//Standard generators of S4(7) are a, b where a is in class 2A,
//b has order 5 and ab has order 7.
//Standard generators of 2.S4(7) = Sp4(7) are preimages A, B where
//B has order 5 and AB has order 7. 
_LR := rec < recformat< F: GrpFP, AI: SeqEnum, G: GrpMat > |
      F := FreeGroup(2) >;
_LR`AI:=[[a,b^-1]]
              where a is (_LR`F).1 where b is (_LR`F).2;
//two reps interchanged by AI[1]
_LR`G :=
/*
Original group: MatrixGroup(ATLASGroup("2S47"))
From DB /nb/reps/d24.2S47.direct.M
Schur index: 1
Character: ( 24, -24, 0, 0, 3, 4, 0, -4, -1, -3, 0, -3, 3, 0, 7*zeta(7)_7^4 + 
7*zeta(7)_7^2 + 7*zeta(7)_7 + 3, -7*zeta(7)_7^4 - 7*zeta(7)_7^2 - 7*zeta(7)_7 - 
4, -4, 3, -zeta(7)_7^4 - zeta(7)_7^2 - zeta(7)_7 - 1, zeta(7)_7^4 + zeta(7)_7^2 
+ zeta(7)_7, -4, 0, 0, 4, -4, 4, 0, 0, 0, 1, -1, 0, 1, -7*zeta(7)_7^4 - 
7*zeta(7)_7^2 - 7*zeta(7)_7 - 3, 7*zeta(7)_7^4 + 7*zeta(7)_7^2 + 7*zeta(7)_7 + 
4, 4, -zeta(7)_7^4 - zeta(7)_7^2 - zeta(7)_7 - 4, -zeta(7)_7^4 - zeta(7)_7^2 - 
zeta(7)_7 + 3, zeta(7)_7^4 + zeta(7)_7^2 + zeta(7)_7 - 3, zeta(7)_7^4 + 
zeta(7)_7^2 + zeta(7)_7 + 4, -3, 0, 0, 2*zeta(7)_7^4 + 2*zeta(7)_7^2 + 
2*zeta(7)_7 + 1, -2*zeta(7)_7^4 - 2*zeta(7)_7^2 - 2*zeta(7)_7 - 1, -zeta(7)_7^4 
- zeta(7)_7^2 - zeta(7)_7, zeta(7)_7^4 + zeta(7)_7^2 + zeta(7)_7 + 1, 0, 0, 
zeta(7)_7^4 + zeta(7)_7^2 + zeta(7)_7, -zeta(7)_7^4 - zeta(7)_7^2 - zeta(7)_7 - 
1, 0, 0, 0, 1, -1, 1, -1, -1, -1, -1, -1, -1, -zeta(7)_7^4 - zeta(7)_7^2 - 
zeta(7)_7, zeta(7)_7^4 + zeta(7)_7^2 + zeta(7)_7 + 1, -zeta(7)_7^4 - zeta(7)_7^2
- zeta(7)_7 - 1, zeta(7)_7^4 + zeta(7)_7^2 + zeta(7)_7, 0, -zeta(7)_7^4 - 
zeta(7)_7^2 - zeta(7)_7, zeta(7)_7^4 + zeta(7)_7^2 + zeta(7)_7 + 1, zeta(7)_7^4 
+ zeta(7)_7^2 + zeta(7)_7 + 1, -zeta(7)_7^4 - zeta(7)_7^2 - zeta(7)_7 - 1, 
-zeta(7)_7^4 - zeta(7)_7^2 - zeta(7)_7, zeta(7)_7^4 + zeta(7)_7^2 + zeta(7)_7, 
