I have searched for calendar plugins and can't find one that does the following. I am considering paying a developer to get this plugin built, but am not sure what the process is to do this (I know WP jobs exists, but have never used it)
Synced calendars – Only group admins (from BuddyPress) can post/edit their own calendars. Group admins cannot edit other group's calendars. Members who subscribe to groups can see 1 calendar with all items of all groups. There will be a mini calendar in the sidebar widget area to everyone can quickly jump to any day.