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. 152154

The entry Patterson symmetry in the headline gives the symmetry of the `vector set' generated by the operation of the space group on an arbitrary set of general positions. More prosaically, it may be described as the symmetry of the set of the interatomic vectors of a crystal structure with the selected space group. The Patterson symmetry is a crystallographic space group denoted by its Hermann–Mauguin symbol. It is in fact one of the 24 centrosymmetric symmorphic space groups (see Section 1.3.3.3 ) in three dimensions and one of 7 in two dimensions. For each of the 230 space groups, the Patterson symmetry has the same Bravaislattice type as the space group itself and its point group is the lowestindex centrosymmetric supergroup of the point group of the space group. The `pointgroup part' of the symbol of the Patterson symmetry represents the Laue class to which the plane group or space group belongs (cf. Table 2.1.2.1). By way of examples: space group No. 100, P4bm, has a Bravais lattice of type tP and point group 4mm. The centrosymmetric supergroup of 4mm (see Fig. 3.2.1.3 ) is 4/mmm, so the Patterson symmetry is P4/mmm; space group No. 66, Cccm, has a Bravais lattice of type oC and point group mmm. This point group is centrosymmetric, so the Patterson symmetry is Cmmm.
Note: For the four space groups Amm2 (38), Aem2 (39), Ama2 (40) and Aea2 (41), the standard symbol for their Patterson symmetry, Cmmm, is added (between parentheses) after the actual symbol Ammm in the spacegroup tables.
The Patterson symmetry is intimately related to the symmetry of the Patterson function (see Flack, 2015). The latter, P_{F2}(uvw), is the inverse Fourier transform of the squared structurefactor amplitudes. Patterson functions possess the crystallographic symmetry of the symmorphic spacegroup representative of the arithmetic crystal class (see Section 1.3.4.4.1 ) to which the space group belongs. Table 2.1.3.3 lists these crystallographic symmetries of the Patterson function and the Patterson symmetries for the space groups and plane groups. However, further symmetry is also present, as desribed below for the three common forms of the Patterson function:

References
Fischer, K. F. & Knof, W. E. (1987). Space groups for imaginary Patterson and for difference Patterson functions used in the lambda technique. Z. Kristallogr. 180, 237–242.Flack, H. D. (2015). Patterson functions. Z. Kristallogr. 230, 743–748.
Shubnikov, A. V. & Belov, N. V. (1964). Coloured Symmetry, pp. 198–210. Oxford: Pergamon Press.
Wilson, A. J. C. (1993). Laue and Patterson symmetry in the complex case. Z. Kristallogr. 208, 199–206.