**Title:** Detecting large-scale invariants of infinite groups

**Abstract:** Finitely presented groups can be studied geometrically by means of the Cayley graph. The geometry of the Cayley graph has a direct influence on the algebraic properties of the group; for instance, the growth rate of the graph determines if the group is nilpotent. However, it can be difficult to determine the geometric properties of the group. We show how subdivision rules and cube complexes can be used to calculate geometric invariants of infinite groups.