How to create a Group Challenge?

Your group has to actually really be a group. If you are alone in the group, it is no group, it is still only you, and hence you cannot challenge anyone, thus the option is not available. Invite people, and when someone joins, you'll see the option to add a challenge.

Only owners (or members with admin rights) can create the challenges. I see you wrote you created the group, so you should be the owner. In that case it could be perhaps a matter of privacy settings - possibly both members have to share at least the profile with the group (in User Profile settings) - I am not sure about that, though, it is just a wild guess.

Edit: there is also a blue button "+ Challenge" in the right top corner of the group screen, so perhaps the tab Challenges appears in the menu only once you create a challenge, using that button.