A Minimal Generating Set of Intermediate-Symmetry Fedorov Groups

Minimization of generating sets (sets of generators) indicated in the International Tables for Crystallography has been performed for tetragonal, trigonal, and hexagonal space groups. It is established that generating sets of some groups cannot be minimized to a set of minimally possible power (minimal set) for a given group, which suggests that the generating set used in the International Tables for Crystallography should be improved.