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We start with the description of permutation groups in ''polymake''. An object of type [[https://polymake.org/release_docs/latest/group.html#group__Group__5 | Group]] records the abstract properties of the groups that do not depend on any particular representation, which essentially are just the ''ORDER'', ''CHARACTER_TABLE'', and ''CONJUGACY_CLASS_SIZES''. Moreover, a ''Group'' object can contain several subobjects that encode actions (representations) of the group, most notably a ''PERMUTATION_ACTION'' that encodes permutations of indices. If the Group object is contained inside a ''Cone'', ''Polytope'', ''PointConfiguration'', or ''VectorConfiguration'', it may be encoded more specifically as a ''RAY_ACTION'', ''FACET_ACTION'', etc. See the [[https://polymake.org/doku.php/release_docs/latest/group.html | documentation]] for more information on the action types. | We start with the description of permutation groups in ''polymake''. An object of type [[https://polymake.org/release_docs/latest/group.html#group__Group__5 | Group]] records the abstract properties of the groups that do not depend on any particular representation, which essentially are just the ''ORDER'', ''CHARACTER_TABLE'', and ''CONJUGACY_CLASS_SIZES''. Moreover, a ''Group'' object can contain several subobjects that encode actions (representations) of the group, most notably a ''PERMUTATION_ACTION'' that encodes permutations of indices. If the Group object is contained inside a ''Cone'', ''Polytope'', ''PointConfiguration'', or ''VectorConfiguration'', it may be encoded more specifically as a ''RAY_ACTION'', ''FACET_ACTION'', etc. See the [[https://polymake.org/doku.php/release_docs/latest/group.html | documentation]] for more information on the action types. |