  A static black hole with spherical symmetry is obtained and examined in the
framework of Einstein-Yang-Mills-dilaton theory. The obtained black hole
solution allowed us to derive and investigate entropy, temperature and heat
capacity. To better examine the thermodynamics of the black hole extended phase
space is also used. On this ground the equation of state is obtained and
studied. We have also investigated the Gibbs free energy and it is shown that
below the critical temperature the system demonstrates phase transitions of the
first as well as of the zeroth order which is notable feature for other types
of dilaton black holes. At the end critical exponents for the black hole are
calculated.
