the ranks of the classes of the chevalley group $g_{2}(4)$

Let $g $ be a finite simple group and $x$ be a non-trivial conjugacy class of $g.$ the {rank} of $x$ in $g$, denoted by $rank(g{:}x),$ is defined to be the minimal number of elements of $x$ generating $g$. in this paper we establish the ranks of all the conjugacy classes of elements for chevalley group $g_{2}(4)$ using the structure constants method. the groups, algorithms and programming, gap [14] is used frequently in our computations.