From Spinach Documentation Wiki
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.
group.name - 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).