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GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it

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G:=Group((3,4)(5,6),(2,6,4),(1,2,3)(4,5,6)); 
F:=FreeGroup(3);
F:=F/[F.1^2, F.2^3, F.3^3, (F.2*F.3)^4, (F.2*F.3^-1)^5,
             F.1^-1*F.2^-1*F.3*F.2*F.3*F.2^-1*F.3*F.2*F.3^-1];
m3 := [
[[-1,1,-1,-1,1,0],
[1,1,-1,0,0,1],
[-1,0,1,1,-1,-1],
[0,-1,1,0,-1,0],
[1,-1,-1,0,-1,1],
[-1,-1,0,-1,1,1]],

[[1,0,-1,0,1,0],
[0,1,0,-1,0,1],
[0,0,1,0,1,0],
[0,0,0,1,0,1],
[0,0,0,0,1,0],
[0,0,0,0,0,1]],

[[1,0,0,0,0,0],
[0,1,0,0,0,0],
[0,1,1,0,0,0],
[1,-1,0,1,0,0],
[1,-1,0,-1,1,0],
[-1,-1,-1,1,0,1]]]*Z(3)^0;