Majorana theory was introduced by A. A. Ivanov as an axiomatic framework in which to study objects related to the Monster group and its 196884 dimensional representation, the Griess algebra. The objects at the centre of the theory are known as Majorana algebras and can be studied either in their own right or as Majorana representations of certain groups. I will give a brief introduction to the theory before presenting the methods and results of my recent work developing an algorithm to construct the Majorana representations of a given group. 

This work is based on a paper by Á. Seress and is joint with M. Pfeiffer.