Perm group.m

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Permutation group database. Returns basic information about permutation groups up to S6. Syntax:


The following group names are available: S2, S3, S4, S5, S6, S4A, the latter one being the largest Abelian subgroup of S4.

Output fields:              - long name of the group
    group.order             - number of elements in the group
    group.nclasses          - number of classes in the group
    group.class_sizes       - a row vector giving  number of elements
                              in each class
    group.class             - a cell array of matrices giving the ele-
                              ments belonging to each class. The ele-
                              ments are given as row vectors of permu-
                              tation strings stacked vertically into
                              a matrix.
    group.n_irreps          - number of irreducible representations in
                              the group
    group.irrep_dims        - a row vector giving dimensions of irre-
                              ducible representation

    group.class_characters  - a matrix of characters for each irredu-
                              cible representation (in rows) of each
                              class (in columns).