_LR := rec < recformat< F: GrpFP, AI: SeqEnum, G: GrpMat > |
      F := FreeGroup(2) >;
_LR`AI := [ [a^-1,b^-1] ] where a is (_LR`F).1 where b is (_LR`F).2;
//Standard generators of S4(5) are a and b where a is in class 2B, b is in class
//3B and ab is in class 13C. The last condition is equivalent to: ab has order
//13 and ababb has order 12.
//Standard generators of 2.S4(5) are preimages A and B where B has order 3 and
//AB has order 13.

//2 constituents
_LR`G :=
/*
Original group: PermutationGroup(ATLASGroup("2S45"))
From DB /nb/reps/d52.2S45.si2.nfdeg4.M
Schur index: 2
Character: ( 52, -52, 0, 1, 4, 0, 2, -2, 5*zeta(5)_5^3 + 5*zeta(5)_5^2 - 8, 
-5*zeta(5)_5^3 - 5*zeta(5)_5^2 - 13, 2, 2, zeta(5)_5^3 + zeta(5)_5^2, 
-zeta(5)_5^3 - zeta(5)_5^2 - 1, -3, -4, -1, 3, 0, 0, 5*zeta(5)_5^3 + 
5*zeta(5)_5^2 + 13, -5*zeta(5)_5^3 - 5*zeta(5)_5^2 + 8, -2, -5*zeta(5)_5^3 - 
5*zeta(5)_5^2, 5*zeta(5)_5^3 + 5*zeta(5)_5^2 + 5, 5*zeta(5)_5^3 + 5*zeta(5)_5^2,
-5*zeta(5)_5^3 - 5*zeta(5)_5^2 - 5, -2, 0, 0, 0, 0, zeta(5)_5^3 + zeta(5)_5^2 + 
1, -zeta(5)_5^3 - zeta(5)_5^2, 0, 1, -1, 0, 0, 0, zeta(5)_5^3 + zeta(5)_5^2 - 1,
-zeta(5)_5^3 - zeta(5)_5^2 - 2, -1, zeta(5)_5^3 + zeta(5)_5^2 + 1, zeta(5)_5^3 +
zeta(5)_5^2, -zeta(5)_5^3 - zeta(5)_5^2, -zeta(5)_5^3 - zeta(5)_5^2 - 1, 0, 0, 
0, 0, 0, 0, zeta(5)_5^3 + zeta(5)_5^2 + 1, zeta(5)_5^3 + zeta(5)_5^2 + 2, 
-zeta(5)_5^3 - zeta(5)_5^2, zeta(5)_5^3 + zeta(5)_5^2, -zeta(5)_5^3 - 
zeta(5)_5^2 - 1, -zeta(5)_5^3 - zeta(5)_5^2 + 1, 1 )
*/

MatrixGroup<52,K | [
Matrix(K,52,52,
[[2/25,4/25,1/25,3/25],[4/25,3/25,2/25,1/25],
[-2/25,-4/25,-1/25,-3/25],[2/25,-1/25,1/25,3/25],
[-1/25,-2/25,2/25,1/25],[0,0,0,0],[1/25,2/25,
-2/25,-1/25],[1/25,2/25,-2/25,-1/25],[-2/25,1/25,
-1/25,-3/25],[4/25,3/25,2/25,1/25],[0,0,0,0],
[2/25,4/25,1/25,3/25],[-4/25,2/25,-2/25,4/25],
[8/25,-4/25,4/25,2/25],[12/25,4/25,6/25,8/25],
[4/25,-2/25,2/25,6/25],[8/25,-4/25,4/25,2/25],[
-4/25,-8/25,-2/25,-6/25],[0,0,0,0],[-8/25,4/25,
-4/25,-2/25],[0,0,0,0],[-4/25,2/25,-2/25,4/25],
[6/25,2/25,-2/25,4/25],[-12/25,-4/25,-6/25,-8/25],
