//Standard generators of L2(37) are a and b where a has order 2, b has order 3
//and ab has order 37.
//Standard generators of the double cover 2.L2(37) = SL2(37) are preimages A and
//B where B has order 3 and AB has order 37.
_LR := rec < recformat< F: GrpFP, AI: SeqEnum, G: GrpMat > |
      F := FreeGroup(2) >;
_LR`AI:=[[a^-1, a^-1*b*a*b^-1*a*b*a*b^-1*a^-1*b*a*b*a*b^-1*a^-1*b^-1*a*b^-1*a*
                             b*a*b^-1*a^-1*b*a*b*a*b^-1*a^-1*b*a^-1*b^-1*a*b]]
             where a is (_LR`F).1 where b is (_LR`F).2;
//18 constituents
_LR`G :=
/*
Original group: c9Group("sl237p")
From DB /nb/reps/l2/2l237/d36.2l237.deg18.si2.X6.M
Schur index: 2
Character: ( 36, -36, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -zeta(19)_19^11 - 
zeta(19)_19^8, -zeta(19)_19^16 - zeta(19)_19^3, -zeta(19)_19^14 - zeta(19)_19^5,
-zeta(19)_19^13 - zeta(19)_19^6, -zeta(19)_19^17 - zeta(19)_19^2, 
-zeta(19)_19^10 - zeta(19)_19^9, zeta(19)_19^17 + zeta(19)_19^16 + 
zeta(19)_19^15 + zeta(19)_19^14 + zeta(19)_19^13 + zeta(19)_19^12 + 
zeta(19)_19^11 + zeta(19)_19^10 + zeta(19)_19^9 + zeta(19)_19^8 + zeta(19)_19^7 
+ zeta(19)_19^6 + zeta(19)_19^5 + zeta(19)_19^4 + zeta(19)_19^3 + zeta(19)_19^2 
+ 1, -zeta(19)_19^12 - zeta(19)_19^7, -zeta(19)_19^15 - zeta(19)_19^4, 0, 0, 0, 
0, 0, 0, -1, -1, zeta(19)_19^11 + zeta(19)_19^8, zeta(19)_19^16 + zeta(19)_19^3,
-zeta(19)_19^17 - zeta(19)_19^16 - zeta(19)_19^15 - zeta(19)_19^14 - 
zeta(19)_19^13 - zeta(19)_19^12 - zeta(19)_19^11 - zeta(19)_19^10 - 
zeta(19)_19^9 - zeta(19)_19^8 - zeta(19)_19^7 - zeta(19)_19^6 - zeta(19)_19^5 - 
zeta(19)_19^4 - zeta(19)_19^3 - zeta(19)_19^2 - 1, zeta(19)_19^13 + 
zeta(19)_19^6, zeta(19)_19^12 + zeta(19)_19^7, zeta(19)_19^15 + zeta(19)_19^4, 
zeta(19)_19^17 + zeta(19)_19^2, zeta(19)_19^10 + zeta(19)_19^9, zeta(19)_19^14 +
zeta(19)_19^5, 1, 1 )
*/

MatrixGroup<36,K | [
Matrix(K,36,36,
[[-326/51023,2515/153069,625/7289,-427/7289,10966/153069,
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9508/153069,19715/153069],[-2614/153069,13040/153069,
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33023/153069],[12083/51023,24551/153069,4057/153069,
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12226/153069,912/51023,8801/153069,1711/7289,3076/51023
],[724/21867,12416/153069,35006/153069,37766/153069,
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21758/153069,7338/51023,15230/153069,4483/21867,36727/153069,
35648/153069,16/197,1319/51023,25162/153069,13556/153069
],[-9735/51023,-37708/153069,-8962/51023,-52292/153069,
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6073/51023,1086/51023,3593/153069],[605/4137,9769/51023,
41786/153069,3713/153069,17534/153069,18307/153069,
32962/153069,503/7289,3782/51023,5968/51023,12939/51023,
3587/21867,3160/21867,9353/51023,22028/153069,10222/51023,
5622/51023,3021/51023],[6362/153069,22228/153069,
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4841/21867,21353/153069,17827/153069,9647/153069,5233/153069,
8341/153069,49421/153069,5114/51023,1977/51023,2953/51023,
8350/153069],[5486/153069,-3854/153069,1768/21867,19/1379,
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],[7815/51023,11365/153069,18637/153069,1366/21867,
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4363/21867],[57514/153069,21986/153069,13340/51023,
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12912/51023,50962/153069,20386/153069,4657/21867,1484/7289,
24770/153069,37789/153069,35638/153069,12560/51023,
1384/7289],[16085/153069,8845/153069,-5074/51023,
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221/153069,4990/51023,-2767/51023,-3288/51023,4919/153069,
