//Standard generators of L2(41) are a and b where a has order 2, b has order 3
//and ab has order 41.
//Standard generators of the double cover 2.L2(41) = SL2(41) are preimages A and
//B where B has order 3 and AB has order 41.
_LR := rec < recformat< F: GrpFP, AI: SeqEnum, G: GrpMat > |
      F := FreeGroup(2) >;
_LR`AI:=[[a^-1,b*a*b*a*b*a*b*a*b^-1*a*b*a*b*a*b^-1*a*b^-1*a*b ]]
             where a is (_LR`F).1 where b is (_LR`F).2;
//two constituents interchanged by _LR`AI[1][1]
_LR`G :=
/*
Original group: c9Group("sl241p")
From DB /nb/reps/l2/2l241/d20.2l241.M
Schur index: 2
Character: ( 20, -20, -1, 0, 0, 0, 1, -1, -1, -1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 
0, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -zeta(41)_41^38 - 
zeta(41)_41^35 - zeta(41)_41^34 - zeta(41)_41^30 - zeta(41)_41^29 - 
zeta(41)_41^28 - zeta(41)_41^27 - zeta(41)_41^26 - zeta(41)_41^24 - 
zeta(41)_41^22 - zeta(41)_41^19 - zeta(41)_41^17 - zeta(41)_41^15 - 
zeta(41)_41^14 - zeta(41)_41^13 - zeta(41)_41^12 - zeta(41)_41^11 - 
zeta(41)_41^7 - zeta(41)_41^6 - zeta(41)_41^3 - 1, zeta(41)_41^38 + 
zeta(41)_41^35 + zeta(41)_41^34 + zeta(41)_41^30 + zeta(41)_41^29 + 
zeta(41)_41^28 + zeta(41)_41^27 + zeta(41)_41^26 + zeta(41)_41^24 + 
zeta(41)_41^22 + zeta(41)_41^19 + zeta(41)_41^17 + zeta(41)_41^15 + 
zeta(41)_41^14 + zeta(41)_41^13 + zeta(41)_41^12 + zeta(41)_41^11 + 
zeta(41)_41^7 + zeta(41)_41^6 + zeta(41)_41^3, 1, 1, 1, 1, 1, 1, zeta(41)_41^38 
+ zeta(41)_41^35 + zeta(41)_41^34 + zeta(41)_41^30 + zeta(41)_41^29 + 
zeta(41)_41^28 + zeta(41)_41^27 + zeta(41)_41^26 + zeta(41)_41^24 + 
zeta(41)_41^22 + zeta(41)_41^19 + zeta(41)_41^17 + zeta(41)_41^15 + 
zeta(41)_41^14 + zeta(41)_41^13 + zeta(41)_41^12 + zeta(41)_41^11 + 
zeta(41)_41^7 + zeta(41)_41^6 + zeta(41)_41^3 + 1, -zeta(41)_41^38 - 
zeta(41)_41^35 - zeta(41)_41^34 - zeta(41)_41^30 - zeta(41)_41^29 - 
zeta(41)_41^28 - zeta(41)_41^27 - zeta(41)_41^26 - zeta(41)_41^24 - 
zeta(41)_41^22 - zeta(41)_41^19 - zeta(41)_41^17 - zeta(41)_41^15 - 
zeta(41)_41^14 - zeta(41)_41^13 - zeta(41)_41^12 - zeta(41)_41^11 - 
zeta(41)_41^7 - zeta(41)_41^6 - zeta(41)_41^3 )
*/

MatrixGroup<20,K | [
Matrix(K,20,20,
[[-29/165,1/25,-2/75,-2/825],[4/165,17/150,-1/50,
7/1650],[5/33,19/150,-1/150,19/1650],[-2/165,1/75,
1/75,1/825],[2391/6820,2737/18600,269/6200,359/68200],
[-33/124,1969/18600,213/6200,299/18600],[-419/1364,
-679/9300,-289/9300,133/51150],[-877/1860,-451/6200,
-181/6200,37/18600],[67/330,-1/100,-1/300,-23/3300],[
-13/165,11/150,1/50,13/1650],[5/33,-3/100,1/300,1/660],
[-9/110,-1/150,-1/150,4/825],[-79/330,0,1/75,1/1650],
[23/330,1/100,1/300,-1/3300],[-13/55,17/300,-1/300,
23/3300],[-13/110,-1/60,1/300,-1/660],[-59/330,-4/75,
-2/75,-3/550],[91/330,1/25,2/75,-7/1650],[39/110,1/60,
