group whose socle is a sporadic simple group, and in conclusion, there are exactly seven such designs, one of which admits a point‐imprimitive automorphism group and the remaining are point‐primitive.