13301/153069],[3378/51023,16073/153069,14606/153069,
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-6781/153069,-410/51023,7747/153069,1454/21867,-896/21867,
14012/153069,22523/153069,2962/51023,-15121/153069,7320/51023
],[6302/153069,-6495/51023,-9151/153069,7058/153069,
-1567/21867,3098/21867,2687/51023,-19226/153069,-12220/153069,
-406/21867,20117/153069,-2390/21867,-950/153069,-11119/153069,
6800/153069,-25453/153069,21095/153069,-1078/7289],[
20705/153069,9881/153069,4832/153069,3518/21867,6964/51023,
2084/21867,30859/153069,8291/153069,-4784/51023,21094/153069,
8558/51023,6891/51023,594/7289,196/21867,275/4137,
23803/153069,6014/153069,9617/153069],[-11093/153069,
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4294/51023,4751/51023,-10991/153069,-4061/21867,-25363/153069,
-26680/153069,-18866/153069,-107/153069,-292/7289,1094/21867,
6119/153069,-32926/153069,-34015/153069],[-844/21867,
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-2285/153069,-3491/51023,5406/51023,-6683/153069,27212/153069,
5625/51023,9913/153069,-344/51023,4064/51023,-634/51023,
2945/21867,9641/153069],[18112/153069,2633/21867,2155/21867,
-904/153069,2941/51023,40997/153069,-5260/153069,44573/153069,
11020/153069,635/7289,-1348/51023,2204/153069,7468/51023,
3127/51023,2350/21867,5123/153069,86/777,8817/51023],
[-7274/153069,-4059/51023,-3077/21867,-18644/153069,
-17321/153069,-12175/153069,-28640/153069,1534/21867,
-7747/51023,-28387/153069,422/153069,-44/777,2970/51023,
-4358/51023,1964/153069,3011/153069,-823/21867,-21317/153069
],[6030/51023,-178/21867,254/21867,2193/51023,-5797/153069,
-33197/153069,6145/153069,-7915/153069,-1544/153069,
1077/51023,-5632/51023,10292/153069,-11254/153069,
-825/51023,8266/153069,-3084/51023,-9376/153069,232/4137
],[-2152/153069,-8318/153069,8986/153069,21184/153069,
-490/21867,1826/21867,-2593/51023,-3146/153069,-251/21867,
4722/51023,1145/7289,15037/153069,2315/153069,3823/21867,
31187/153069,-1051/21867,19045/153069,2880/51023],[
11827/153069,14288/153069,-2008/51023,1271/51023,-4789/51023,
-1600/153069,-3354/51023,-1009/51023,656/21867,3652/153069,
-9407/153069,12911/153069,2312/153069,26402/153069,
634/153069,5666/153069,-2090/153069,-11602/153069],[
15188/153069,2714/21867,-1012/21867,7197/51023,3299/153069,
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8356/51023,-4643/153069,11924/153069,-6708/51023,7957/153069,
16175/153069,5/1379,19319/153069],[8959/153069,16003/153069,
551/21867,3137/51023,753/7289,4364/153069,-3047/51023,
2221/51023,9475/153069,3074/153069,-4930/51023,-21694/153069,
-835/153069,-11863/153069,-6754/153069,-682/153069,-745/7289,
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-3246/51023,-21715/153069,-2084/51023,-16073/153069,
-14968/153069]])    ,
Matrix(SparseMatrix(K,36,36,[<1,19,1>,<1,26,-1>,<2,3,
1>,<2,19,1>,<3,19,1>,<3,21,-1>,<4,10,1>,<4,19,1>,
<5,14,1>,<5,19,1>,<6,19,1>,<6,31,-1>,<7,19,1>,<7,
23,-1>,<8,5,1>,<8,19,1>,<9,19,1>,<9,20,-1>,<10,
15,1>,<10,19,1>,<11,19,1>,<11,32,-1>,<12,17,1>,<12,
19,1>,<13,19,1>,<14,8,1>,<14,19,1>,<15,4,1>,<15,
19,1>,<16,7,1>,<16,19,1>,<17,19,1>,<17,28,-1>,<18,
19,-1>,<18,27,1>,<19,13,-1>,<19,19,-1>,<20,19,-1>,
<20,33,1>,<21,2,-1>,<21,19,-1>,<22,19,-1>,<22,35,1>,
<23,16,-1>,<23,19,-1>,<24,18,1>,<24,19,-1>,<25,19,
-1>,<25,22,1>,<26,19,-1>,<26,29,1>,<27,19,-1>,<27,
24,1>,<28,12,-1>,<28,19,-1>,<29,1,-1>,<29,19,-1>,
<30,19,-1>,<30,30,1>,<31,19,-1>,<31,34,1>,<32,19,
-1>,<32,36,-1>,<33,9,-1>,<33,19,-1>,<34,6,-1>,<34,
19,-1>,<35,19,-1>,<35,25,1>,<36,11,1>,<36,19,1>]))
]> where w := K.1 where K := ext<K|Polynomial(K,[1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1])> where K is RationalField();

return _LR;
