Members are free to create their own group.
Setting up your own group gives you administrative control of the group. You will be able to manage membership and control of membership.
Click on the 'Create content' link.

Once you click on the 'Create content' link, you will see a list of options appear in the menu, and a page will open up describing each type content.
Click on either of the 'Groups' links.
Type in your group's name, and give it a description. The red stars indicate these both need to be filled in.

If you want new members to the site to have the option of joining your group when they sign up to the web site, then hit this box.
This is the message new members will see when they join your site.

Membership
Open? This means anybody who is a member of the site can become a member of your group.
Moderated. Somebody requests to join. Then you visit the group page member's list and you'll see them awaiting membership confirmation.
Invite only. Users can't even request to join, and if you uncheck the option for it to appear in the registration page, and uncheck the option for it to appear in the group directory page, then it (and it's contents) will be all but invisible to you and your select members.
Closed. Nobody in and ... nobody out! without the administrator's say-so. A pretty heavy-handed option, and not sure in what context you would want to enforce membership...
Listing
If you leave this checked, your group will be listed in the directory on the main groups page.
Privacy
You can ensure your group is only visible to its members by clicking on this box.
You may have an image you want to attach. Hit the 'Choose File' button, or if you've already uploaded an image from your user account's 'File browser', then click on the button under 'Existing image'.
Give it a title, and that's that.
Hit the save button when you're done. You will see the published page. If you're not happy with something, you can always hit the 'edit' button at the top of the page and change things, or even 'Delete' it by hitting the hitting the 'Edit' button and scrolling down to the bottom of the page, where you will see it alongside the save and preview buttons.
You're now the founder of your own group.
If you're keen it is also possible to develop your own look for the site. You'll need to get in touch with thegnomeproject's admin for that.