THE 2-CHARACTER TABLE DOES NOT DETERMINE A GROUP

Frobenius had defined the group determinant of a group G which is a po lynomial in n = Absolute value of G variables. Formanek and Sibley hav e shown that the group determinant determines the group. Hoehnke and J ohnson show that the 3-characters (a part of the group determinant) de termine 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 complete description of such an H is available in Comm. Alg ebra 9 (1981), 627-640.