In ''Compact manifolds with special holonomy" by D. Joyce, on p. 242, the group $G_2$ is defined to be the subgroup of $GL(7,R)$ preserving the $3$-form:
$$ \varphi_0 := dx_{123} + dx_{145} + dx_{167} + dx_{246} - dx_{257} - dx_{347} - dx_{356}, $$
where $dx_{ijl} := dx_i \wedge dx_j \wedge dx_l$. Why does this group have dimension $14$?