Construction of finite groups

Abstract

We introduce three practical algorithms to construct certain finite groups up to isomorphism. The first one can be used to construct all soluble groups of a given order. This method can be restricted to compute the soluble groups with certain properties such as nilpotent, non-nilpotent or supersoluble groups. The second algorithm can be used to determine the groups of order pn · q with a normal Sylow subgroup for distinct primes p and q. The third method is a general method to construct finite groups which we use to compute insoluble groups. © 1999 Academic Press.