2-blocks and 2-modular characters of the Chevalley groups G2(q) - Hiss, Gerhard; Shamash, Josephine (Mathematics of computation, 1992)
We first determine the distribution of the ordinary irreducible characters of the exceptional Chevalley group G2(q), q odd, into 2-blocks. This is done by using the method of central characters. Then all but two of the irreducible 2-modular characters are determined. The results are given in the form of decomposition matrices. The methods here involve concepts from modular representation theory and symbolic computations with the computer algebra system MAPLE. As a corollary, the smallest degree of a faithful representation of G2(q), q odd, over a field of characteristic 2 is obtained.