# Symmetry groups of 3D systems which are periodic in one direction and homogeneous in the other 2 directions

What kind of symmetry groups, analogue of 3D crystallographic space groups, can describe the spatial symmetries of 3D systems which have discrete periodicity in only one direction, but are homogeneous in the 2D transverse plane?

What is the classification and the representation theory of such kind of symmetry groups?

If the system is only discretely periodic in one dimension, the only point groups are the trivial group $C_1$ and the group $Z_2$ generated by reflections about a point.