-1/300,-7/3300],[-4/11,-17/75,-1/15,-14/825],[-19/55,
-4/75,-4/75,1/825],[1/5,31/150,1/150,1/150],[1/55,
19/150,-1/150,19/1650],[-73/165,-1/75,-1/75,3/275],[
-203/4092,467/6200,631/18600,1741/204600],[-82/155,-1/155,
2/93,4/465],[133/660,-11/150,-1/150,-17/3300],[-109/310,
-911/4650,-301/4650,-23/2325],[38/165,4/75,0,-1/330],
[-37/165,-7/300,-1/60,-1/1100],[83/330,-1/150,1/150,
-1/550],[79/330,-7/60,1/100,-13/3300],[-17/330,3/100,
-1/300,-1/660],[2/55,7/100,1/100,7/1100],[-1/110,1/75,
1/75,-2/825],[7/66,1/75,-1/75,-2/275],[46/165,-1/75,
0,-13/1650],[3/11,-1/300,1/60,-13/3300],[-4/55,-3/100,
-1/100,-3/1100],[19/330,-1/25,-1/75,-2/825],[9/55,
1/25,1/25,1/275],[-1/15,-2/15,0,0],[5/33,-23/150,
7/150,-1/550],[3/55,-3/50,1/150,-3/550],[-349/10230,
-43/18600,-53/18600,-413/204600],[166/465,-1229/9300,
-419/9300,-149/9300],[-2069/6820,-707/6200,-237/6200,
-481/204600],[831/3410,119/775,112/2325,409/51150],[
-31/165,7/300,1/100,29/3300],[1/33,-1/150,0,-1/330],
[-41/330,1/30,0,2/825],[-71/330,2/75,-1/150,-1/550],
[29/330,7/300,-1/300,1/220],[-13/66,-11/150,-2/75,-1/275
],[-1/15,-1/12,-3/100,-1/300],[2/15,1/75,1/150,0],[
1/330,17/300,1/300,7/1100],[-1/30,-1/20,-7/300,-1/300],
[19/330,1/75,1/50,7/1650],[1/2,37/300,1/300,-1/300],
[-31/165,-11/75,-1/75,-1/825],[41/165,1/150,1/150,
-19/1650],[-23/165,-11/150,-1/150,-7/550],[-29/165,
-7/75,-2/75,-2/825],[-1093/4092,-1673/18600,-101/6200,
-893/204600],[491/4092,-91/1860,-17/1860,-29/3410],
[401/1364,-149/4650,11/4650,-703/102300],[423/6820,
-2/775,-11/2325,-299/102300],[-19/330,-29/300,-7/300,
-1/1100],[12/55,1/25,0,-1/550],[8/165,3/50,1/150,
7/825],[1/11,-19/300,-1/300,-19/3300],[28/165,-7/150,
1/150,-1/275],[27/110,13/300,7/300,7/3300],[89/330,
11/300,3/100,-23/3300],[71/330,17/300,1/100,-1/660],
[9/22,1/100,3/100,-1/1100],[-13/55,-1/50,-1/50,1/275],
[-17/66,-9/100,-1/60,-1/132],[4/55,17/100,7/100,1/44],
[7/165,-11/150,2/75,2/825],[-46/165,2/25,-1/50,1/825],
[-17/165,7/150,-1/50,17/1650],[21/55,-8/75,2/75,7/825
],[-91/1860,331/6200,503/18600,-59/6200],[-3769/20460,
1397/18600,-171/6200,-763/204600],[-1509/6820,887/9300,
-121/3100,491/51150],[-4163/20460,331/6200,-737/18600,
533/204600],[7/165,-4/75,1/100,-7/1650],[7/33,3/100,
2/75,7/3300],[26/165,-1/300,1/30,1/1100],[13/165,
-1/300,1/50,7/3300],[-26/165,17/150,1/60,1/110],[
13/55,9/100,1/25,7/1100],[4/165,-13/300,0,1/132],[
-101/330,2/75,-1/60,2/275],[-19/110,-1/300,1/150,7/660],
[-8/165,-1/75,3/100,4/825],[1/11,-3/100,1/50,1/1100],
[53/165,-1/12,1/75,1/220],[-17/165,2/75,-1/150,-8/825],
[13/55,-3/50,1/150,8/825],[8/165,-3/25,1/75,-4/825],
[-23/165,-1/150,-1/150,-7/550],[-6887/20460,239/6200,
-313/18600,2597/204600],[61/6820,-847/18600,23/18600,
653/204600],[1823/20460,-421/2325,29/2325,-423/34100],[
