To compute |Co0| it is best to consider Λ4, the set of vectors of type 4. Any type 4 vector is one of exactly 48 type 4 vectors congruent to each other modulo 2Λ, falling into 24 orthogonal pairs A set of 48 such vectors is called a frame or cross. N has as an orbit a standard frame of 48 vectors of form (±8, 023). The subgroup fixing a given frame is a conjugate of N. The group 212, isomorphic to the Golay code, acts as sign changes on vectors of the frame, while M24 permutes the 24 pairs of the frame. Co0 can be shown to be transitive on Λ4. Conway multiplied the order 212|M24| of N by the number of frames, the latter being equal to the quotient . That product is the order of "any" subgroup of Co0 that properly contains N; hence N is a maximal subgroup of Co0 and contains 2-Sylow subgroups of Co0. N also is the subgroup in Co0 of all matrices with integer components.