I'm not so sure that "relationship" has to be used in this example. Would you mind offering more information as to why you believe "relation" is not appropriate? In a grammatical sense, the sentence is correct (in my opinion); however, when I think about it, I have heard people saying "relationship" more than "relation" in similar cases. Why that's the case? I'm not sure. Perhaps someone else can follow-up. Again, I don't think "relation" is incorrectly used in a grammatical sense. It could just be one of those funny things where people tend to use the word, "relationship," more frequently.
Also, on an unrelated note, the word "among" should be used instead of "between." "Among" is used for more than 2 things, while "between" is strictly used for 2 things (this is a mistake that native English speakers, myself included, make frequently). In this case, since you're talking about six categories, "among" is the correct word.
I hope this helps!