Kw. Johnson et Sk. Sehgal, THE 2-CHARACTER TABLE DOES NOT DETERMINE A GROUP, Proceedings of the American Mathematical Society, 119(4), 1993, pp. 1021-1027
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.