International
Tables for Crystallography Volume A Spacegroup symmetry Edited by M. I. Aroyo © International Union of Crystallography 2016 
International Tables for Crystallography (2016). Vol. A, ch. 2.1, pp. 160161

As explained in Sections 1.3.3.2 and 1.4.2.3 , the coordinate triplets of the General position of a space group may be interpreted as a shorthand description of the symmetry operations in matrix notation. The geometric description of the symmetry operations is found in the spacegroup tables under the heading Symmetry operations.
Numbering scheme. The numbering of the entries in the blocks Symmetry operations and General position (first block below Positions) is the same. Each listed coordinate triplet of the general position is preceded by a number between parentheses (p). The same number (p) precedes the corresponding symmetry operation. For space groups with primitive cells, the two lists contain the same number of entries.
For space groups with centred cells, several (2, 3 or 4) blocks of Symmetry operations correspond to the one General position block. The numbering scheme of the general position is applied to each one of these blocks. The number of blocks equals the multiplicity of the centred cell, i.e. the number of centring translations below the subheading Coordinates, such as .
Whereas for the Positions the reader is expected to add these centring translations to each printed coordinate triplet themselves (in order to obtain the complete general position), for the Symmetry operations the corresponding data are listed explicitly. The different blocks have the subheadings `For (0, 0, 0)+ set', `For set', etc. Thus, an obvious onetoone correspondence exists between the analytical description of a symmetry operation in the form of its generalposition coordinate triplet and the geometrical description under Symmetry operations. Note that the coordinates are reduced modulo 1, where applicable, as shown in the example below.
Example: Ibca (73)
The centring translation is . Accordingly, above the general position one finds and . In the block Symmetry operations, under the subheading `For set', entry (2) refers to the coordinate triplet . Under the subheading `For set', however, entry (2) refers to . The triplet is selected rather than , because the coordinates are reduced modulo 1.
The coordinate triplets of the general position represent the symmetry operations chosen as coset representatives of the decomposition of the space group with respect to its translation subgroup (cf. Section 1.4.2 for a detailed discussion). In space groups with two origins the origin shift may lead to the choice of symmetry operations of different types as coset representatives of the same coset (e.g. mirror versus glide plane, rotation versus screw axis, see Tables 1.4.2.2 and 1.4.2.3 ) and designated by the same number (p) in the generalposition blocks of the two descriptions. Thus, in (129), (p) = (7) represents a 2 and a 2_{1} axis, both in , whereas (p) = (16) represents a g and an m plane, both in .
Designation of symmetry operations. An entry in the block Symmetry operations is characterized as follows.
Examples
Details on the symbolism and further illustrative examples are presented in Section 1.4.2.1 .