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I can reformulate more precisely my problem :

first, I have an exact sequence

0 -> K -> G -> H -> 0 H is PSL(2,Z/7Z) so order(H) is 168. G is < x,y | x^-1 * y * x * y^-1 * x * y * x^-1 * y^-1 * x >

I try to find a presentation of K for computing the rank of K/[K,K].

I have a representation of G in PSL(2,O_3) and the homomorphism

G -> H for this presentation but it seem to give no more information because

the order of G is infinite. What could I do ?

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