Lifting McKay graphs and relations to prime extensions

We give an algorithmic procedure for constructing the quivers and homogeneous relations of the Brauer correspondents of blocks of the abelian noncyclic defect group in the almost simple groups in the ATLAS. This is one step in a program to compute the structure of the indecomposable projectives for these blocks. As an illustration, we determine an explicit tilting complex for the nonprincipal 3-block of the central extension of PSL(3,4) by C₂.