Generation of finite groups with cyclic Sylow subgroups

M. C. Slattery [Generation of groups of square-free order, J. Symbolic Comput. 42 (2007), 6, 668-677] described computational methods to enumerate, construct and identify finite groups of squarefree order. We generalise Slattery's result to the class of finite groups that have cyclic Sylow subgroups and provide an implementation for the computer algebra system GAP.