On the Minimal Distance between Group Tables

We examine the minimal distance (number of differing entries) between different group tables of the same order n. Here group table means a matrix of order n with entries from a fixed set of n symbols, which (with suitable border elements) is the multiplication table of a group. (The border elements are not considered part of the table. A group is defined up to isomorphism by its multiplication table without border elements.) With the exception of some pairs of groups of orders 4 and 6, which are listed explicitly, different group tables of order n differ in at least 2n places; and with the exception of some pairs of groups of orders 4, 6, 8 and 9, which are listed explicitly, tables of non-isomorphic groups of order n always differ in strictly more than 2n places.