@sergbuto Please note there is an issue with the .cif file you share.
The lines about IT 1 / space group P1 are consistent with each other, both describe the lowest space group symmetry at all, even within the triclinic Bravais class generally described by a unit cell of a \ne b \ne c and \alpha \ne \beta \ne \gamma. On the other hand, earlier lines describe a = b \ne c and \alpha = \beta = 90^\circ and \gamma = 120^\circ which is characteristic for the hexagonal Bravais class of considerably higher symmetry than triclinic. Of course, technically you can describe a structure of hexagonal unit cell as a triclinic one, however for one this requires to maintain many more lines in the loop describing individual atoms by (fractional) unit cell coordinates, than necessary. Second, doing so obfuscates symmetry relationships between individual atoms / fragments of molecules, or whole molecules in the unit cell (think routines like ADDSYM in Platon, reference).
Somewhat related to this is a block missing, which explicitly acknowledges the symmetry operators in the unit cell specific to the particular space group (P1, P\bar{1}, P2_1, P2_1/c, etc.) or a space group’s particular setting (e.g., P2_1/c vs P2_1/a) by symmetry operations. These describe internal mirror and glide planes, centres of inversion, proper axes of rotation, rotoreflections, etc in way how to copy-paste the atoms in the loop of
loop_
_atom_site_label
_atom_site_fract_x
_atom_site_fract_y
_atom_site_fract_z
C 0.7762 0.5000 0.0000
C 0.8138 0.7061 0.0000
C 0.7762 0.7762 0.5000
...
to their then new positions. Some programs address this implicitly by reading the Hermann-Maguin symmetry symbol, or/and the IT number. The explicit way however is a block like
loop_
_symmetry_equiv_pos_site_id
_symmetry_equiv_pos_as_xyz
1 x,y,z
in case of triclinic P1. For \ce{ZnS} in the hexagonal wurtzite structure type, it is
loop_
_symmetry_equiv_pos_as_xyz
x,y,z
-y,x-y,z
y-x,-x,z
-y,-x,z
y-x,y,z
x,x-y,z
-x,-y,1/2+z
y,y-x,1/2+z
x-y,x,1/2+z
y,x,1/2+z
x-y,-y,1/2+z
-x,y-x,1/2+z
where e.g., the line -y,-x,z instructs to paste a copy of any atom at any (x,y,z) at the corresponding (-x, -y, z), etc. See as an example the attached .cif by record COD 1011195.
Contrasting to a .cif file about a model based on diffraction experiments, many fields in a «synthetic .cif file» naturally remain unfilled (sample size, wavelength of radiation, ranges of experimentally accessed (hkl), etc.) and in consequence, checkcif reports many more spots to work on. It still is good practice to fill these fields wherever reasonably possible (see IUCr’s cif dictionaries, or programs like encifer (already shipped with CCDC’s community edition of Mercury).