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Frobenius had defined the group determinant of a group G which is a polynomial in n = \G\ variables. Formanek and Sibley have shown that the group determinant determines the group. Hoehnke and Johnson show that the 3-characters (a part of the group determinant) determine the group. In this paper it is shown that the 2-characters do not determine the group. If we start with a group G of a certain type then a group H with the same 2-character table must form a Brauer pair with G . A completedoi:10.2307/2159960 fatcat:2vxuyieo2rd7hbaamvernomza4