A badge in the shape of the Children of the Cathedral symbol. On one side you notice bumps and indentations, almost reminding you of a key.”
COC badge (red) is a miscellaneous item in Fallout.
Once you arrive to the Cathedral, you need to go through a staircase in the back of the main room. However, the door leading to that room is locked. To get there, you need this badge (or you can lockpick the door. Most of the Children in the main room, like Lasher, will carry one.