Its Schur multiplier has order 2, and its outer automorphism group is trivial.
In 1982 Robert Griess showed that Ru cannot be a subquotient of the monster group.
Reducing this lattice modulo the principal ideal gives an action of the Rudvalis group on a 28-dimensional vector space over the field
Duncan (2006) used the 28-dimensional lattice to construct a vertex operator algebra acted on by the double cover.
Such an involution partitions the 4060 points of the graph into 2030 pairs, which can be regarded as 1015 double transpositions in the alternating group A4060.