Choose a maximal Brauer pair (D,bD) for the block. Its inertial quotient is NG(D,bD)/(DCG(D)), and its order is the inertial index. For cyclic D of order q, this is a prime-to-pdivisor of p−1. The number of edges of the block's Brauer tree is this index, and the exceptional multiplicity is (q−1)/e(B).
