On some designs constructed from the groups PSL2(q) , q=53,61,64

In this paper, we use the primitive permutation representations of the simple groups PSL2(53), PSL2(61) and PSL2(64) and construct 1-designs by the Key-Moori Method 1. It is shown that the groups PSL2(53), PSL2(53):2, PSL2(61), PSL2(61):2, PSL2(64), PSL2(64):2, PSL2(64):3 and PSL2(64):6 appear as the full automorphism groups of these obtained designs.