  Let F_n be the free group of rank n and let Aut^+(F_n) be its special
automorphism group. For an epimorphism pi : F_n -> G of the free group F_n onto
a finite group G we call Gamma^+(G,pi) = {f in Aut^+(F_n) | pi*f = pi} the
standard congruence subgroup of Aut^+(F_n) associated to G and pi. In the case
n = 2 we fully describe the abelianization of Gamma^+(G,pi) for finite abelian
groups G. Moreover, we show that if G is a finite non-perfect group, then
Gamma^+(G,pi) < Aut^+(F_2) has infinite abelianization.
