'Between' is best as as it emphasises the interaction of the two groups. I could accept 'by' but don't like 'of''. 'Among' is wrong as only two groups are involved.
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between
?preposition& adverb
- 1 at, into, or across the space separating (two objects, places, or points).
- 2 in the period separating (two points in time).
- 3 [as prep.] indicating a connection or relationship involving