[0,0,0,0],[0,0,0,0],[0,0,0,0],[0,0,0,0],
[-2/25,-4/25,4/25,-8/25],[2/25,4/25,-4/25,8/25],
[0,0,0,0],[-6/25,-2/25,-8/25,-4/25],[0,0,0,0],
[0,0,0,0],[0,0,0,0],[0,0,0,0],[0,0,0,0],
[-6/25,-2/25,2/25,-4/25],[0,0,0,0],[6/25,2/25,
8/25,4/25],[0,0,0,0],[0,0,0,0],[0,0,0,0],
[-12/25,-4/25,-6/25,-8/25],[0,0,0,0],[0,0,0,0],
[0,0,0,0],[8/25,6/25,4/25,12/25],[0,0,0,0],[
4/25,8/25,2/25,6/25],[12/25,4/25,6/25,8/25],[-4/25,
2/25,-2/25,-6/25],[-1/25,3/25,2/25,1/25],[0,0,0,
0],[-3/25,-1/25,-4/25,-2/25],[2/25,4/25,1/25,3/25],
[-2/25,1/25,-1/25,-3/25],[-1/25,-2/25,2/25,1/25],
[4/25,3/25,2/25,1/25],[-2/25,1/25,-1/25,-3/25],
[0,0,0,0],[-1/25,-2/25,-3/25,1/25],[-3/25,-1/25,
1/25,-2/25],[1/25,-3/25,-2/25,-1/25],[0,0,0,0],
[0,0,0,0],[0,0,0,0],[2/25,4/25,-4/25,8/25],
[0,0,0,0],[0,0,0,0],[2/25,-6/25,6/25,-2/25],
[8/25,6/25,4/25,12/25],[0,0,0,0],[0,0,0,0],
[0,0,0,0],[0,0,0,0],[0,0,0,0],[-2/25,-4/25,
4/25,-8/25],[0,0,0,0],[-4/25,2/25,-2/25,4/25],
[-6/25,-2/25,-8/25,-4/25],[0,0,0,0],[-4/25,2/25,
-2/25,4/25],[8/25,6/25,4/25,12/25],[2/25,4/25,-4/25,
8/25],[0,0,0,0],[4/25,-2/25,2/25,6/25],[-2/25,
6/25,-6/25,2/25],[6/25,2/25,8/25,4/25],[-4/25,2/25,
-2/25,4/25],[0,0,0,0],[0,0,0,0],[0,0,0,0],
[6/25,2/25,-2/25,4/25],[12/25,4/25,6/25,8/25],[
-2/25,-4/25,4/25,-8/25],[0,0,0,0],[0,0,0,0],
[2/25,-6/25,6/25,-2/25],[-4/25,2/25,-2/25,4/25],
[6/25,2/25,8/25,4/25],[0,0,0,0],[0,0,0,0],
[-4/25,-8/25,-2/25,-6/25],[-2/25,-4/25,-1/25,-3/25
],[2/25,-1/25,1/25,3/25],[1/25,2/25,3/25,-1/25],
[2/25,-1/25,1/25,3/25],[1/25,2/25,-2/25,-1/25],[
1/25,2/25,3/25,4/25],[2/25,-1/25,1/25,-2/25],[0,0,
0,0],[4/25,3/25,2/25,1/25],[4/25,3/25,2/25,1/25],
[3/25,1/25,4/25,2/25],[0,0,0,0],[0,0,0,0],[
0,0,0,0],[-12/25,-4/25,-6/25,-8/25],[0,0,0,0],
[0,0,0,0],[-2/25,-4/25,4/25,-8/25],[8/25,6/25,
4/25,12/25],[0,0,0,0],[0,0,0,0],[0,0,0,0],
[-6/25,-2/25,2/25,-4/25],[-12/25,-4/25,-6/25,-8/25],
[-2/25,-4/25,4/25,-8/25],[4/25,-2/25,2/25,6/25],[
-8/25,-6/25,-4/25,-12/25],[0,0,0,0],[0,0,0,0],
[-4/25,-8/25,-2/25,-6/25],[-6/25,-2/25,2/25,-4/25],
[8/25,-4/25,4/25,2/25],[0,0,0,0],[8/25,-4/25,
