So I would like to give my members the ability to create a friendship group where they can invite friends ect. 

Is this already a thing or is it some sort of plugin? How would I go about doing this?

Not perfectly sure what a friendship group is, but maybe clubs in 4.2 can do what you are after. 

 

There is no such thing as friends in IPS.  However, certain content items allow members the ability to invite other members for an exclusive group.  Both gallery albums and blogs allow the owners to invite people.  

As @opentype suggested, the new feature of Clubs in IPS 4.2 will probably be the closest thing for you where a person can start a private club and invite other users into the club.