Moduli Spaces of (Co)Closed G2-Structures on Nilmanifolds

We compute the dimensions of some moduli spaces of left-invariant closed and coclosed G₂-structures on 7-dimensional nilmanifolds, showing that they are not related to the third Betti number. We also prove that, in contrast to the case of closed G₂-structures, the group of automorphisms of a coclosed G₂-structure is not necessarily abelian.