On Some Combinatorial Structures Constructed from the Groups L(3,5)‎, U(5,2)‎, and S(6,2)‎

الملخص EN

We describe a construction of primitive 2-designs and strongly regular graphs from the simple groups L(3,5), U(5,2), and S(6,2).

The designs and the graphs are constructed by defining incidence structures on conjugacy classes of maximal subgroups of L(3,5), U(5,2), and S(6,2).

In addition, from the group S(6,2), we construct 2-designs with parameters (28,4,4) and (28,4,1) having the full automorphism group isomorphic to U(3,3):Z2.