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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 Cayleyalgebra $\mathfrak{C}$ with the field of quaternion numbers $\boldmath{H}$ inthe definition of the groups above, and these groups are denoted as in titleabove. Our aim is to determine the structure of these groups. We callrealization to determine the structure of the groups.

On realizations of the Lie groups $  G_{2,\boldmath\scriptstyle{H}},F_{4,\boldmath\scriptstyle{H}},E_{6,\boldmath\scriptstyle{H}},E_{7,\boldmath\scriptstyle{H}},E_{8,\boldmath\scriptstyle{H}}  $, second edition