Class sums and their products

This is the first of two chapters that teach the automated construction of character tables. In the analysis of flexible molecules you may need a character table that is not tabulated in this book or any book. Such molecules can be analyzed using permutation groups, but there are so many permutation groups that no one tabulates their character tables. When you need the character table of a permutation group, you usually have to make it yourself. This is a treacherous and uncertain job by hand, but the Mathematica automation offered here will do any group without requiring human thought at all. All you need to know about the group is its multiplication table.