  We use group schemes to construct optimal packings of lines through the
origin. In this setting, optimal line packings are naturally characterized
using representation theory, which in turn leads to a necessary integrality
condition for the existence of equiangular central group frames. We conclude
with an infinite family of optimal line packings using the group schemes
associated with certain Suzuki 2-groups, specifically, extensions of Heisenberg
groups. Notably, this is the first known infinite family of equiangular tight
frames generated by representations of nonabelian groups.
