While any Connector can invite people to join a group, only the group's administrator can edit the group's description, details, and contact information, or delete inappropriate content.
To allow another Connector in your group to be an administrator, go to the group by selecting it's name from the top of the page. Then scroll to the Connector you'd like to promote, hover over their photo, and select "make admin" from the dialog that pops up.
If you started an Idealist group, you are already an administrator.
If you are not the group's admin, you can ask the current administrator to make you an admin.