
//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;
//3 constituents
_LR`G :=
/*
Original group: c9Group("sl241p")
From DB /nb/reps/l2/2l241/d40.2l241.deg6.X8.M
Schur index: 2
Character: ( 40, -40, -2, 0, 0, 0, 2, zeta(7)_7^5 + zeta(7)_7^4 + zeta(7)_7^3 + 
zeta(7)_7^2 + 1, -zeta(7)_7^5 - zeta(7)_7^2, -zeta(7)_7^4 - zeta(7)_7^3, 0, 0, 
0, 0, zeta(7)_7^4 + zeta(7)_7^3, zeta(7)_7^5 + zeta(7)_7^2, -zeta(7)_7^5 - 
zeta(7)_7^4 - zeta(7)_7^3 - zeta(7)_7^2 - 1, 0, 0, 0, 0, -zeta(7)_7^5 - 
zeta(7)_7^2, -zeta(7)_7^4 - zeta(7)_7^3, zeta(7)_7^5 + zeta(7)_7^4 + zeta(7)_7^3
+ zeta(7)_7^2 + 1, -zeta(7)_7^5 - zeta(7)_7^2, zeta(7)_7^5 + zeta(7)_7^4 + 
zeta(7)_7^3 + zeta(7)_7^2 + 1, -zeta(7)_7^4 - zeta(7)_7^3, 0, 0, 0, 0, 0, 0, 0, 
0, -1, -1, zeta(7)_7^5 + zeta(7)_7^2, zeta(7)_7^4 + zeta(7)_7^3, zeta(7)_7^5 + 
zeta(7)_7^2, -zeta(7)_7^5 - zeta(7)_7^4 - zeta(7)_7^3 - zeta(7)_7^2 - 1, 
-zeta(7)_7^5 - zeta(7)_7^4 - zeta(7)_7^3 - zeta(7)_7^2 - 1, zeta(7)_7^4 + 
zeta(7)_7^3, 1, 1 )
*/

MatrixGroup<40,K | [
Matrix(K,40,40,
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37165761/71305478,5111246/35652739,41948968/35652739],
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1877883/35652739,-20013788/35652739,12978999/71305478],
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78331257/71305478,-8117589/35652739,72557664/35652739],
[-12752653/71305478,511252/35652739,27138913/71305478,
15019553/71305478,-7793201/71305478,7980938/35652739],
[-4773509/35652739,12472165/71305478,-36671791/71305478,
10105673/35652739,-47511863/71305478,18683204/35652739],
[-7448458/35652739,-22563645/71305478,-25992083/71305478,
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[-45495877/71305478,-52492201/71305478,9390757/71305478,
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[48281654/35652739,-608217/35652739,75241035/71305478,
20191179/71305478,750016/869579,91736653/71305478],[
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-14971343/35652739,-81862053/71305478,-44807238/35652739],
[34152340/35652739,14957665/35652739,-1249945/71305478,
77048967/71305478,17101150/35652739,24359979/71305478],
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[37448577/35652739,8130087/35652739,31937295/71305478,
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[7151863/35652739,-8096360/35652739,-3545009/35652739,
17563210/35652739,-8564028/35652739,3449458/35652739],
[1064071/869579,-7302992/35652739,53590429/71305478,
24386055/71305478,21006467/35652739,71740345/71305478],
[-36802360/35652739,-19092033/71305478,19002863/71305478,
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[-37074623/35652739,-7435646/35652739,-23908177/71305478,
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[-22173663/35652739,-40205985/71305478,-12615773/35652739,
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[36098681/71305478,3268339/35652739,61334365/71305478,
7598085/71305478,-16791981/71305478,40906577/35652739],
[-13362576/35652739,-20138730/35652739,-34591775/71305478,
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[25795975/35652739,15118148/35652739,36105931/71305478,
17055309/71305478,20287905/35652739,32743661/71305478],
[-41427381/71305478,-17163683/35652739,-8440526/35652739,
4219522/35652739,-23154317/71305478,-49548539/71305478],
[39586628/35652739,11346582/35652739,21885861/35652739,
19108972/35652739,16263723/35652739,26104401/35652739],
[45509008/35652739,12697468/35652739,30348098/35652739,
23103496/35652739,5622296/35652739,46468999/35652739],
[25551181/35652739,-23192899/71305478,137398083/71305478,
-12868395/35652739,45766707/71305478,24185342/35652739],
[19903407/35652739,-28074267/71305478,11549602/35652739,
24814667/71305478,-8266479/71305478,2225783/71305478],
[-6439329/71305478,9612459/35652739,-41814179/71305478,
38215683/71305478,-33732563/71305478,16069621/35652739],
[22662951/35652739,28072670/35652739,-3949376/35652739,
