Question: are you looking to hide one specific group "name" from all students, or hide "who" belongs to that group? ...or are you looking to hide all groups from students.
There are three pieces to consider:
1 - You can prevent students from seeing ALL group memberships on the participants page entirely, not on a per group basis.
If you do that, it will allow students to only see the roles column:
2 - Even if you did that, students can still see groups users are in on the profile pages of other users (at the bottom of the course details section). So you'd have to entirely turn off Groups visibility in your site policies.
3 - Even after that, if you utilize forums, students can see all groups in the course (not who is in it however) through certain forum formats, such as "Forum - Each Person Posts One Discussion"
So just wanted to point these things out for your consideration...