Aoi Ryugoku is the Enforcer of the Student Council. That means her job is to maintain peace throughout the school. She is a very physically imposing person, so it's no mystery why Megami chose her for this position. However, she's been known to take her job a little too seriously.
There are a handful of students at school who hide one of their eyes for some personal reason, but Aoi is currently the only student who is 100% confirmed to actually be missing an eye.