Consider the symmetry group of rotations in $3$ dimensions of the triangular prism, acting on colourings of the faces of a triangular prism with $4$ colours (red, blue, yellow and green). Note that the triangular faces are equilateral triangles. triangular prism
Use the counting theorem to determine the number of colourings of the faces of the prism with $4$ colours, where two colourings are considered the same if one can be obtained from the other by applying an element from the symmetry group of rotations of the prism.
For the counting theorem I know that the size of my $|G| = 12$ since there are $12$ symmetries for my triangular prism and the fix (Identity) will be $3^4$. I'm having trouble finding out what my other fix functions should be.