They were all in the exercise yard of C Block at the time of the attack.
The victim was bouncing a ball against a wall before he was set upon by the trio, who kicked and punched him in the head and body for about two minutes.
He suffered a cut and lump to his head.
Brown was in prison after being sentenced for various crimes earlier in 2020, one that included a jailhouse assault.
Defence lawyer Richard Bedford said Brown may have been charged with common assault previously, but police and Corrections taking a harder line meant more serious charges were becoming more common.