I am trying exercises of Ch-14 Introductory Combinatorics by Richard Brualdi .
The questions in which author asks to find Edge symmetry group and Face symmetry group of regular tetrahedron are really lengthy to work out. I did the case for finding symmetry group of regular tetrahedron and it had 24 elements. During the class discussion ( before giving the exercise) the instructor told us that the Symmetry group, edge symmetry group and face symmetry group are isomorphic.
My question is, can someone tell some way to prove that Edge symmetry group and face symmetry group is isomorphic to Symmetry group without actually finding the Edge symmetry group and face symmetry group ?
OR
A less lengthy way to find Edge symmetry group and face symmetry group?