BuddyPress.org

@tubruk to troubleshoot why you can’t create groups, you will need to strip down to default BuddyPress installation because a custom theme or a plugin may be interfering with what can easily be done – creating groups – with a clean BuddyPress installation.

That’s why I suggest that you change your theme to default theme and deactivate all plugins except BuddyPress. Clear cache. Then see if you can create groups.
– If you can create groups, then change theme back to your custom theme and check if you can create groups. If not, then the problem is your custom theme. Contact theme author.
– If you can create groups, then activate BP plugins one by one to see which one is interfering with your group creation. If a plugin interferes with your group creation, contact plugin author.