Here's your straight ahead, bread and butter kind of Daily Didactic Diversion. There is no name for a group of peacocks. Parliament it is. Beats me as to why that is. Pete Stephenson got this from the September 2000 issue of National Geographic magazine, and is now forever personally liable for any and all damages resulting from a copyright infringement claim by the National Geographic Society.
Thems is the breaks.
Don't hold back. Let us know how you feel. You can have a parliament of owls. But the proper name for a group of peacocks is an ostentation. That must be awfully embarrassing.