Creating a mutual group between 2 groups

For EasySocial, my objective is to create a new mutual group which serves an existing 2 groups. Each of the 2 groups are private, but searchable, and have up to 50-100 members. The new mutual group purpose is to facilitate communications and sharing between the 2 groups and will also be private, and invite only. What is the most efficient method to invite all members of the 2 groups to join this 3rd group? Is there anything better than typing in the users one at a time, in the invite field? Such as inviting a group, which then notifies each member of the group that invite is waiting for them to accept.