4/25,2/25],[-2/25,6/25,-6/25,2/25],[6/25,2/25,-2/25,
4/25],[0,0,0,0],[0,0,0,0],[0,0,0,0],[6/25,
2/25,8/25,4/25],[4/25,-2/25,2/25,6/25],[8/25,-4/25,
4/25,2/25],[0,0,0,0],[0,0,0,0],[-4/25,2/25,
-2/25,4/25],[-6/25,-2/25,2/25,-4/25],[0,0,0,0],
[6/25,2/25,-2/25,4/25],[0,0,0,0],[0,0,0,0],
[0,0,0,0],[0,0,0,0],[-3/25,-1/25,-4/25,-2/25],
[2/25,4/25,1/25,3/25],[-3/25,-1/25,-4/25,-2/25],[
0,0,0,0],[4/25,3/25,2/25,1/25],[-2/25,1/25,-1/25,
2/25],[4/25,3/25,2/25,1/25],[2/25,-1/25,1/25,3/25],
[-1/25,-2/25,-3/25,1/25],[0,0,0,0],[-1/25,-2/25,
-3/25,-4/25],[-1/25,3/25,2/25,1/25],[-4/25,2/25,
-2/25,-6/25],[0,0,0,0],[-4/25,-8/25,-2/25,-6/25],
[0,0,0,0],[8/25,6/25,4/25,12/25],[0,0,0,0],
[2/25,-6/25,6/25,-2/25],[-6/25,-2/25,2/25,-4/25],
[4/25,-2/25,2/25,6/25],[0,0,0,0],[-2/25,6/25,
-6/25,2/25],[0,0,0,0],[-6/25,-2/25,-8/25,-4/25],
[0,0,0,0],[2/25,-6/25,6/25,-2/25],[0,0,0,0],
[0,0,0,0],[0,0,0,0],[-4/25,2/25,-2/25,4/25],
[0,0,0,0],[-2/25,-4/25,4/25,-8/25],[0,0,0,0],
[0,0,0,0],[0,0,0,0],[-8/25,4/25,-4/25,-2/25],
[-2/25,6/25,-6/25,2/25],[-8/25,-6/25,-4/25,-12/25],
[0,0,0,0],[2/25,4/25,-4/25,8/25],[0,0,0,0],
[4/25,-2/25,2/25,6/25],[0,0,0,0],[-4/25,2/25,
-2/25,-6/25],[0,0,0,0],[0,0,0,0],[0,0,0,0],
[-6/25,-2/25,-8/25,-4/25],[6/25,2/25,8/25,4/25],
[-2/25,-4/25,4/25,-8/25],[0,0,0,0],[-1/25,-2/25,
-3/25,-4/25],[3/25,1/25,4/25,2/25],[1/25,2/25,3/25,
4/25],[-1/25,3/25,2/25,1/25],[-2/25,-4/25,-1/25,
-3/25],[0,0,0,0],[2/25,4/25,1/25,3/25],[2/25,
4/25,1/25,3/25],[1/25,-3/25,-2/25,-1/25],[3/25,1/25,
4/25,2/25],[0,0,0,0],[-1/25,-2/25,-3/25,-4/25],
[2/25,4/25,-4/25,8/25],[-4/25,2/25,-2/25,4/25],
[-6/25,-2/25,-8/25,-4/25],[8/25,-4/25,4/25,2/25],
[-4/25,2/25,-2/25,4/25],[-8/25,-6/25,-4/25,-12/25],
[0,0,0,0],[4/25,-2/25,2/25,-4/25],[0,0,0,0],[
2/25,4/25,-4/25,8/25],[12/25,4/25,6/25,8/25],[6/25,
2/25,8/25,4/25],[0,0,0,0],[0,0,0,0],[0,0,0,
0],[0,0,0,0],[6/25,2/25,-2/25,4/25],[-6/25,-2/25,
2/25,-4/25],[0,0,0,0],[-2/25,6/25,-6/25,2/25],
[0,0,0,0],[0,0,0,0],[0,0,0,0],[0,0,0,0],
[0,0,0,0],[-12/25,-4/25,-6/25,-8/25],[0,0,0,0],
[2/25,-6/25,6/25,-2/25],[0,0,0,0],[0,0,0,0],
[0,0,0,0],[6/25,2/25,8/25,4/25],[0,0,0,0],
