Multiplicity-Free Permutation Characters in GAP

This note shows a few examples of GAP computations concerning multiplicity-free permutation characters, with an emphasis on the classification of the faithful multiplicity-free permutation characters of the sporadic simple groups and their automorphism groups given in [BL96]. For examples on GAP computations with permutation characters in general, see the note [Bre]. For further questions about GAP, consult its Reference Manual; in particular, for the description of the commands for character tables, see the chapter “Character Tables”. Section 1 of this note shows how to interpret the individual data available in the database. In Section 2, the main idea is to gather information from the database as a whole, by filtering items with suitable properties. Finally, Section 3 gives an impression how GAP can be used to obtain results such as the classification of described in [BL96].