$S_3 = GL(2, F_2)$. It has $3$ irreps - trivial, sign, standard 2d.
Can one help me to understand general words about Irreps of $G(F_q)$ ("principal series", "parabolically induced", "cuspidal", "complimentrary series", "Steinberg irrep") in this particular example ? I mean who of these irreps is who ?
Notes on the subject I am looking:
Paul Garrett: http://www.math.umn.edu/~garrett/m/v/toy_GL2.pdf
Amritanshu Prasad http://www.imsc.res.in/~amri/html_notes/notes.html#notesch2.html