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In computational group theory, a black box group (black-box group) is a group G whose elements are encoded by bit strings of length N, and group operations are performed by an oracle (the "black box"). These operations include: • taking a product g·h of elements g and h,• taking an inverse g−1 of element g,• deciding whether g = 1. This class is defined to include both the permutation groups and the matrix groups. The upper bound on the order of G given by |G| ≤ 2N shows that G is finite.