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Given a singular surface X, one can extract information on it byinvestigating the fundamental group $\pi_1(X - Sing_X)$. However, calculationof this group is non-trivial, but it can be simplified if a certain invariantof the branch curve of X - called the braid monodromy factorization - is known.This paper shows, taking the Cayley cubic as an example, how this fundamentalgroup can be computed by using braid monodromy techniques and their liftings.This is one of the first examples that uses these techniques to calculate thissort of fundamental group.

Fundamental group for the complement of the Cayley's singularities