Facebook – Is it possible to quickly invite people to join a group rather than just adding them

This is not possible in Facebook. It's by design.

Per the Facebook FAQ - How can I become a group admin?

You're automatically an admin if you create a group. Otherwise, if you join a group that already has one or more admins, you can ask any of the existing admins to add you as an admin. If you're a member of a group with no admins, you can become an admin by clicking Make Me Admin under Members in the right column.

However, it appears that Facebook needs to update this FAQ, since there's no longer a right column with a Members sections. Instead, the Make Me Admin option is now under the settings icon (looks like a gear) at the top right of the group page.

So, you will need to privately contact one of your group members and ask him/her to become an admin using the instructions above. He or she will then be able to add you to the group and make you an admin again.

How do I add more admins to my group?

• Click on the About tab
• Find a member by scrolling through the page or entering a name in the search box
• Click Make Admin under the name of the member you wish to add as an admin