0, 0, 0, 0, 0, 1, 1, 1, 1, 1, zeta(7)_7^4 + zeta(7)_7^2 + zeta(7)_7, 
-zeta(7)_7^4 - zeta(7)_7^2 - zeta(7)_7 - 1, zeta(7)_7^4 + zeta(7)_7^2 + 
zeta(7)_7 + 1, -zeta(7)_7^4 - zeta(7)_7^2 - zeta(7)_7, zeta(7)_7^4 + zeta(7)_7^2
+ zeta(7)_7, zeta(7)_7^4 + zeta(7)_7^2 + zeta(7)_7 + 1, -zeta(7)_7^4 - 
zeta(7)_7^2 - zeta(7)_7 - 1, -zeta(7)_7^4 - zeta(7)_7^2 - zeta(7)_7, 0, 0 )
*/

MatrixGroup<24,K | [
Matrix(K,24,24,
[[-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],[0,0],[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],[0,0],[1/2,3/2],
[-3/2,-1/2],[1,0],[3/2,1/2],[-1,-1],[1,2],
[0,1],[1,0],[1,0],[1,2],[1,-1],[2,0],[
0,1],[0,-1],[0,0],[-1,-1],[-3,-2],[0,0],
[1,2],[0,0],[2,0],[1,0],[-1,0],[1,0],
[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],[-2,
0],[1,3/2],[1,2],[0,-1/2],[-2,-9/2],[2,1],
[3,-1],[-3,-3],[3,-1/2],[0,1/2],[2,7/2],[3,
0],[-2,-1],[0,-1],[0,0],[-1,-1],[-1,-1],
[0,0],[-2,0],[0,0],[1,0],[-1,1],[-1,0],
[1,1],[-5/2,-5/2],[-3/2,-2],[-1,1],[-3/2,1],
[4,7/2],[-5,-1],[-3,1],[3,2],[-3,3/2],[-2,
-1/2],[0,-1/2],[-2,2],[-1,-1],[2,1],[0,0],
[3,0],[3,-1],[0,0],[-2,-1],[0,0],[0,2],
[0,0],[0,-1],[-2,0],[-5/2,-1/2],[1/2,0],[
1,0],[-1/2,1],[1,3/2],[-1,0],[0,0],[0,0],
[-1,1/2],[0,-1/2],[0,-1/2],[-1,0],[0,0],
[0,0],[0,0],[1,0],[0,0],[0,0],[0,0],[
0,0],[0,0],[0,0],[0,0],[-1,0],[3/2,3/2],
[1/2,1/2],[0,-1],[-1/2,-1/2],[0,1],[2,0],[0,
-1],[-1,0],[-1,0],[1,-1],[-1,-1],[-2,-1],
[1,0],[-1,0],[0,0],[-1,0],[-1,2],[0,0],
[2,0],[0,0],[-1,-1],[0,0],[1,1],[0,0],
[-1/2,5/2],[-1/2,0],[4,0],[3/2,1],[-1,-3/2],
[2,2],[1,0],[0,-1],[3,-1/2],[0,3/2],[2,
-1/2],[3,0],[0,2],[-1,-1],[0,0],[-1,-1],
[-3,-2],[0,0],[0,2],[0,0],[2,0],[1,0],
[-1,0],[1,0],[9/2,9/2],[-1/2,1/2],[3,-2],
[3/2,-1/2],[-1,-2],[5,1],[0,-1],[-2,-2],[
3,-1],[1,1],[0,-1],[2,-1],[1,2],[-2,-1],
[0,0],[-2,-1],[-3,0],[0,0],[2,2],[0,0],
[1,-1],[1,0],[0,1],[1,0],[-3/2,1/2],[3/2,
