Constructing the Monster amalgam

The Monster group M contains a pair {C,N} of subgroups, where is the centralizer of an involution and N∼22+11+2⋅11.(M24×Sym3) is the normalizer of an elementary subgroup of order four with N∩C having index three in N. The amalgam {C,N} plays an important role in the existing constructions and uniqueness proofs for the Monster. We suggest a transparent construction of this amalgam.