This note has three aims. First it shows how the GAP system [GAP04] can be utilized to construct character tables of certain central extensions from known character tables; the GAP functions used for that are part of the GAP Character Table Library [Bre04]. Second it documents several constructions of character tables which are contained in the GAP Character Table Library. Third it serves as a ...

In this paper, we provide an introduction to the representation theory of finite groups. We begin by defining representations, G-linear maps, and other essential concepts before moving quickly towards initial results on irreducibility and Schur’s Lemma. We then consider characters, class functions, and show that the character of a representation uniquely determines it up to isomorphism. Orthogo...