Editing Conway group (section)

==Involutions in Co<sub>0</sub>==
Any [[involution (mathematics)#group theory|involution]] in Co<sub>0</sub> can be shown to be [[Conjugacy class|conjugate]] to an element of the Golay code. Co<sub>0</sub> has 4 conjugacy classes of involutions.

A permutation matrix of shape 2<sup>12</sup> can be shown to be conjugate to a [[Binary Golay code#Mathematical definition|dodecad]]. Its centralizer has the form 2<sup>12</sup>:M<sub>12</sub> and has conjugates inside the monomial subgroup. Any matrix in this conjugacy class has trace 0.

A permutation matrix of shape 2<sup>8</sup>1<sup>8</sup> can be shown to be conjugate to an [[Binary Golay code#Mathematical definition|octad]]; it has trace 8. This and its negative (trace −8) have a common centralizer of the form {{nowrap|(2<sup>1+8</sup>×2).O<sub>8</sub><sup>+</sup>(2)}}, a subgroup maximal in Co<sub>0</sub>.