27191833/35652739,977022/35652739,35430333/35652739],
[-5542881/71305478,4994498/35652739,-3398958/35652739,
23445233/35652739,-16740687/71305478,38911503/71305478],
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[-7833957/35652739,-20736349/35652739,-32051065/71305478,
16324081/71305478,-21235788/35652739,-30979815/71305478],
[4793507/35652739,37484979/71305478,-26613587/71305478,
19329786/35652739,123441/71305478,479315/869579],[
-96371539/71305478,-35275101/71305478,-65969543/71305478,
-18230525/35652739,-16733925/35652739,-72108489/71305478],
[8058119/35652739,-5547370/35652739,-2898970/35652739,
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[-39782753/35652739,-36776501/71305478,-41888275/71305478,
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[-39272707/71305478,31705/1739158,-61135375/71305478,
6214824/35652739,-5330727/35652739,-54135691/71305478],
[-22961737/71305478,-16224395/71305478,-35718195/71305478,
-6380581/35652739,-2561340/35652739,-1700711/1739158],
[-10822129/35652739,11565349/71305478,-12428557/71305478,
1772772/35652739,-32717411/71305478,12836700/35652739],
[-53612739/71305478,24476363/71305478,-44608665/71305478,
-5224059/35652739,-11169833/35652739,-36836731/71305478],
[-29508264/35652739,-26130011/71305478,-59589117/71305478,
7417795/35652739,-57742381/71305478,-22843646/35652739],
[4996481/35652739,13699974/35652739,-31004067/35652739,
28345025/35652739,-16747891/35652739,405538/869579],
[3584145/71305478,20246098/35652739,-40224925/71305478,
43823909/71305478,-7461661/71305478,11332455/35652739],
[115762859/71305478,23011557/71305478,39260895/35652739,
37201731/71305478,-445791/35652739,60747780/35652739],
[-3341063/35652739,3728558/35652739,17256868/35652739,
6685728/35652739,-11467009/35652739,21521353/35652739],
[16867334/35652739,20815672/35652739,8996005/35652739,
16610194/35652739,-4046832/35652739,27789596/35652739],
[11544973/71305478,43716881/71305478,6652793/71305478,
-841808/35652739,202491/35652739,-10223455/71305478],
[-3630685/35652739,9542421/35652739,-758647/35652739,
-4871691/35652739,14732577/35652739,-9484541/35652739],
[18506187/35652739,-39095647/71305478,40007869/71305478,
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[-70494135/71305478,-7528197/35652739,-27603343/71305478,
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[95043991/71305478,-9043342/35652739,27140949/71305478,
44691671/71305478,42677059/71305478,5607556/35652739],
[511744/869579,-13468075/71305478,49057807/71305478,
262741/869579,5008635/71305478,16251305/35652739],[
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-14960222/35652739,-20477562/35652739,-29527531/71305478],
[9700926/35652739,-24176319/71305478,8375021/35652739,
-21897049/71305478,27567431/71305478,-16422781/71305478],
[-6400598/35652739,-39366537/71305478,-7051277/35652739,
-53285737/71305478,2689687/71305478,-37630827/71305478],
[-6095409/35652739,-24844415/35652739,11197972/35652739,
-23261531/35652739,388066/869579,-28656438/35652739],
[-40497551/35652739,103091/1739158,-1414937/35652739,
-82464277/71305478,45766859/71305478,-62540783/71305478],
[-54044006/35652739,-3314298/35652739,-54383197/71305478,
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[-18772589/71305478,-7100709/71305478,-69859113/71305478,
7812199/35652739,-29634054/35652739,-35349419/71305478],
[-70809931/71305478,-3372589/35652739,-30315268/35652739,
-17438574/35652739,-66369837/71305478,-30670631/71305478],
[16302676/35652739,-29714203/71305478,25227452/35652739,
-856771/71305478,67294621/71305478,-4677051/71305478],
[33321631/71305478,51225123/71305478,46372499/71305478,
6310260/35652739,5199023/35652739,89366819/71305478],
[-8928411/71305478,10181711/71305478,-22780897/71305478,
-10746813/35652739,5924750/35652739,-11343117/71305478],
[13838543/35652739,21212667/35652739,30844815/71305478,
15263139/71305478,-1191191/35652739,30338277/71305478],
