Character degrees of extensions of \(\mathrm{PSL}_2(q)\) and \(\mathrm{SL}_2(q)\). (Q2856526)

The author determines, for all values of \(q>3\), the degrees of the irreducible complex characters of every group \(H\) such that \(S\leq H\leq\Aut(S)\), where \(S\) is the projective special linear group \(\mathrm{PSL}_2(q)\). Also, the author determines the character degrees of certain extensions of the special linear group \(\mathrm{SL}_2(q)\). Explicit knowledge of the character tables of \(\mathrm{SL}_2(q)\), \(\mathrm{GL}_2(q)\), \(\mathrm{PSL}_2(q)\), and \(\mathrm{PGL}_2(q)\) is used along with standard Clifford theory to obtain the degrees.