Characters of the automorphism group of the group \(GL_ 6(2)\) (Q1820866)

The group \(G=GL(6,2)\) has 60 classes. Let \(\bar G=Aut G\), K a certain \(\bar G\)-class. If \(K\subset G\) then K is positive; if \(K\subset \bar G- G\), then K is negative. \(\bar G\) has 16 fused, 28 non-fused and 28 negative classes, i.e. the class-number of \(\bar G\) is 72. The Frobenius- Schur indicators of irreducible characters of \(\bar G\) are equal to \(+1\), i.e. all irreducible representations of G are realizable over the reals. The author constructs the character table of Ḡ.