How far apart can the group multiplication tables be?

Put dist(G(·), G(*)) = card{(a, b) eG2; a · b ≠ a * b} for any two groups G(·), G(*) with the same underlying set and δ(G(·)) = min dist(G(·), G(*)), where G(*) runs through all groups with dist(G(·), G(*)) ≠ 0. It holds that δ(G(·)) e {6n − 24, 6n − 20, 6n − 18} for any n ⩾ 51, n being the order of G. Moreover, groups G(·) and G(*) are isomorphic whenever dist(G(·), G(*)) ⩽ n2/9.