How do I create a group feature on a website?

Website Building
#1

For example Steam community groups. Im using php and such to create a website for school. I would like to allow users to create groups, show groupmembers and allow people to join.

Does anyone know how to make this, the basics behind it or the name?
Google didn’t give me anything.

Thanks in advance.

#2

Hi. Can someone please confirm if this is indeed possible?

#3

I 'm using VBB . It’s very good

#5