On the action of the sporadic simple Baby Monster group on its conjugacy class 2B

Abstract: We determine the character table of the endomorphism ring of the permutation module associated with the multiplicity-free action of the sporadic simple Baby Monster group B on its conjugacy class 2B, where the centraliser of a 2B-element is a maximal subgroup of shape 2¹⁺²².Co₂. This is one of the first applications of a new general computational technique to enumerate big orbits.