1-Designs from the group $PSL_{2}(59)$ and their automorphism groups

Abstract

In this paper, we consider the projective special linear group $PSL_2(59)$
and construct some 1-designs by applying the Key-Moori method on $PSL_2(59)$.
Moreover, we obtain parameters of these designs and their automorphism groups.
It is shown that $PSL_2(59)$ and $PSL_2(59):2$ appear as the automorphism group of the constructed designs.