2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/69825A Steiner quadruple system of order v is a 3-(v,4,1) design, and will be denoted SQS(v). Using the classification of finite 2-transitive permutation groups all SQS(v) with a flag-transitive automorphism group are completely classified, thus solving the "still open and longstanding problem of classifying all flag-transitive 3-(v,k,1) designs" for the smallest value of k. Moreover, a generalization of a result of H. Lueneburg (1965, Math. Z. 89, 82-90) is achieved.11 pagesCombinatoricsGroup TheoryPrimary 51E10; Secondary 05B05, 20B25text