[-34492867/35652739,-735715/71305478,-3844610/35652739,
-48143847/71305478,-14157339/71305478,-11435837/71305478
],[-282981/71305478,-306033/869579,43721109/35652739,
-10847970/35652739,24934057/71305478,41115923/71305478],
[21737443/71305478,-2155829/71305478,-16822838/35652739,
53036289/71305478,-12385584/35652739,6519070/35652739],
[31225343/71305478,28163677/71305478,11007945/35652739,
39770103/71305478,-4609574/35652739,29620374/35652739],
[-21274803/71305478,22197025/71305478,3933677/35652739,
11668853/71305478,-13877749/35652739,1258651/35652739],
[-7193527/71305478,-9244152/35652739,9450388/35652739,
-656288/35652739,7950743/71305478,-351315/71305478],
[91237431/71305478,18332858/35652739,10993221/35652739,
27305254/35652739,28528485/71305478,56040625/71305478],
[11533798/35652739,7484979/71305478,-531229/35652739,
32587139/71305478,37725479/71305478,-12021065/71305478],
[-27097659/71305478,13384447/71305478,-17851401/35652739,
-15611213/71305478,-8055324/35652739,-11923479/35652739],
[-45861137/71305478,-26312172/35652739,-14489348/35652739,
-12955765/35652739,-66175141/71305478,-37719475/71305478],
[-7665301/35652739,3367069/71305478,-20540937/71305478,
-5738267/35652739,22624435/71305478,-5830368/35652739],
[-35820801/35652739,-20674673/71305478,-16154823/71305478,
-25575326/35652739,-32788065/71305478,-21608912/35652739
],[405215/1739158,-35428555/71305478,2627532/35652739,
9799317/71305478,12394062/35652739,-10680196/35652739],
[61435883/71305478,-8309989/71305478,26964993/71305478,
20296575/35652739,12692737/35652739,-5572135/71305478],
[2774588/35652739,9490326/35652739,18996767/35652739,
8799716/35652739,5015306/35652739,25875959/35652739],
[23936371/35652739,5631225/35652739,20603429/71305478,
840699/1739158,1684516/35652739,12028135/71305478],[
-51700141/71305478,27305671/71305478,-32015149/71305478,
-1931209/35652739,-1771166/35652739,-36884451/71305478],
[-27994037/35652739,-18079682/35652739,-56067061/71305478,
-42059965/71305478,4402517/35652739,-77163265/71305478],
[3177161/35652739,-40445863/71305478,-13871693/35652739,
-30928885/71305478,48742987/71305478,-58406549/71305478],
[63324331/71305478,12274130/35652739,969713/1739158,
21399081/71305478,36200401/71305478,29246183/35652739],
[12985063/71305478,-1795133/35652739,39156071/71305478,
41563571/71305478,-25647253/71305478,18524559/35652739],
[-95863681/71305478,-16266635/71305478,-39276741/35652739,
-37858429/71305478,-16410692/35652739,-35575009/35652739],
[3531631/71305478,23544501/35652739,-13893941/35652739,
-798688/35652739,11983265/71305478,8666295/71305478],[
-27559991/35652739,-20570313/35652739,-33575943/71305478,
-73383941/71305478,6104973/35652739,-74319663/71305478],
[59472365/71305478,-6761343/71305478,26209017/35652739,
6930977/71305478,3014580/35652739,22526696/35652739],
[36146630/35652739,13433641/71305478,43324665/35652739,
37273489/71305478,28894723/71305478,93388891/71305478],
[42568509/71305478,-21593981/71305478,-31029905/35652739,
75549717/71305478,1649771/35652739,-23719893/35652739],
[-23754408/35652739,-15065232/35652739,-14601887/35652739,
-22410966/35652739,-19938972/35652739,-30856444/35652739],
[-68399311/71305478,3466983/71305478,13684049/71305478,
-17771829/35652739,-20162198/35652739,-18286169/71305478
],[15175927/35652739,-651573/1739158,6139903/71305478,
-4402993/35652739,-2176695/71305478,6609567/35652739],
[29453145/35652739,-3964903/35652739,-6154163/71305478,
35635843/71305478,17906051/35652739,-12283275/71305478],
[-59604393/71305478,-35106339/71305478,-32827785/71305478,
-24953333/35652739,-269127/869579,-21991933/71305478],
[37484067/71305478,44115157/71305478,18123910/35652739,
13646633/71305478,9557602/35652739,32201013/35652739],
[-13582985/71305478,9020959/71305478,16712223/35652739,
-35552559/71305478,-3211099/35652739,-293445/35652739]])
]> where w := K.1 where K := ext<K|Polynomial(K,[1,1,1,1,1,1,1])>
where K is RationalField();

return _LR;
