Let X be a compact connected Riemann surface of genus g and let f∶ X →P1 be a meromorphic function of degree n. Classes of such covers are in one to one correspondence with the primitive systems, which are tuples of elements (x1,x2,⋯,xr) in the symmetric group Sn taken up to conjugation and the action of the braid group, such that x1.x2.⋯.xr=1 and G=〈x1,x2,⋯,xr〉 is a primitive subgroup G of Sn. This thesis is a contribution to the classification of primitive genus g ≤ 2 systems of sporadic almost simple groups.