The 5-modular Character Table of the Lyons Group
In this talk we will illustrate the state of the art methods in computational modular representation theory of finite groups. Our focus will be on the example of the 5-modular character table of the sporadic simple Lyons group Ly. This table was computed jointly with Alexander Ryba, Queens College, CUNY, New York. We will explain, why one could consider the Lyons group as a characteristic 5 group. As a starting point of our computations we will then take the 111-dimensional representation over the field with 5 elements, conjectured to exist by Meyer, Neutsch and constructed by Meyer, Neutsch, and Parker. An important ingredient in our proof will be the interplay between modular character theory and the theory of condensation of representations, in particular condensations of tensor products and symmetrizations.