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The authors consider the extended Hecke groups H(λq) generated by T(z) =-1 / z, S(z) = -1/(z+λq) and R(z) = 1 / -z with λq = 2cos(π/q) for q ≥ 3 an integer. Inthis paper, the even subgroup He(λq), the second commutator subgroup H"(λq) and theprincipa