How many symmetry operations are needed to generate a space group?

Abstract

Despite interesting applications in chemistry, mineralogy and materials science, the rank d of a space group G has never been the main focus of crystallographic investigations before. As a rule, the conventional generating subset of a space group listed in Volume A of International Tables of Crystallography does not fit for correctly estimating d(G). The initial generating subset was modified and the code was developed and written in GAP environment to obtain reliable values of d(G) (ranging from 2 to 6) for all the 230 space-group types.