179/1364,-499/6200,433/18600,2023/204600],[9/110,11/100,
1/100,1/550],[-4/11,-1/30,-4/75,-1/3300],[-2/11,
-1/300,-7/300,-7/825],[-5/66,1/100,1/300,7/1650],
[13/55,-19/150,1/75,-23/3300],[-5/33,-2/25,1/150,
-1/660],[7/66,-7/100,-1/60,-23/1650],[7/110,0,0,
-7/1100],[13/165,-9/100,1/300,-1/825],[5/33,-17/150,
0,-17/3300],[3/55,1/75,-2/75,-29/3300],[-37/165,
-7/300,-1/60,-3/275],[8/165,-13/150,-1/50,-4/825],
[-38/165,2/75,-1/150,-1/275],[-2/15,-1/30,-1/30,0],
[37/165,-19/150,1/150,-2/825],[1687/10230,1523/18600,
-127/18600,-1867/204600],[35/186,23/248,-13/744,1/744],
[-1699/6820,857/6200,-479/18600,3491/204600],[-323/5115,
451/3720,19/1240,133/40920],[-3/55,-1/25,-1/50,-1/220],
[5/66,1/150,1/30,-1/1100],[13/330,-11/150,1/75,3/1100],
[7/66,-11/150,0,-7/660],[-82/165,3/25,-1/75,43/3300],
[23/110,11/150,1/30,19/3300],[9/110,-13/150,1/75,-1/660
],[-9/110,-9/100,-3/100,-1/550],[-41/165,11/300,-1/100,
4/825],[-17/55,3/25,0,1/1100],[1/66,1/50,1/30,17/3300
],[39/110,-1/50,1/50,1/220],[-41/165,1/75,-1/50,-1/550
],[41/165,-13/150,1/75,-4/825],[14/165,1/75,1/75,-1/550
],[-17/165,1/150,1/150,1/275],[-6053/20460,-3137/18600,
-1127/18600,-2857/204600],[137/20460,-113/6200,-389/18600,
-1259/204600],[6521/20460,104/775,59/4650,-139/34100],
[1183/4092,-2717/18600,-47/18600,-2197/204600],[-5/66,
-1/60,-1/300,1/1100],[16/33,-17/150,1/75,-1/550],
[-2/15,41/300,1/300,1/100],[23/330,-37/300,1/100,
-23/3300],[2/33,2/75,1/50,-1/165],[-6/55,-2/75,
-1/150,-2/825],[17/66,-13/300,1/300,1/1100],[-1/6,
2/75,0,1/150],[5/33,-13/300,1/100,-17/3300],[4/165,
-3/50,1/75,-13/825],[64/165,3/25,1/75,13/1650],[16/55,
-7/300,-1/300,-19/3300],[-2/33,-1/150,-1/150,-1/1650],[
-13/55,1/150,1/150,1/275],[-2/15,-11/150,-1/150,-1/150],
[-5/33,-1/50,-1/50,-4/825],[-19/465,923/18600,211/6200,
41/6200],[-1717/10230,941/4650,67/1550,166/8525],[
-113/1364,23/18600,-707/18600,-637/204600],[-2357/5115,
-551/4650,-53/2325,-103/25575],[16/165,1/60,1/100,1/3300
],[7/33,1/15,1/75,3/550],[-1/3,1/12,1/100,1/300],
[1/6,-1/12,1/300,-1/100],[34/165,-7/150,-1/75,-2/275],
[10/33,-1/30,1/75,-1/275],[-7/33,-4/75,-1/50,1/825],[
-89/330,-19/300,-1/60,-7/1100],[-2/165,19/150,1/50,1/825
],[-1/11,-4/75,-1/75,2/825],[29/165,1/75,1/50,2/825],
[23/165,1/50,1/150,-1/1650],[-5/33,4/25,2/75,7/825],
[8/33,-1/150,-1/150,2/825],[8/33,1/10,1/30,1/110],
[-7/55,1/10,1/30,1/165],[-116/5115,97/3100,-3/3100,
661/102300],[-191/3410,-7/18600,-99/6200,1663/204600],
[-1429/10230,119/4650,-11/775,-61/51150],[-227/3410,
-1843/18600,367/18600,-673/204600],[-62/165,-11/300,-1/300,
1/1100],[16/165,4/75,2/75,1/275],[-2/55,-1/50,1/50,
1/275],[4/55,-1/10,-1/50,-2/275],[-13/55,0,1/50,1/275
],[-26/165,0,-1/150,2/825],[-8/55,-2/25,-1/50,-3/550],
[41/330,-7/300,1/100,1/132],[29/165,4/75,0,2/825],
