Group-subgroup pair

A group-subgroup pair is specified by a group, a subgroup and the transformation relating the basis of the group with that of the subgroup. The group and supergroup can be specified by their space-group numbers, or you can start to type the space-group symbols (using _ before a subscript) and possible options to choose from will be shown.

For any group-subgroup pair the following data can be obtained:

  • transformation of the subgroup in the basis of the supergroup;
  • splitting of the supergroup Wyckoff positions with respect to the subgroup; and
  • left and right coset decomposition of the supergroup with respect to the subgroup.

If the matrix that relates both groups is not valid, an error message is shown. If you do not know the matrix, use the group-subgroup graph program to find all transformations that correspond to a specific index for the group-subgroup relation.