On Graham Higman's famous PORC paper

We investigate Graham Higman's paper Enumerating p-groups, II, in which he formulated his famous PORC conjecture. We look at the possibilities for turning his theory into a practical algorithm for computing the number of pclass two groups of order p n for small n. We obtain the PORC formulae for the number of r-generator groups of p-class two for r 6. In addition, we obtain the PORC formula for the number of p-class two groups of order p 8 . One of the ideas used in implementing Higman's theory has led to a signicant speed up in Eamonn O'Brien's ClassTwo function in Magma. In addition, we are able to simplify some of the theory. In particular, Higman's paper con