  In this paper, we discuss how to apply GAP to do computations in modular
representation theory. Of particular interest is the generating number of a
group algebra, which measures the failure of the generating hypothesis in the
stable module category. We introduce a computational method to do this
calculation and present it in pseudo-code. We have also implemented the
algorithm in GAP and managed to do computations of examples that we were not
able to do before. The computations lead to conjectures on the ghost numbers of
the groups $Q_8$ and $A_4$.
