Construction of Finite Groups

We1999 Academic Pressintroduce 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 orderCopyrightpn • qwith a normal Sylow subgroup for distinct primespandq. The third method is a general method to construct finite groups which we use to compute insoluble groups.