I have no friends too and I could create a private group.
Maybe take a good look at the menu's to figure out how..
Well, let's see here. I go to Start. And then I hover over 'Open Play' and I get a yellow box. I hover over 'Solo Play' and I get a yellow box. I hover over 'Private Group' and I get a red box.
When I click 'Open Play', I'm greeted by a spinning ship. When I click 'Solo Play', I'm greeted by a spinning ship. When I click 'Private Group', nothing happens.
Pretty sure I know how menus work. If there is something I need to enable or setup before 'Private Group' will work, it sure would be fantastic for the menu system to let me know. But since there is no such helpful feature, I made an assumption that by not having any in-game friends added, or belonging to any in-game groups, this option wouldn't make much sense for me, so the developers intentionally made it unavailable.
Glad to know I could count on you for explaining how you are able to create a private group without having any in-game friends. Oh great space wizard, please bless us with thine knowledge!