Computing the genus of a manifold?

Question

I was reading week 193 of John Baez' blog, and he mentions that $E_8$ can be realized as the symmetry group of a certain 57-dimensional manifold;

Recently, some mathematical physicists have been studying a construction of E8 as the symmetries of a 57-dimensional manifold equipped with extra structure:

1. Murat Gunaydin, Koepsell and Hermann Nicolai, Conformal and quasiconformal realizations of exceptional Lie groups, Commun. Math. Phys. 221 (2001), 57-76, also available as hep-th/0008063

2. Thomas A. Larsson, Structures preserved by exceptional Lie algebras, available as math-ph/0301006.

It turns out that it's very curious that the dimension happens to be 57, and I was wondering what the genus of this manifold might be? Would it be easy to compute? Perhaps it too is an interesting number related to all this Lie theory business.