We study the large scale geometry of the upper triangular subgroup of
PSL(2,Z[1/n]), which arises naturally in a geometric context. We prove a
quasi-isometry classification theorem and show that these groups are
quasi-isometrically rigid with infinite dimensional quasi-isometry group. We
generalize our results to a larger class of groups which are metabelian and are
higher dimensional analogues of the solvable Baumslag-Solitar groups BS(1,n)