Discrepancy in matrix representations of symmetry between crystal and cartesian coordinates

This is to record what I observed. QE 6.6 is used.

• For a simple cubic (ibrav=1) system, the matrix representations of the symmetry in crystal and cartesian coordinates are not coincide for some symmetry operations like 90 deg rotation or 120 deg rotation.
  scf.in and scf.out

• For a hexagonal (ibrav=4) system with space group P6_3/mmc (194), the matrix reps. seem to give different space group P6_3/mcm (193). First I run a calculation with space_group=194 and obtain a list of matrix reps. of symmetry. Then I used matrix reps. in crystal coordinates to check whether they are really belong to space group 194. To do this, IDENTIFY GROUP of Bilbao Crystallographic Server is used. I assumed the matrix applies to the coordinates from the left. If I assume the reverse (i.e. matrix applies from the right) then it gives space group 194. If this is an intended behavior, I think it should be clarified somewhere in the document.
  scf.in and scf.out