Groupmate is probably not an official word but people would understand in special situations. It would be better to use a word that tells people what kind of group it is. If they are people you work with say Coworkers. If they are in a scientific research group then they are Labmates or Teammates. If you have to use group, say fellow group members.

You can hyphenate it (group-mate), and the 'error' will disappear; it is a concocted composite word, but acceptable. Hyphenated words lose their hyphens as they become accepted into common usage. You can bet classmate was once class-mate.

Never heard it used until now. Perhaps you can get credit for coining it!

This word doesn't exist in english, but you can use: teammate :)

The Oxford dictionary says no, but I have heard the word, and it is readily comprehensible. I would use it. I am surprised it is not in the dictionary. "During the Outward Bound expedition, one of my groupmates was seriously injured." If you used "teammate," you are implying that you consider the group to be a team, and maybe you don't think that. Blair's suggestion "fellow group members" strikes me as awkward. Maybe the mavens would want you to spell it "group-mate" or "group mate." As it is one concept, I think it is best spelled like you did. Don't use on the TOEFL. I am a liberal, and I believe that language is made by people speaking it. So, I guess, no, the dictionary says it is not an official word, but I think it should be. Sorry I answered the question twice. "comments" removes all of the formatting.