Let $G$ be the group of symmetries of a regular tetrahedron $T$, including orientation-reversing symmetries.
(a) Decompose the set of faces of $T$ into orbits, and describe the stabiliser of a face.
I need help with the first part of the question.
I think the stabiliser of a face corresponds to the dihedral group $D_3$
(b) Determine the order of G
It is $12$