  We compute the renormalized running coupling of SU(3) gauge theory coupled to
N_f = 2 flavors of massless Dirac fermions in the 2-index-symmetric (sextet)
representation. This model is of particular interest as a minimal realization
of the strongly interacting composite Higgs scenario. A recently proposed
finite volume gradient flow scheme is used. The calculations are performed at
several lattice spacings with two different implementations of the gradient
flow allowing for a controlled continuum extrapolation and particular attention
is paid to estimating the systematic uncertainties. For small values of the
renormalized coupling our results for the beta-function agree with perturbation
theory. For moderate couplings we observe a downward deviation relative to the
2-loop beta-function but in the coupling range where the continuum
extrapolation is fully under control we do not observe an infrared fixed point.
The explored range includes the locations of the zero of the 3-loop and the
4-loop beta-functions in the MSbar scheme. The absence of a non-trivial zero in
the beta-function in the explored range of the coupling is consistent with our
earlier findings based on hadronic observables, the chiral condensate and the
GMOR relation. The present work is the first to report continuum
non-perturbative results for the sextet model.
