Ordered simplex volume weighted

Let $A=\{(x,y,z)\in\mathbb{R}^{3}:0\le x\le y\le z\le 1\}$. Let $\alpha$ be the value of the integral $\displaystyle\iiint_{A}xyz\,dx\,dy\,dz$. Then, $384\alpha$ is equal to __________.