-1/2],[3,1],[-3/2,3/2],[0,0],[0,-1],[-2,-2],
[-1,0],[1,0],[-3,-1],[3,1],[0,1],[-2,0],
[0,0],[0,0],[1,0],[2,0],[0,0],[-2,0],[
0,0],[0,1],[1,1],[1,0],[0,0],[13/2,-1/2],
[-1/2,-1/2],[-6,-4],[3/2,-3/2],[1,1],[0,-2],
[-1,1],[1,1],[-2,-1],[1,0],[-5,-2],[-2,-1],
[4,0],[0,1],[0,0],[0,1],[1,2],[0,0],[3,
-1],[0,0],[-2,-1],[-1,-2],[1,0],[-1,-1],
[4,3],[1,-1],[3,-2],[0,1],[3,-1],[0,0],
[-1,0],[1,-1],[3,0],[-3,1],[0,-1],[3,1],
[1,2],[1,0],[0,0],[1,-1],[0,-2],[0,0],
[0,2],[0,0],[2,1],[2,0],[0,-1],[0,0],
[-3,3],[-2,1/2],[5,2],[3,3/2],[4,1/2],[2,
4],[2,3],[5,0],[4,5/2],[-1,3/2],[1,-3/2],
[5,3],[-1,2],[0,-1],[0,0],[0,-1],[-3,-3],
[0,0],[-1,2],[0,0],[3,1],[1,0],[-1,0],
[1,0],[-5,-4],[4,1],[-1,4],[-5,-1],[-3,0],
[-2,-1],[3,-3],[-3,0],[-3,0],[1,-3],[2,4],
[-3,-1],[-2,-3],[1,0],[1,0],[1,2],[2,2],
[0,0],[-2,-3],[0,0],[-2,0],[-2,1],[0,0],
[0,0],[1,0],[-4,-5/2],[-2,-1],[1,1/2],[3,
9/2],[-3,0],[-4,2],[4,3],[-4,3/2],[1,1/2],
[-3,-7/2],[-3,1],[1,0],[1,1],[0,0],[0,0],
[1,0],[0,0],[1,0],[0,0],[0,1],[0,-1],
[0,0],[-1,0],[-1/2,-1/2],[5/2,0],[1,0],
[-5/2,1],[2,3/2],[-2,-2],[-1,-2],[-2,0],
[-1,1/2],[-3,-5/2],[1,3/2],[-2,1],[-1,-1],
[1,1],[0,0],[3,1],[4,1],[0,0],[-2,-1],[
0,0],[-1,1],[0,1],[2,0],[-1,0],[5/2,1/2],
[7/2,0],[-2,-3],[-5/2,0],[-7,-7/2],[-1,-2],
[0,-4],[-7,-2],[-3,-9/2],[1,1/2],[3,5/2],
[-2,-4],[2,0],[0,0],[0,0],[0,0],[-1,0],
[1,0],[0,0],[0,0],[-1,-1],[-1,0],[-1,0],
[0,0],[1,1],[1,-3],[2,-1],[-1,2],[-3,4],
[-3,-2],[-8,-3],[0,5],[-4,-1],[-3,-1],[5,
-2],[-4,0],[-1,1],[0,1],[0,0],[2,1],[3,
0],[0,0],[-1,1],[0,0],[-1,1],[3,1],[2,
0],[0,-1],[1,0],[4,0],[-3,-2],[-2,1],[2,
3],[-1,-2],[-1,-3],[-2,1],[-3,1],[-2,-4],
[-2,1],[-5,0],[1,-2],[1,1],[0,0],[2,2],
[3,3],[0,0],[0,-2],[1,0],[-3,0],[-2,0],
[1,0],[-1,0],[-11/2,-13/2],[-7/2,-1/2],[-5,
1],[-5/2,3/2],[8,5],[-7,-1],[1,4],[4,1],
[-4,3],[-1,-2],[-5,0],[-4,3],[0,-3],[3,2],
[0,0],[3,0],[4,0],[0,0],[-2,-3],[0,0],
