On the Fischer-Clifford matrices of the non-split extension $2^6{{}^{\cdot}}G_2(2)$

The group $2^6{{}^{\cdot}} G_2(2)$ is a maximal subgroup of the Rudvalis group $Ru$ of index 188500 and has order 774144 = $2^{12}.3^3.7$‎. ‎In this paper‎, ‎we construct the character table of the group $2^6{{}^{\cdot}} G_2(2)$ by using the technique of Fischer-Clifford matrices‎.