Bilbao Crystallographic Server Find Transformation

How to find the correct transformation

• If your subgroup H is maximal in the group G then you can click here in order to find the possible indexes and transformation matrices.

• If your subgroup H is not maximal in G and you know the index G:H = n then one have to construct the lattice of maximal subgroups from the group to the desired subgroup. Then using the transformation matrices for each (already) maximal subgroup you can find the transformation matrix. Of course there are a lot of different chains of max subgroups. All this work can be done clicking here.

• The knowledge of index and/or transformation matrix is mandatory. Finally if you don't know the index you can draw the group/subgroup leattice which have to help you to figure out the index of subgroup. In order to construct and draw the lattice of maximal subgroups click here.