Does the English language have a hypernym for words like "pair", "triad", "tetrad", and "pentad"? I'm not sure where to look.
I believe these are all examples of cardinal quantifiers
cardinal numbers, or cardinals for short, are a generalization of the natural numbers used to measure the cardinality (size) of sets. [Wikipedia]
Quantifier: (n) an expression that indicates the scope of a term to which it is attached. [OED]
So, given a pair, triad, tetrad, etc., each is defined by its cardinal attributes (2, 3, 4, n) along with an identifiable and consistent expression regarding the property of each number.
Mathematicians and computer scientists sometimes use the word tuple or the construct n-tuple (e.g., 2-tuple, 3-tuple, etc.). (This is derived/generalized from words like “double”, “triple”, “quadruple”, “quintuple” and “sextuple”.) This differs from pair, triad, etc., and the other suggestions (set, group, collection, etc.) in that tuple implies that order is significant. For example, [red, green, blue] is not the same 3-tuple as [blue, green, red].
I don’t know whether this would be understood by somebody not in one of the above fields. (I’m not even sure how well it is known within those fields.)