Properties
The Rudvalis group acts as a rank 3 permutation group on 4060 points, with one point stabilizer the Ree group 2F4(2), the automorphism group of the Tits group. This representation implies a strongly regular graph in which each vertex has 2304 neighbors and 1755 non-neighbors. Two adjacent vertices have 1328 common neighbors; two non-adjacent ones have 1208 (Griess 1998, p. 125)
Its Schur multiplier has order 2, and its outer automorphism group is trivial.
Its double cover acts on a 28-dimensional lattice over the Gaussian integers. The lattice has 4×4060 minimal vectors; if minimal vectors are identified if one is 1, i, –1, or –i times another then the 4060 equivalence classes can be identified with the points of the rank 3 permutation representation. Reducing this lattice modulo the principal ideal
gives an action of the Rudvalis group on a 28-dimensional vector space over the field with 2 elements. Duncan (2006) used the 28-dimensional lattice to construct a vertex operator algebra acted on by the double cover.
Parrott (1976) characterized the Rudvalis group by the centralizer of a central involution. Aschbacher & Smith (2004) gave another characterization as part of their identification of the Rudvalis group as one of the quasithin groups.
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