[-1,2],[-3,-1],[0,-1],[-3,1],[11/2,-3/2],
[3/2,-1],[-5,-5],[-3/2,-1],[-1,3/2],[0,-3],
[-1,-1],[-2,0],[-4,-5/2],[2,-1/2],[-4,-3/2],
[-4,-3],[5,0],[-1,1],[0,0],[0,1],[0,3],
[0,0],[4,-1],[0,0],[-3,-2],[-1,-2],[0,0],
[-2,-1],[3/2,1/2],[1/2,0],[-2,0],[1/2,-1],
[1,-1/2],[1,0],[0,-1],[1,0],[1,1/2],[-1,
-1/2],[-1,1/2],[0,0],[0,-1],[0,0],[0,0],
[0,0],[1,1],[0,0],[0,-1],[0,0],[-1,0],
[-1,0],[0,0],[0,0],[1,-1],[-7,-1/2],[-4,
1],[3,1/2],[9,-1/2],[-2,3],[1,6],[6,-1],
[3,11/2],[0,3/2],[-7,-1/2],[3,5],[-1,-2],
[3,0],[0,0],[-1,-2],[1,-2],[0,0],[-1,-1],
[0,0],[3,2],[-2,-1],[-1,-1],[0,2]])    ,
Matrix(K,24,24,
[[1/2,-9/2],[-3/2,-3/2],[-6,0],[-1/2,1/2],[
-4,0],[-4,-1],[-2,0],[-1,2],[-4,-1],[2,1],
[1,0],[-2,-1],[1,-1],[0,0],[1,0],[-1,-1],
[0,0],[0,-1],[0,-1],[-2,0],[0,0],[0,0],
[0,0],[0,0],[-17/4,-15/4],[-3/4,7/4],[-1,3],
[-5/4,-3/4],[-5/2,1/2],[-1/2,1/2],[1,1],[0,0
],[-3/2,1/2],[2,-1],[0,1],[-3/2,-1/2],[-3/2,
-3/2],[0,0],[-1/2,-1/2],[-3/2,1/2],[1/2,1/2],
[-1/2,-1/2],[-3/2,-3/2],[0,1],[-1/2,-1/2],[-1,
0],[0,0],[0,0],[-17/4,-15/4],[-3/4,3/4],[-2,
3],[-1/4,-3/4],[1/2,5/2],[-9/2,-1/2],[2,3],
[3,2],[-5/2,3/2],[1,0],[-1,-1],[-3/2,1/2],
[-1/2,-1/2],[1,1],[1/2,1/2],[-1/2,1/2],[3/2,
1/2],[-1/2,-1/2],[-1/2,-3/2],[-1,0],[-1/2,1/2],
[0,0],[1,0],[0,0],[-25/4,-7/4],[-11/4,-3/4],
[1,4],[11/4,3/4],[3/2,4],[-3/2,5/2],[-1,3],
[5,3],[-3/2,3],[1,1/2],[0,-5/2],[-1/2,3/2],
[-3/2,-1/2],[0,0],[-1/2,-1/2],[-3/2,-1/2],
[-1/2,-1/2],[-3/2,-1/2],[-1/2,1/2],[0,1],[
1/2,1/2],[1,0],[0,0],[0,0],[11/4,9/4],[1/4,
-3/4],[1,0],[-5/4,-1/4],[-11/2,-1],[3/2,1/2],
[-2,-2],[-2,1],[-1/2,-1],[1,1/2],[4,-1/2],
[-1/2,-3/2],[-1/2,3/2],[-1,-1],[1/2,1/2],[-3/2,
-1/2],[-5/2,-1/2],[1/2,-1/2],[1/2,3/2],[-1,0],
[1/2,-1/2],[2,1],[0,1],[2,0],[-7/2,-9/2],
[-3/2,3/2],[-3,0],[1/2,1/2],[0,-1],[-4,-1],
[0,2],[-1,0],[-3,-1],[0,0],[0,1],[0,0],
[0,-1],[1,1],[-1,-1],[0,-1],[1,-1],[0,-1],
[-2,-1],[-1,0],[0,0],[-1,0],[0,0],[-1,1],