[1/6,1/300,1/100,1/300],[7/55,2/75,1/150,1/1650],[
-14/165,19/300,1/60,13/1100],[8/165,1/150,1/150,-19/1650
],[-6/55,13/150,1/50,3/275],[-14/165,1/50,1/50,1/550
],[-28/165,-1/150,-1/150,-8/825],[-38/1023,143/18600,
133/18600,1013/204600],[157/1860,-173/1550,-33/1550,
-73/9300],[-343/1364,-271/6200,137/18600,547/204600],
[1723/6820,309/3100,227/9300,73/25575],[-13/330,-2/25,
-2/75,1/1650],[-2/55,-1/60,1/300,1/3300],[19/110,1/20,
3/100,3/1100],[2/5,-7/100,-1/100,-1/100],[-8/165,
-3/100,-1/60,1/660],[101/330,-7/150,-1/75,-2/275],
[5/22,-13/300,-1/300,-31/3300],[-27/110,2/75,-1/75,
13/1650],[1/6,-1/100,-1/300,-1/300],[8/165,1/100,1/60,
-1/660],[23/330,-1/30,0,1/330],[7/110,-1/60,1/300,
1/3300],[-8/165,7/150,-1/50,-1/550],[14/165,-7/150,
1/50,4/825],[2/15,1/150,1/150,1/150],[16/165,-11/150,
-1/150,-8/825],[9/110,11/200,1/200,23/6600],[541/20460,
-607/9300,-157/9300,-58/25575],[-1231/6820,-2483/18600,
-131/6200,-1103/204600],[-83/1860,-197/2325,1/4650,7/9300
],[-1/10,-2/75,1/75,1/150],[-31/165,-1/100,-1/300,
7/3300],[-47/110,-7/100,-1/100,3/1100],[-3/55,-1/20,
-3/100,-1/220],[12/55,13/300,1/300,-17/3300],[13/330,
1/30,0,1/165],[-5/66,-3/100,-1/60,-19/3300],[-43/330,
-2/25,-2/75,-17/1650],[-9/110,1/60,-1/300,1/660],[
1/55,1/60,-1/300,1/660],[-127/330,-7/150,-1/75,1/550],
[31/330,1/100,1/60,13/3300],[32/165,-2/15,0,-1/165],
[4/165,11/75,1/75,7/1650],[0,1/15,0,0],[2/55,-1/15,
0,1/330],[787/2046,379/4650,34/775,69/8525],[3643/20460,
-143/18600,487/18600,179/68200],[-137/10230,247/4650,
-19/2325,-223/51150],[-867/6820,-641/18600,349/18600,
-281/204600],[1/33,-7/150,0,-1/330],[67/330,-1/60,
1/100,-1/3300],[2/165,1/30,0,-1/825],[-8/33,7/150,
1/75,3/275],[-2/55,-9/100,-3/100,-7/1100],[-29/165,
-7/75,-1/25,-2/825],[13/110,1/100,-1/100,-13/1100],[
-47/165,-13/150,-1/75,1/550],[26/165,1/60,1/300,1/1100],
[-2/33,0,1/150,-1/1650],[8/165,-1/75,1/75,1/550],[
-1/11,-2/75,-1/150,-7/1650],[-13/165,-4/75,1/75,1/825],
[8/165,7/150,-1/50,-4/825],[1/11,-2/75,-2/75,-2/825],[
2/15,1/25,1/25,1/150],[3449/20460,53/930,1/31,57/6820],
[643/5115,-19/310,7/186,-1/10230],[2227/10230,-49/6200,
583/18600,-139/68200],[9/62,7/3100,-13/3100,-59/9300],
[-83/330,-4/75,-1/150,1/550],[53/330,-1/60,-1/300,
-3/1100],[-7/22,-1/50,0,1/550],[17/110,3/50,0,-3/550
],[-3/110,7/75,1/75,-1/1650],[1/22,1/25,1/25,3/550],
[-1/330,-1/10,-1/150,-1/330],[109/330,1/75,1/50,-1/330
],[-1/3,-11/300,-1/100,1/300],[31/330,-7/300,1/300,
-3/1100],[17/110,-1/50,-1/50,-3/550],[8/165,13/300,
-1/100,17/3300],[-2/11,4/75,-1/75,4/825],[2/55,0,
0,1/330],[-8/165,4/75,-1/75,4/825],[-26/165,0,0,
1/110],[-73/186,-1/775,-11/4650,13/1550],[-8123/20460,
-2411/18600,-87/6200,603/68200],[199/2046,-81/1550,
-29/2325,-21/17050],[-887/4092,-1753/18600,-81/6200,
-1373/204600],[8/33,-13/150,-1/75,-3/275],[47/330,
