On Veronese’s Decomposition Theorem and the Geometry of Outer Automorphisms of \(S_6\)

In this paper, the Desargues Configuration in \({P}^2(k)\), where \(k\) is a field of characteristic \( \neq 2\), is characterized combinatorially en route to define Desargues Block Designs and associate them with certain families of dihedral subgroups of \(S_6\) through the use of the outer automorphisms of \(S_6\).