Let F n be the free group of rank n and let Aut + (F n ) be its special automorphism group. For an epimorphism π : F n → G of the free group F n onto a finite group G we call Γ + (G, π) = {ϕ ∈ Aut + (F n ) | πϕ = π} the standard congruence subgroup of Aut + (F n ) associated to G and π. In the case n = 2 we fully describe the abelianization of Γ + (G, π) for finite abelian groups G. Moreover, we show that if G is a finite non-perfect group, then Γ + (G, π) ≤ Aut + (F 2 ) has infinite abelianization.

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