Abstract

We give an explicit construction for the isomophism A8 GL4 (2). The involutions of cycle type 23 in the symmetric group S6, together with the null-set, can be given the structure of an elementary abelian group of order 16, in such a way that S6 preserves the group operation. This gives an embedding ( of S6 into the general linear group GL4(2). Regarding S6 as a subgroup of the alternating group A8, we show that ( extends to A8. Coincidence of group orders implues that this extension is an isomorphism.