International
Tables for Crystallography Volume A Spacegroup symmetry Edited by M. I. Aroyo © International Union of Crystallography 2015 
International Tables for Crystallography (2015). Vol. A, ch. 1.4, pp. 5051

Given the analytical description of the symmetry operations by matrix–column pairs , their geometric meaning can be determined following the procedure discussed in Section 1.2.2 . The notation scheme of the symmetry operations applied in the spacegroup tables was designed by W. Fischer and E. Koch, and the following description of the symbols partly reproduces the explanations by the authors given in Section 11.1.2 of IT A5. Further explanations of the symbolism and examples are presented in Section 2.1.3.9 .
The symbol of a symmetry operation indicates the type of the operation, its screw or glide component (if relevant) and the location of the corresponding geometric element (cf. Section 1.2.3 and Table 1.2.3.1 for a discussion of geometric elements). The symbols of the symmetry operations explained below are based on the Hermann–Mauguin symbols (cf. Section 1.4.1.4), modified and supplemented where necessary.
The notation scheme is extensively applied in the symmetryoperations blocks of the spacegroup descriptions in the tables of Chapter 2.3 . The numbering of the entries of the symmetryoperations block corresponds to that of the coordinate triplets of the general position, and in space groups with primitive cells the two lists contain the same number of entries. As an example consider the symmetryoperations block of the space group shown in Fig. 1.4.2.1. The four entries correspond to the four coordinate triplets of the generalposition block of the group and provide the geometric description of the symmetry operations chosen as coset representatives of with respect to its translation subgroup.
For space groups with conventional centred cells, there are several (2, 3 or 4) blocks of symmetry operations: one block for each of the translations listed below the subheading `Coordinates'. Consider, for example, the four symmetryoperations blocks of the space group Fmm2 (42) reproduced in Fig. 1.4.2.2. They correspond to the four sets of coordinate triplets of the general position obtained by the translations , , and , cf. Fig. 1.4.2.2. The numbering scheme of the entries in the different symmetryoperations blocks follows that of the general position. For example, the geometric description of entry (4) in the symmetryoperations block under the heading `For set' of Fmm2 corresponds to the coordinate triplet , which is obtained by adding to the translation part of the printed coordinate triplet (cf. Fig. 1.4.2.2).