  In order to define the exceptional compact Lie groups $G_2,F_4,E_6,E_7,E_8$,
we usually use the Cayley algebra $\mathfrak{C}$ or its complexification
$\mathfrak{C}^C$. In the present article, we consider replacing the Cayley
algebra $\mathfrak{C}$ with the field of quaternion numbers $\boldmath{H}$ in
the definition of the groups above, and these groups are denoted as in title
above. Our aim is to determine the structure of these groups. We call
realization to determine the structure of the groups.
