Question

What information is contained in space group symbol? What symmetry operations are present in P-1 and P21/c space groups? please explain this question as in depth as possible. i think it is refering to symmetry but i am not sure what exactly. provide an example of what it is asking please

Answer 1

A space group is the symmetry group of a configuration in space. usually the notation of a space group is by four symbols. L_ijk      where L is the lattice like primitive, body centered, face centered, etc.

                 i,j,k stands for symmetry elements for different symmetry directions.

                 i for primary, j for secondary and k for tertiary

for example, in P-1 P shows that the space group is primitive. It has no any rotation axis other than identity rotation. so -1 shows identity rotation.

              ( here note that there is also another identity rotation along +axis, which we call P1 space group)

these two are triclinic and does not have j,k notation due to absence of rotation and reflection symmetry.

P21/c is monoclinic, centrosymmetric where P represents the space group is primitive, with two rotational andon reflectional symmetry. C indicates glide plane