The projective special orthogonal group PSO⁺₈(3) is a group obtained from the special orthogonal group PSO⁺₈(3) on factoring by the group of scalar matrices it contains. The group PSO⁺₈(3) has a maximal subgroup of the form 2⁶.S₈ with index 3838185.  The group Q = 2⁶.S₈ is a non-split group extension of an elementary abelian 2-group of order 64 by the symmetric group S₈.  In the present talk, we look at construct of such extension and compute its character table by using the Fischer-Clifford theory. We will also look at generating pairs for the Fischer's largest sporadic simple group Fi'₂₄. ​​