  We investigate the discrete $\beta$ function of the 2-flavor SU(3) sextet
model using the finite volume gradient flow scheme. Our results, using clover
improved nHYP smeared Wilson fermions, follow the (non-universal) 4-loop
$\overline{\textrm{MS}}$ perturbative predictions closely up to $g^2 \approx
5.5$, the strongest coupling reached in our simulation. At strong couplings the
results are in tension with a recently published work using the same gradient
flow renormalization scheme with staggered fermions. Since these calculations
define the discrete $\beta$ function in the same continuum renormalization
scheme, they should lead to the same continuum predictions, irrespective of the
lattice fermion action.
  In order to test systematic effects in our computation we compare two
different lattice operators, three different flow definitions, and two volume
extrapolations. We find agreement among these different approaches in the
continuum limit when the gradient flow parameter $c\gtrsim0.35$. Considering
the potential phenomenological impact of this model, it is important to
understand the origin of the disagreement between our work and the staggered
fermion results.
