The 3-modular character table of the automorphism group of the O&#39;Nan group
One of the open problems of the modular Atlas project (www.math.rwth-aachen.de/~MOC/work.html) is the determination of the 3-modular character table of ON.2, the automorphism group of the O'Nan group ON. Recently, a connection of the O'Nan group to the theory of elliptic curves has been described in "Pariah Moonshine" by Duncan, Mertens, and Ono, see https://www.nature.com/articles/s41467-017-00660-y. In this talk we give a survey of the properties of ON and ON.2, and describe how we determined the 3-modular character table using theoretical and computational methods. The main tools involved are character theoretic and condensation. This is joint work with A. Ryba, Queens College, N.Y.