Abstract. 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.

AMS Subject Classification (1991): 05B15, 20N05, 20A99

Received October 14, 1994 and in revised form September 5, 1996. (Registered under 5769/2009.)