Space-group symmetry data

Generators: Set of generators for a given space group
General position: General-position coordinate triplets for a given space group
Wyckoff positions: Wyckoff-positions data for a given space group
Normalizers: Euclidean, chirality-preserving Euclidean and affine normalizers for a given space group
Interactive 3D visualization: Interactively visualize a 3D unit cell containing the symmetry-equivalent points of a general position. Click on points and symmetry operations to see how they are related

Symmetry relations between space groups

Maximal subgroups: Maximal subgroups of indices 2, 3 and 4 (Wyckoff-position splitting schemes, coset decomposition and transformation to the supergroup basis)
Series of isomorphic subgroups: Maximal isomorphic subgroups of indices higher than 4 (Wyckoff-position splitting schemes, coset decomposition and transformation to the supergroup basis)
Minimal supergroups: Minimal supergroups of indices up to 9 (Wyckoff-position splitting schemes, coset decomposition and transformation to the supergroup basis)
Group-subgroup relations: Group-subgroup pair specified by the transformation between the conventional bases of the group and the subgroup (Wyckoff-position splitting schemes, coset decomposition and transformation to the supergroup basis)
Graph of maximal subgroups: Graph of maximal subgroups for a group-subgroup pair (with and without a specific index)
Supergroups: Supergroups of specific index

Generators: Set of generators for a given point group
General position: General-position coordinate triplets for a given point group
Wyckoff positions: Wyckoff-positions data for a given point group
Interactive 3D visualization: Interactive visualization for a given point group