Let F n, n ^ 2 denote the free group generated by n letters x 1,...,..., x n and Aut(F n) be the automorphism group of F n. Certain subgroup of the group Aut(F n) are considered. First of all examine the palindromic automorphism group nA(F n). This group first defined Collins in [1], which is related to congruence subgroups of SL(n, Z), and symmetric automorphism group of the free group. It is calculate the center of the palindromic automorphism group. For this used combinatorics on words of the group Fn. Second theme of this paper connect with faithfulness of a linear representation of the group elementary palindromic automorphisms MIA(F n). It is show that some concrete representation are not linear. For this use the subgroup 1A(Fn) of group Aut(Fn) [15].