//Standard generators of Sz(8) are a and b where a has order 2, b has order 4,
//ab has order 5, abb has order 7 and ababbbabb has order 7. The condition that
//abb has order 7 is redundant.
//Standard generators of a particular double cover 2.Sz(8) are preimages A and B
//where AB has order 5, ABB has order 7 and ABABBBABB has order 7. Note that
//if (a, b) is fixed, then these relations only hold in one of the three double
//covers.
_LR := rec < recformat< F: GrpFP, AI: SeqEnum, G: GrpMat > |
      F := FreeGroup(2) >;
_LR`AI := [[a, b^2*a*b^2*a*b^-1*a*b*a*b^-1*a*b^-1*a*b]]
                     where a is(_LR`F).1 where b is (_LR`F).2;

//two reps fixed by auto
_LR`G := sub<GL(28,Integers()) |
\[ 0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,
1,1,0,0,-1,0,3,-1,1,0,-1,-1,0,-1,1,0,1,-1,0,2,0,-2,-1,
-1,0,-1,-1,-1,-1,0,1,1,0,-3,0,-1,-1,1,0,0,-1,-1,-1,-1,
0,0,-1,0,2,1,-2,0,-1,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,
1,2,0,1,-1,-1,2,-2,0,0,-2,-1,-1,0,0,0,0,0,-1,1,1,-1,
-1,-1,0,0,-1,-1,-2,0,2,1,1,-2,-1,0,-2,2,0,1,-1,0,0,0,
0,1,0,-1,1,1,-1,0,-1,1,0,2,0,-2,-1,-3,0,2,2,3,2,0,1,
0,2,-1,2,0,2,-2,1,2,-3,-2,-1,0,0,-1,0,0,2,1,-2,0,-3,
-2,2,-2,3,-1,0,-2,0,-2,-1,-2,0,-1,-2,3,2,1,-2,0,0,0,-1,
0,-2,-1,2,1,1,-3,-1,0,-1,2,1,1,-1,0,0,-2,0,1,-1,-1,2,
3,-1,1,-1,1,0,2,0,-2,-1,-1,1,1,-3,1,0,-1,2,1,1,0,0,0,
-2,1,1,-2,-1,1,3,1,1,0,1 ],
\[ 0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,
0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,
0,0,0,-1,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,
0,0,0,0,0,0,-1,0,1,0,1,-1,-2,1,-2,0,0,-1,-1,-1,-1,-1,
-1,0,0,-1,1,2,1,-2,0,-1,1,-1,0,-1,0,1,1,1,-1,-2,0,-2,
1,0,1,-1,1,-1,0,-1,1,0,-2,1,2,1,1,0,1,1,0,1,0,-1,-1,
-1,1,1,0,1,-1,0,0,1,0,0,0,0,-1,0,1,-1,-1,0,0,0,0,0,
-1,0,1,0,1,-1,-1,1,-1,0,0,-1,-1,0,0,0,0,0,0,-1,1,1,0,
-1,0,0,0,0,1,-1,-2,1,-1,3,2,-4,2,-2,0,1,2,0,2,0,1,-1,
2,2,-4,-2,1,4,1,1,0,2,1,1,-1,-2,-3,-1,4,2,2,2,-1,0,0,
2,0,2,1,1,-2,2,2,-4,-4,1,-1,1,-2,0,0,2,1,-2,0,-3,-2,4,
-1,3,0,0,-1,0,-2,0,-1,1,-3,-1,3,1,-2,-3,-1,0,0,-2,-2,0,
2,1,3,0,-4,-2,-3,-1,0,0,0,-1,0,-2,-1,-1,1,-3,-1,3,3,-2,
0,-1,2,0,0,1,1,-2,-1,-2,1,2,0,2,-1,0,-1,1,-1,0,1,1,-2,
0,3,-1,-2,-2,-1,0,0,0,-1,0,2,1,2,-1,-2,1,-2,0,0,-1,-1,
-1,0,-1,-1,1,0,-2,1,3,2,-2,0,-1,0,0 ] >;

return _LR;
