The symmetry group of a three-dimensional crystal pattern is called its space group . In E 2 , the symmetry group of a two-dimensional crystal pattern is called its plane group . In E 1 , the symmetry group of a one-dimensional crystal pattern is called its line group . To each crystal pattern belongs an infinite set of translations T , which are symmetry operations of that pattern. The set of all T forms a group known as the translation subgroup T of the space group G of the crystal pattern. T is an Abelian group.