[0,0,0,0],[0,0,0,0],[-4/25,2/25,-2/25,-6/25],
[0,0,0,0],[8/25,6/25,4/25,12/25],[-6/25,-2/25,
-8/25,-4/25],[-8/25,4/25,-4/25,-2/25],[0,0,0,0],
[-1/25,-2/25,-3/25,-4/25],[1/25,2/25,-2/25,-1/25],
[3/25,1/25,-1/25,2/25],[0,0,0,0],[-2/25,-4/25,
-1/25,-3/25],[-3/25,-1/25,-4/25,-2/25],[3/25,1/25,
4/25,2/25],[3/25,1/25,-1/25,2/25],[1/25,2/25,3/25,
4/25],[4/25,3/25,2/25,1/25],[1/25,2/25,-2/25,-1/25],
[0,0,0,0],[4/25,-2/25,2/25,6/25],[0,0,0,0],
[6/25,2/25,-2/25,4/25],[0,0,0,0],[0,0,0,0],
[0,0,0,0],[0,0,0,0],[8/25,-4/25,4/25,2/25],[
8/25,-4/25,4/25,2/25],[0,0,0,0],[6/25,2/25,-2/25,
4/25],[0,0,0,0],[-8/25,-6/25,-4/25,-12/25],[2/25,
4/25,-4/25,8/25],[2/25,4/25,-4/25,8/25],[2/25,-6/25,
6/25,-2/25],[0,0,0,0],[0,0,0,0],[0,0,0,0],
[0,0,0,0],[12/25,4/25,6/25,8/25],[0,0,0,0],
[0,0,0,0],[-4/25,2/25,-2/25,4/25],[0,0,0,0],
[4/25,-2/25,2/25,6/25],[12/25,4/25,6/25,8/25],[0,
0,0,0],[4/25,-2/25,2/25,6/25],[-8/25,4/25,-4/25,
-2/25],[0,0,0,0],[6/25,2/25,8/25,4/25],[-4/25,
-8/25,-2/25,-6/25],[4/25,8/25,2/25,6/25],[0,0,0,0],
[0,0,0,0],[4/25,-2/25,2/25,-4/25],[-8/25,-6/25,
-4/25,-12/25],[0,0,0,0],[1/25,2/25,3/25,4/25],
[-1/25,3/25,2/25,1/25],[-3/25,-1/25,1/25,-2/25],[
-1/25,3/25,2/25,1/25],[2/25,4/25,1/25,3/25],[2/25,
-1/25,1/25,3/25],[-1/25,-2/25,-3/25,1/25],[0,0,0,
0],[3/25,1/25,4/25,2/25],[3/25,1/25,4/25,2/25],
[1/25,2/25,-2/25,-1/25],[0,0,0,0],[0,0,0,0],
[0,0,0,0],[6/25,2/25,8/25,4/25],[0,0,0,0],
[0,0,0,0],[6/25,2/25,-2/25,4/25],[-4/25,2/25,
-2/25,-6/25],[0,0,0,0],[0,0,0,0],[0,0,0,0],
[-12/25,-4/25,-6/25,-8/25],[6/25,2/25,8/25,4/25],
[6/25,2/25,-2/25,4/25],[8/25,-4/25,4/25,2/25],[
4/25,-2/25,2/25,6/25],[0,0,0,0],[0,0,0,0],[
-8/25,-6/25,-4/25,-12/25],[-12/25,-4/25,-6/25,-8/25],
[-4/25,2/25,-2/25,4/25],[0,0,0,0],[-4/25,2/25,
-2/25,4/25],[-4/25,-8/25,-2/25,-6/25],[12/25,4/25,
6/25,8/25],[0,0,0,0],[0,0,0,0],[0,0,0,0],
[2/25,-6/25,6/25,-2/25],[8/25,-4/25,4/25,2/25],
[-4/25,2/25,-2/25,4/25],[0,0,0,0],[0,0,0,0],
[2/25,4/25,-4/25,8/25],[-12/25,-4/25,-6/25,-8/25],
[0,0,0,0],[12/25,4/25,6/25,8/25],[0,0,0,0],
[0,0,0,0],[0,0,0,0],[0,0,0,0],[1/25,2/25,
