GAP Manual: 48.10. Conventions for Character Tables

The following few conventions should be noted: item[The identity element] is expected to be in the first class. item[Characters] are lists of cyclotomics (see Chapter Cyclotomics) or unknowns (see chapter Unknowns); they do not physically ``belong'' to a table, so when necessary, functions ``regard'' them as characters of a table which is given as another parameter. item[Conversely], most functions that take a character table as a parameter and work with characters expect these characters as a parameter, too.

Some functions, however, expect the characters to be stored in the irreducibles field of the table (e.g. TestCharTable TestCharTable) or allow application either to a list of characters given by a parameter or to the irreducibles field (e.g. Indicator Indicator) if this parameter is missing. item[The trivial character] need not be the first one in a list of characters. item[Sort convention:] Whenever SortClassesCharTable SortClassesCharTable or SortCharTable SortCharTable is used to sort the classes of a character table, the fusions into that table are not adjusted; only the permutation field of the sorted table will be actualized.

If one handles fusions only using GetFusionMap GetFusionMap and StoreFusion StoreFusion, the maps are adjusted automatically with respect to the value of the field permutation of the destination table. So one should not change this field by hand. Fusion maps that are entered explicitly (e.g. because they are not stored on a table) are expected to be sorted, they will not be adjusted.