CMOQR 2015 Problem 3

Let $N$ be a 3-digit number with three distinct non-zero digits. We say that $N$ is mediocre if it has the property that when all six 3-digit permutations of $N$ are written down, the average is $N$ . For example, $N = 481$ is mediocre, since it is the average of $\{418, 481, 148, 184, 814, 841\}$ .

Determine the largest mediocre number.