  Yang-Mills theory and QCD are well-defined for any Lie group as gauge group.
The choice G2 is of great interest, as it is the smallest group with trivial
center and being at the same time accessible to simulations. This theory has
been found to have many properties in common with SU(3) Yang-Mills theory and
QCD, permitting to study the role of the center. Herein, these investigations
are extended to topological properties of G2 Yang-Mills theory. After giving
the instanton construction for G2, topological lumps with instanton topological
charge are identified in cooled lattice configurations. The corresponding
topological susceptibility is determined in the vacuum and at low and high
temperatures, showing a significant response to the phase structure of the
theory.
