Construction of Finite Groups

H.U. Besche, B. Eick
1999 Journal of symbolic computation  
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 p n · 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.
doi:10.1006/jsco.1998.0258 fatcat:limqcxsqanfrplrnd6rzgo3k44