Three Dimensional Geometry: JEE Main 2023 Mathematics question

Let two vertices of a triangle ABC be (2, 4, 6) and (0, $-$2, $-$5), and its centroid be (2, 1, $-$1). If the image of the third vertex in the plane $x+2y+4z=11$ is $(\alpha,\beta,\gamma)$, then $\alpha\beta+\beta\gamma+\gamma\alpha$ is equal to :