3/25,4/25],[3/25,1/25,4/25,2/25],[0,0,0,0],[-3/25,
-1/25,-4/25,-2/25],[2/25,4/25,1/25,3/25],[-2/25,1/25,
-1/25,-3/25],[0,0,0,0],[-1/25,-2/25,-3/25,1/25],
[1/25,-3/25,-2/25,-1/25],[-1/25,3/25,2/25,1/25],
[-1/25,-2/25,2/25,1/25],[3/25,1/25,-1/25,2/25],[
4/25,8/25,2/25,6/25],[-4/25,2/25,-2/25,4/25],[0,0,
0,0],[0,0,0,0],[2/25,-6/25,6/25,-2/25],[6/25,
2/25,-2/25,4/25],[0,0,0,0],[0,0,0,0],[-2/25,
-4/25,4/25,-8/25],[2/25,4/25,-4/25,8/25],[0,0,0,0],
[0,0,0,0],[-8/25,-6/25,-4/25,-12/25],[0,0,0,0],
[0,0,0,0],[-4/25,2/25,-2/25,-6/25],[0,0,0,0],
[-8/25,-6/25,-4/25,-12/25],[0,0,0,0],[0,0,0,0
],[8/25,-4/25,4/25,2/25],[4/25,-2/25,2/25,-4/25],
[-2/25,-4/25,4/25,-8/25],[-4/25,2/25,-2/25,-6/25],
[0,0,0,0],[0,0,0,0],[4/25,-2/25,2/25,-4/25],
[0,0,0,0],[6/25,2/25,8/25,4/25],[0,0,0,0],
[0,0,0,0],[-6/25,-2/25,-8/25,-4/25],[0,0,0,0],
[12/25,4/25,6/25,8/25],[12/25,4/25,6/25,8/25],[0,
0,0,0],[-6/25,-2/25,2/25,-4/25],[0,0,0,0],[0,0,
0,0],[8/25,-4/25,4/25,2/25],[3/25,1/25,4/25,2/25],
[0,0,0,0],[-1/25,3/25,2/25,1/25],[-1/25,-2/25,
-3/25,1/25],[-4/25,-3/25,-2/25,-1/25],[-2/25,1/25,
-1/25,2/25],[-2/25,1/25,-1/25,-3/25],[-4/25,-3/25,
-2/25,-1/25],[0,0,0,0],[-2/25,-4/25,-1/25,-3/25],
[-1/25,-2/25,-3/25,-4/25],[-3/25,-1/25,-4/25,-2/25],
[0,0,0,0],[0,0,0,0],[0,0,0,0],[4/25,8/25,
2/25,6/25],[0,0,0,0],[0,0,0,0],[4/25,-2/25,
2/25,-4/25],[6/25,2/25,-2/25,4/25],[0,0,0,0],
[0,0,0,0],[0,0,0,0],[0,0,0,0],[0,0,0,0],
[-4/25,-8/25,-2/25,-6/25],[0,0,0,0],[2/25,-6/25,
6/25,-2/25],[8/25,-4/25,4/25,2/25],[0,0,0,0],
[2/25,-6/25,6/25,-2/25],[6/25,2/25,-2/25,4/25],
[4/25,8/25,2/25,6/25],[0,0,0,0],[-12/25,-4/25,
-6/25,-8/25],[-4/25,2/25,-2/25,4/25],[-8/25,4/25,
-4/25,-2/25],[2/25,-6/25,6/25,-2/25],[0,0,0,0],
[0,0,0,0],[0,0,0,0],[-8/25,-6/25,-4/25,-12/25],
[4/25,-2/25,2/25,6/25],[-4/25,-8/25,-2/25,-6/25],
[0,0,0,0],[0,0,0,0],[4/25,-2/25,2/25,-4/25],
[2/25,-6/25,6/25,-2/25],[-8/25,4/25,-4/25,-2/25],
[0,0,0,0],[0,0,0,0],[2/25,4/25,-4/25,8/25],
[-1/25,3/25,2/25,1/25],[-1/25,-2/25,-3/25,1/25],
[-1/25,3/25,2/25,1/25],[0,0,0,0],[-2/25,1/25,
-1/25,-3/25],[1/25,2/25,-2/25,-1/25],[-2/25,1/25,
