An explicit embedding of the Tits group in the compact real form of   $E_6$
  We construct a set of $27\times 27$ unitary matrices which give an explicit embedding of the Tits group in the compact real form of the Lie group of type $E_6$. A subset gives an embedding of $\mathrm{PSL}_2(25)$ in $F_4$. 
Robert A. Wilson
math.GR