GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it
G:=Group((1,2)(4,5),(2,3,4)(5,7,6)); F:=FreeGroup(2); F:=F/[F.1^2,F.2^3,(F.1*F.2)^7,Comm(F.1,F.2)^4]; m2 := [[[0,0,1],[1,1,1],[1,0,0]],[[0,1,0],[1,1,0],[0,0,1]]]*Z(2); m7 := [[[0,0,1],[0,-1,0],[1,0,0]],[[0,0,1],[0,-1,-1],[1,2,1]]]*Z(7)^0;