[-4,-2],[0,0],[-2,1],[1,1],[1,-1],[-5,2],
[3,2],[1,0],[-1,1],[1,2],[0,0],[2,1],
[1,0],[2,0],[1,0],[0,-2],[-1,-3],[0,-1],
[-2,0],[-2,0],[2,1],[0,0],[-1,-1],[0,1],
[-9/2,-3/2],[1/2,3/2],[1,3],[-1/2,1/2],[-1,1],
[2,4],[2,0],[1,0],[0,2],[2,-1],[-1,0],[
-1,0],[0,-1],[0,-1],[0,-1],[-2,0],[-2,0],
[-2,-1],[-1,0],[0,2],[0,-1],[0,0],[0,0],
[1,0],[-9/4,-7/4],[1/4,5/4],[-1,2],[-5/4,-5/4
],[5/2,2],[-1/2,-1/2],[1,2],[3,1],[-1/2,2],
[-1,-3/2],[-2,1/2],[-3/2,3/2],[-3/2,-3/2],[1,
1],[-1/2,1/2],[1/2,3/2],[5/2,3/2],[-1/2,1/2],
[-1/2,-3/2],[1,0],[-3/2,1/2],[-1,0],[1,0],
[0,0],[-3/2,-1/2],[5/2,-1/2],[1,1],[-5/2,3/2],
[-5,0],[0,1],[-2,-3],[-3,1],[-1,0],[-1,-1],
[4,1],[-2,-1],[-1,0],[0,-1],[0,0],[0,0],
[-1,-1],[-1,-1],[-2,1],[0,1],[0,0],[1,1],
[0,0],[1,0],[5/4,-5/4],[-1/4,7/4],[-1,0],
[-7/4,-3/4],[-3/2,0],[5/2,1/2],[0,0],[-1,0],
[-1/2,0],[1,-3/2],[-1,1/2],[-3/2,-1/2],[1/2,
-1/2],[-1,0],[-1/2,-1/2],[-3/2,1/2],[-1/2,3/2
],[-1/2,-1/2],[1/2,-1/2],[0,1],[-3/2,-3/2],[
0,0],[1,1],[1,0],[4,4],[2,-5/2],[2,-3],
[0,3/2],[-2,-5/2],[3,-1],[-4,-6],[-5,-1],
[2,-5/2],[-3,-1/2],[4,5/2],[0,-1],[-1,0],
[-1,-1],[0,0],[2,0],[0,0],[1,1],[0,1],[
1,-1],[0,0],[0,1],[-1,0],[0,0],[15/2,1/2],
[1/2,2],[-1,-6],[-1/2,-1],[4,-1/2],[4,-5],
[-2,1],[0,-1],[2,-5/2],[-4,-3/2],[-4,-1/2],
[0,0],[2,1],[-1,2],[-2,0],[2,2],[3,3],
[0,1],[3,0],[2,-1],[-3,-1],[0,-1],[3,1],
[-1,-1],[-29/4,1/4],[9/4,7/4],[4,5],[-5/4,1/4],
[11/2,5/2],[-3/2,3/2],[3,1],[3,1],[3/2,9/2],
[-4,-3],[1,2],[-1/2,7/2],[-9/2,-3/2],[2,1],
[-1/2,1/2],[3/2,3/2],[7/2,1/2],[-1/2,1/2],[-7/2,
-3/2],[1,0],[-1/2,3/2],[0,2],[1,0],[1,1],
[11/4,-3/4],[-15/4,-3/4],[-2,-1],[7/4,-1/4],
[5/2,2],[-3/2,1/2],[-1,2],[2,1],[-3/2,1],[
2,1/2],[-3,-5/2],[-1/2,1/2],[5/2,1/2],[0,0],
[1/2,-1/2],[-1/2,-1/2],[-1/2,1/2],[1/2,-1/2],
[3/2,-1/2],[-1,0],[1/2,-1/2],[0,-1],[0,0],
[-1,0],[-15/4,-1/4],[7/4,-3/4],[1,-1],[1/4,
11/4],[1/2,3/2],[-7/2,-5/2],[-3,-1],[-2,0],