-1/60,-1/300,-1/1100],[-53/165,-7/150,-1/75,3/550],
[-7/165,1/30,0,7/1650],[-12/55,1/100,-1/100,13/1100],
[14/165,-1/75,1/75,-1/550],[17/110,9/100,3/100,1/220],
[-2/165,7/150,0,1/825],[-16/165,-1/60,1/100,-1/3300],
[3/55,-2/75,-1/150,1/825],[17/165,7/75,1/25,8/825],
[-4/33,0,-1/150,-1/825],[-2/165,1/50,1/50,13/1650],
[-7/33,-1/50,-1/50,1/825],[-2/15,1/150,1/150,1/150],
[1/55,1/50,1/50,4/825],[1127/3410,2669/18600,-41/18600,
-87/68200],[1949/10230,293/4650,-19/1550,104/25575],
[-415/1364,-727/6200,-511/18600,-221/204600],[904/5115,
91/2325,127/4650,317/51150],[29/165,-19/300,-1/60,-1/1100
],[-13/165,-19/150,-1/50,-2/165],[2/33,1/12,-1/300,
-3/1100],[23/66,1/12,1/100,17/3300],[13/165,-4/75,
-1/50,-13/1650],[-1/165,1/75,1/50,1/1650],[47/165,
7/150,1/75,-1/550],[7/330,-1/60,-1/100,-7/3300],[
-5/33,1/15,1/75,1/550],[-16/165,1/50,1/150,1/330],
[5/33,1/30,-1/75,-1/550],[-1/55,4/75,1/75,7/825],[
-3/55,-1/75,-1/75,-1/825],[-2/55,1/150,1/150,1/275],
[2/11,13/150,1/50,1/550],[-19/165,1/50,1/50,4/825
],[1561/5115,-161/1860,17/620,-191/20460],[-8/1705,
-11/1240,17/3720,-97/13640],[-227/2046,203/1550,-23/2325,
89/51150],[-98/5115,47/18600,-43/18600,-1423/204600],
[2/165,7/300,-1/100,29/3300],[-37/165,4/75,0,2/825],
[-9/55,-1/10,-1/50,-1/275],[-13/55,1/50,-1/50,1/275],
[-2/55,2/25,1/50,1/275],[1/11,-2/75,-1/150,-2/825],
[23/55,0,1/50,-1/550],[25/66,-11/300,-1/300,-1/220],
[-16/165,-4/75,-2/75,-1/275],[-59/330,-19/300,-1/60,
1/220],[16/165,0,-1/150,-1/330],[-13/165,1/300,1/100,
-7/3300],[4/33,7/75,2/75,4/275],[-21/55,-3/25,1/75,
-1/550],[-53/165,-23/150,-1/50,-13/1650],[2/11,7/150,
-1/50,-4/825],[349/1860,-227/1550,-43/2325,-137/9300],
[1417/10230,-116/2325,-2/775,-307/51150],[1031/10230,
2027/18600,59/6200,1777/204600],[1/93,253/9300,-9/3100,
-17/9300],[-1/55,-8/75,-2/75,-19/1650],[-13/165,1/300,
1/100,-7/3300],[0,-2/25,0,0],[2/11,3/50,1/50,1/550],
[-61/330,-7/150,-1/75,1/550],[-43/165,-1/150,0,1/165],
[-7/330,-4/75,-1/50,-13/1650],[4/165,1/25,1/75,7/1650
],[67/330,-19/300,-1/60,-3/220],[-2/55,-1/60,1/300,
1/3300],[19/165,1/30,-1/75,1/550],[1/30,1/100,1/300,
1/300],[-5/11,-2/25,-1/75,-1/825],[2/11,-1/50,-1/50,
-4/825],[-3/55,-1/75,-1/75,-1/825],[-16/165,-1/15,0,
1/330],[413/4092,-32/465,17/930,-179/20460],[-752/1705,
-71/2325,-1/2325,13/8525],[-3/682,2273/18600,163/18600,
2323/204600],[-203/930,379/9300,-87/3100,-61/9300],[
-53/330,1/75,1/50,1/165],[-91/330,11/300,1/100,1/132],
[23/110,-3/50,0,-3/275],[37/110,-1/50,0,-1/275],[
1/30,-1/10,-1/150,-1/150],[-7/22,-1/50,-1/50,1/550],
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-2/825],[13/66,-1/150,-1/75,-7/1100],[19/165,-7/100,
1/300,-4/825]])
]> where w := K.1 where K := ext<K|Polynomial(K,[100,-10,11,1,1])>
where K is RationalField();

return _LR;
