Space group
Classification systems

Space group

Section Title: Classification systems
Table Section Text: None

(Crystallographic) space group types (230 in three dimensions). Two space groups, considered as subgroups of the group of affine transformations of space, have the same space group type if they are conjugate by an orientation-preserving affine transformation.

Affine space group types (219 in three dimensions). Two space groups, considered as subgroups of the group of affine transformations of space, have the same affine space group type if they are conjugate under an affine transformation.

Arithmetic crystal classes (73 in three dimensions). Sometimes called Z-classes.

(geometric) Crystal classes (32 in three dimensions). Sometimes called Q-classes.	Bravais flocks (14 in three dimensions). These are determined by the underlying Bravais lattice type.

Crystal systems. (7 in three dimensions) Crystal systems are an ad hoc modification of the lattice systems to make them compatible with the classification according to point groups.	Lattice systems (7 in three dimensions). The lattice system of a space group is determined by the conjugacy class of the lattice point group (a subgroup of GLn(Z)) in the larger group GLn(Q).

Crystal families (6 in three dimensions). The point group of a space group does not quite determine its lattice system, because occasionally two space groups with the same point group may be in different lattice systems.

Sentence(s)

In three dimensions, there are 219 types in Space group.

final_sentence: In three dimensions, there are 219 types in Space group.