[-5/2,-1/2],[-3,-1],[2,1],[-3/2,1/2],[-3/2,
-1/2],[1,1],[-3/2,-1/2],[5/2,1/2],[7/2,-1/2],
[1/2,1/2],[-5/2,-1/2],[1,0],[-1/2,3/2],[-1,0],
[0,-1],[-2,0],[4,1],[-1,1],[-2,-2],[1,0],
[0,-3],[1,2],[3,1],[-2,-2],[2,0],[2,1],
[-1,0],[3,0],[2,1],[0,-1],[1,0],[-2,-2],
[-4,-2],[1,-1],[1,1],[-1,0],[2,-1],[0,0],
[-1,0],[1,1],[-6,-5],[-5,-1/2],[-5,3],[4,
1/2],[2,5/2],[-6,0],[-1,6],[7,3],[-4,3/2],
[2,5/2],[-2,-5/2],[0,2],[-1,-1],[2,1],[0,
0],[-1,-1],[1,-1],[0,0],[0,-1],[-1,0],[1,
1],[0,-1],[0,-1],[-1,0],[5/2,1/2],[-3/2,1],
[1,1],[3/2,-1],[3,5/2],[5,1],[1,0],[2,0],
[2,3/2],[1,-5/2],[-5,-3/2],[-1,0],[1,-1],[
-2,0],[0,-1],[-2,2],[0,4],[-1,0],[3,-1],
[2,1],[-2,-2],[-1,-1],[1,1],[0,-1],[13/4,
11/4],[-1/4,5/4],[3,-1],[5/4,-5/4],[11/2,-5/2],
[9/2,3/2],[3,1],[1,-4],[13/2,3/2],[-1,0],
[-4,1],[9/2,3/2],[1/2,1/2],[0,-1],[-1/2,-1/2
],[3/2,1/2],[1/2,-1/2],[1/2,1/2],[-1/2,-1/2],
[1,0],[1/2,-1/2],[-1,-1],[-1,-1],[-1,0],
[-23/4,-9/4],[-5/4,23/4],[0,0],[-3/4,-11/4],
[3/2,-5],[-3/2,1/2],[8,5],[-1,-6],[1/2,-1],
[4,3/2],[-4,5/2],[7/2,-1/2],[-1/2,-1/2],[2,1],
[-3/2,-1/2],[-3/2,-3/2],[-1/2,-5/2],[3/2,1/2],[
-3/2,-3/2],[-1,0],[3/2,-1/2],[-3,-1],[-1,-1],
[-1,2],[3/2,-7/2],[-5/2,-5/2],[-6,-4],[5/2,
3/2],[7,-3],[-6,-3],[-1,3],[3,-2],[1,-1],
[-3,4],[-4,1],[4,3],[2,-1],[3,1],[0,0],
[5,-2],[4,-3],[1,1],[-1,-1],[-1,-2],[2,3],
[-2,-2],[-1,-3],[-4,0],[11/4,21/4],[9/4,5/4],[
6,-1],[-1/4,-5/4],[-5/2,-3],[15/2,1/2],[-1,-3],
[-4,-3],[7/2,-2],[-1,-1/2],[3,3/2],[5/2,-3/2],
[-3/2,3/2],[-2,-1],[-3/2,-1/2],[-1/2,1/2],[-3/2,
1/2],[1/2,1/2],[-1/2,3/2],[1,0],[-1/2,-3/2],
[1,1],[-1,1],[1,0],[-7,2],[6,3/2],[5,2],
[-2,1/2],[-4,-3/2],[0,-2],[2,-2],[-5,-1],
[1,-1/2],[-3,-3/2],[7,7/2],[0,-1],[-5,0],
[0,0],[-2,1],[1,1],[1,-1],[0,1],[-3,1],
[2,0],[-1,1],[0,2],[0,0],[1,1]])
]> where w := K.1 where K := ext<K|Polynomial(K,[2,1,1])> where K
is RationalField();

return _LR;
