γ is a permutation on eight elements, though you are not told which permutation it is. If γ is applied to an 8-element set, what is the minimum number of additional times we must apply γ to the resulting set in order to guarantee the set is back in its original configuration when we stop?

Question

γ  is a permutation on eight elements, though you are not told which permutation it is. If γ  is applied to an 8-element set, what is the minimum number of additional times we must apply γ  to the resulting set in order to guarantee the set is back in its original configuration when we stop?