Let $\Lambda$ be a row-finite and source-free higher rank graph with finitely many vertices. The Higman-Thompson like group $\operatorname{\Lambda_{ht}}$ of the graph C*-algebra $\mathcal{O}_\Lambda$ is defined to be a special subgroup of the unitary group in $\mathcal{O}_\Lambda$. It is shown that $\operatorname{\Lambda_{ht}}$ is closely related to the topological full groups of the groupoid associated with $\Lambda$. Some properties of $\operatorname{\Lambda_{ht}}$ are also investigated. We show that its commutator group $\operatorname{\Lambda_{ht}^\prime}$ is simple and that $\operatorname{\Lambda_{ht}^\prime}$ has only one nontrivial uniformly recurrent subgroup if $\Lambda$ is aperiodic and strongly connected. Furthermore, if $\Lambda$ is single-vertex, we prove that $\operatorname{\Lambda_{ht}}$ is C*-simple and also provide an explicit description on the stabilizer uniformly recurrent subgroup of $\operatorname{\Lambda_{ht}}$ under a natural action on the infinite path space of $\Lambda$.