Weak Cayley Table Groups of Crystallographic Groups I

Let [Formula: see text] be a group. A weak Cayley table isomorphism is a bijection [Formula: see text] such that (i) [Formula: see text] is conjugate to [Formula: see text] for [Formula: see text], [Formula: see text] and (ii) [Formula: see text] sends conjugacy classes to conjugacy classes. The set of all such bijections forms a group [Formula: see text]. We study [Formula: see text] for 56 of the 219 three-dimensional crystallographic groups, as well as some other groups. These 56 groups are r