You must have "Full Access" or "Limited Access - HQ Tools" permission to create or edit groups.
Creating "Groups" allows organizations to keep a collection of members together. Groups provide the ability to assign group permissions to pages or send mass emails. If a group is created from the directory or registration, you can attach a group to a page. There are two types of groups on the SportsEngine Platform:
Group: A collection of members that can be added to a single group from the list of members in the directory.
Smart Group: Either created for the list of members or from a registration session. As people become members of the site or register, members will dynamically be placed in these groups.