-1/25,-3/25],[4/25,3/25,2/25,1/25],[-2/25,-4/25,
-1/25,-3/25],[0,0,0,0],[3/25,1/25,-1/25,2/25],
[3/25,1/25,4/25,2/25],[12/25,4/25,6/25,8/25],[0,
0,0,0],[2/25,4/25,-4/25,8/25],[0,0,0,0],[6/25,
2/25,-2/25,4/25],[0,0,0,0],[4/25,-2/25,2/25,-4/25],
[8/25,6/25,4/25,12/25],[-12/25,-4/25,-6/25,-8/25],
[0,0,0,0],[-4/25,2/25,-2/25,4/25],[0,0,0,0],
[8/25,-4/25,4/25,2/25],[0,0,0,0],[4/25,-2/25,
2/25,-4/25],[0,0,0,0],[0,0,0,0],[0,0,0,0],
[2/25,-6/25,6/25,-2/25],[0,0,0,0],[-4/25,-8/25,
-2/25,-6/25],[0,0,0,0],[0,0,0,0],[0,0,0,0],
[-6/25,-2/25,-8/25,-4/25],[-4/25,2/25,-2/25,4/25],
[-6/25,-2/25,2/25,-4/25],[0,0,0,0],[4/25,8/25,
2/25,6/25],[0,0,0,0],[-12/25,-4/25,-6/25,-8/25],
[0,0,0,0],[12/25,4/25,6/25,8/25],[0,0,0,0],
[0,0,0,0],[0,0,0,0],[8/25,-4/25,4/25,2/25],
[-8/25,4/25,-4/25,-2/25],[-4/25,-8/25,-2/25,-6/25],
[0,0,0,0],[0,0,0,0],[2/25,-1/25,1/25,-2/25],
[-2/25,1/25,-1/25,-3/25],[-1/25,-2/25,2/25,1/25],[
0,0,0,0],[-1/25,3/25,2/25,1/25],[1/25,2/25,3/25,
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-3/25,-6/25,-4/25,-2/25],[0,0,0,0],[-2/25,-4/25,
-1/25,2/25],[-2/25,1/25,-1/25,-3/25],[0,0,0,0],
[4/25,3/25,2/25,1/25],[-3/25,-1/25,1/25,-2/25],
[-1/25,-2/25,-3/25,1/25],[1/25,-3/25,-2/25,-1/25],
[-1/25,3/25,-3/25,1/25],[0,0,0,0],[2/25,-1/25,
1/25,-2/25],[0,0,0,0],[-3/25,-1/25,1/25,-2/25],[
1/25,-3/25,-2/25,-1/25],[3/25,1/25,4/25,2/25],[1/25,
2/25,3/25,4/25],[0,0,0,0],[1/25,2/25,3/25,4/25],
[-1/25,-2/25,-3/25,-4/25],[2/25,-1/25,1/25,3/25],
[2/25,4/25,6/25,3/25],[-1/25,3/25,2/25,1/25],[1/25,
2/25,3/25,-1/25],[1/25,2/25,-2/25,4/25],[0,0,0,0],
[0,0,0,0],[2/25,-1/25,1/25,-2/25],[0,0,0,0],
[1/25,-3/25,-2/25,-1/25],[2/25,-1/25,1/25,3/25],
[-1/25,-2/25,2/25,1/25],[2/25,-1/25,1/25,-2/25],[
-1/25,-2/25,-3/25,1/25],[3/25,1/25,-1/25,2/25],[0,
0,0,0],[3/25,1/25,-1/25,-3/25],[-3/25,-1/25,1/25,
-2/25],[3/25,1/25,-1/25,2/25],[-2/25,1/25,-1/25,-3/25
],[3/25,6/25,4/25,2/25],[-6/25,-2/25,-3/25,-4/25],
[1/25,-3/25,-2/25,-1/25]])
]> where w := K.1 where K := ext<K|Polynomial(K,[1,1,1,1,1])>
where K is RationalField();

return _LR;
