  In this work a static spherically symmetric black hole's solution within the
Einstein-Maxwell-Yang-Mills-dilaton theory is derived. The obtained solution is
examined, in particular, we have calculated the Kretschmann scalar which
allowed us to characterize singularity points. Using the obtained black hole's
solution we have studied its thermodynamics. Namely, the temperature was
calculated, the first law was written, and the heat capacity was studied. The
extended thermodynamics approach is utilized to obtain the equation of state.
Within the extended thermodynamics the Gibbs free energy is derived and
investigated. The analysis of the Gibbs free energy shows that below the
critical temperature besides the first order phase transition in addition the
zeroth order phase transition occurs, what is typical for other types of black
holes with dilaton fields. Finally, we have shown that the critical exponents
take the same values as for other types of the dilaton black holes.
