## Program Bravais_inclusions

### Usage

Bravais_inclusions 'file' [-S] [-G]

file: bravais_TYP containing a Bravais group G.
### Description

Lists representatives of the Bravais subgroups (resp. Bravais supergroups
with option -S) of the BRAVAIS GROUP G under the conjugation action of
the normalizer of G in GL_n(Z).

Remark: Without option -G only the symbols of the Bravais groups are given.
### Options

-S: Search for all supergroups
-G: Calculate generators for the groups as well

### Remarks

See also for Bravais_catalog/Datei
and Bravais_type/Symbol
### Examples

- List all names of Bravais groups of degree 4.
- Determine the maximal finite subgroups of GL
_{5}(Z)
- Find the dual pairs of Bravais groups in family 1;1;1;1
- Find all Bravaisgroups of degree 6 consisting of permutation
matrices and their negatives only.
- Do two given groups have Z-equivalent copies which lie in a
finite unimodular group?