Finite permutation representation of a subgroup of picard group

We investigate action of a subgroup G1 of the Picard group on finite sets using coset diagrams. We show that its actions on the sets of 3, 4, 5, 6, 8, and 12 elements yield building blocks of Coset diagrams and that these blocks can be connected together so that a diagram of n vertices can be obtained. We show that various combinations of these blocks represent alternating and symmetric groups of various degrees. We show also that the action of G1 on a set of n vertices is transitive.