  Majorana theory is an axiomatic tool introduced by A. A. Ivanov in 2009 for
studying the Monster group M and its subgroups through the 196884-dimensional
Conway-Griess-Norton algebra. The group U3(5) is the socle of the centralizer
in M of a subgroup of order 25. The involutions of this U3(5)-subgroup are
2A-involutions in the Monster. Therefore, U3(5) possesses a Majorana
representation based on the embedding in the Monster. We prove that this is the
unique Majorana representation of U3(5), and calculate its dimension, which is
798.
