Research of the group of bijective differentiable modulo $p^n$ functions

The group of bijective differentiable modulo $p^n$ functions is researched up to isomorphism. A method of searching for conjugation element in this group is proposed. The method consists in solving a system of linear equations over $\mathbb Z_p$. A technique for generating transitive functions via conjugating the function $f(x)=x+1$ by the bijective differentiable modulo $p^n$ functions is described.