  We use high resolution angle resolved photoemission spectroscopy and density
functional theory with experimentally obtained crystal structure parameters to
study the electronic properties of CaKFe4As4. In contrast to related CaFe2As2
compounds, CaKFe4As4 has high Tc of 35K at stochiometric composition. This
presents unique opportunity to study properties of high temperature
superconductivity of iron arsenic superconductors in absence of doping or
substitution. The Fermi surface consists of three hole pockets at $\Gamma$ and
two electron pockets at the $M$ point. We find that the values of the
superconducting gap are nearly isotropic, but significantly different for each
of the FS sheets. Most importantly we find that the overall momentum dependence
of the gap magnitudes plotted across the entire Brillouin zone displays a
strong deviation from the simple cos(kx)cos(ky) functional form of the gap
function, proposed in the scenario of the Cooper-pairing driven by a short
range antiferromagnetic exchange interaction. Instead, the maximum value of the
gap is observed for FS sheets that are closest to the ideal nesting condition
in contrast to the previous observations in some other ferropnictides. These
results provide strong support for the multiband character of superconductivity
in CaKFe4As4, in which Cooper pairing forms on the electron and the hole bands
interacting via dominant interband repulsive interaction, enhanced by FS
nesting}.
