
//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;
//6 constituents
_LR`G :=
/*
Original group: c9Group("sl241p")
From DB /nb/reps/l2/2l241/d40.2l241.deg12.X15.M
Schur index: 2
Character: ( 40, -40, 1, 0, 0, 0, -1, -zeta(21)_7^4 - zeta(21)_7^3, zeta(21)_7^5
+ zeta(21)_7^4 + zeta(21)_7^3 + zeta(21)_7^2 + 1, -zeta(21)_7^5 - zeta(21)_7^2, 
0, 0, 0, 0, zeta(21)_7^5 + zeta(21)_7^2, -zeta(21)_7^5 - zeta(21)_7^4 - 
zeta(21)_7^3 - zeta(21)_7^2 - 1, zeta(21)_7^4 + zeta(21)_7^3, 0, 0, 0, 0, 
-zeta(21)_3*zeta(21)_7^5 - zeta(21)_3*zeta(21)_7^4 - zeta(21)_3*zeta(21)_7^3 - 
zeta(21)_3*zeta(21)_7^2 - 2*zeta(21)_3*zeta(21)_7 - zeta(21)_3 - zeta(21)_7^5 - 
zeta(21)_7^4 - zeta(21)_7^3 - zeta(21)_7^2 - zeta(21)_7 - 1, 
-zeta(21)_3*zeta(21)_7^5 + zeta(21)_3*zeta(21)_7^2 + zeta(21)_7^2, 
-zeta(21)_3*zeta(21)_7^4 + zeta(21)_3*zeta(21)_7^3 + zeta(21)_7^3, 
zeta(21)_3*zeta(21)_7^5 + zeta(21)_3*zeta(21)_7^4 + zeta(21)_3*zeta(21)_7^3 + 
zeta(21)_3*zeta(21)_7^2 + 2*zeta(21)_3*zeta(21)_7 + zeta(21)_3 + zeta(21)_7, 
zeta(21)_3*zeta(21)_7^4 - zeta(21)_3*zeta(21)_7^3 + zeta(21)_7^4, 
zeta(21)_3*zeta(21)_7^5 - zeta(21)_3*zeta(21)_7^2 + zeta(21)_7^5, 0, 0, 0, 0, 0,
0, 0, 0, -1, -1, zeta(21)_3*zeta(21)_7^5 + zeta(21)_3*zeta(21)_7^4 + 
zeta(21)_3*zeta(21)_7^3 + zeta(21)_3*zeta(21)_7^2 + 2*zeta(21)_3*zeta(21)_7 + 
zeta(21)_3 + zeta(21)_7^5 + zeta(21)_7^4 + zeta(21)_7^3 + zeta(21)_7^2 + 
zeta(21)_7 + 1, -zeta(21)_3*zeta(21)_7^5 + zeta(21)_3*zeta(21)_7^2 - 
zeta(21)_7^5, -zeta(21)_3*zeta(21)_7^5 - zeta(21)_3*zeta(21)_7^4 - 
zeta(21)_3*zeta(21)_7^3 - zeta(21)_3*zeta(21)_7^2 - 2*zeta(21)_3*zeta(21)_7 - 
zeta(21)_3 - zeta(21)_7, zeta(21)_3*zeta(21)_7^4 - zeta(21)_3*zeta(21)_7^3 - 
zeta(21)_7^3, -zeta(21)_3*zeta(21)_7^4 + zeta(21)_3*zeta(21)_7^3 - zeta(21)_7^4,
zeta(21)_3*zeta(21)_7^5 - zeta(21)_3*zeta(21)_7^2 - zeta(21)_7^2, 1, 1 )
*/

MatrixGroup<40,K | [
Matrix(K,40,40,
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],[146/1517,-254/1517,104/1517,-1509/1517,-412/1517,
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],[-1200/1517,1050/1517,23/1517,-28/41,-757/1517,972/1517,
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114/1517,-43/1517,932/1517,-1515/1517,-262/1517,-13/37],
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442/1517,-774/1517,-396/1517,924/1517,-803/1517,-448/1517,
1673/1517,-101/1517,-648/1517],[2057/1517,-283/1517,
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2028/1517,-2551/1517,300/1517,1470/1517,-774/1517],[
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422/1517,-1052/1517,-223/1517,1917/1517,-1366/1517,-633/1517,
1144/1517,301/1517,-1620/1517,895/1517,1409/1517,-1477/1517
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454/1517],[36/1517,-1021/1517,889/1517,-349/1517,-93/1517,
502/1517,654/1517,-406/1517,-721/1517,644/1517,-811/1517,
470/1517],[8/1517,-170/1517,-53/1517,421/1517,-516/1517,
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775/1517,-578/1517,691/1517,-61/1517,-1040/1517],[
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942/1517,380/1517,-961/1517,151/1517,357/1517,-1085/1517
],[-1465/1517,1470/1517,1451/1517,-1356/1517,665/1517,
1377/1517,-1955/1517,-1348/1517,1699/1517,-6/41,-884/1517,
1535/1517],[1607/1517,-704/1517,-1298/1517,1429/1517,
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1339/1517,-1544/1517],[438/1517,19/1517,416/1517,558/1517,
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199/1517,-341/1517,-243/1517,23/41,726/1517,445/1517,
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1238/1517,-440/1517,863/1517],[-194/1517,930/1517,
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133/1517,-498/1517,15/37,678/1517,-400/1517,-527/1517],
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15/41,285/1517,-1525/1517,30/37,838/1517,-351/1517],[
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],[-7/1517,340/1517,359/1517,-470/1517,624/1517,573/1517,
143/1517,-609/1517,-15/1517,-6/1517,580/1517,401/1517],[
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674/1517,75/1517,-230/1517,-50/1517,499/1517,101/1517],
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],[455/1517,-15/41,6/41,591/1517,-642/1517,-78/1517,
404/1517,-29/1517,-707/1517,626/1517,-131/1517,89/1517],
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362/1517,1103/1517,-908/1517,251/1517,-169/1517,-602/1517],
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],[1050/1517,-1322/1517,137/1517,1018/1517,-568/1517,
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319/1517,342/1517,-507/1517,332/1517,1070/1517,-840/1517,
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],[-184/1517,-21/41,144/1517,-52/1517,-637/1517,-667/1517,
360/1517,408/1517,295/1517,-266/1517,-838/1517,-624/1517],
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],[1292/1517,-663/1517,-933/1517,968/1517,-1447/1517,
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721/1517,-30/41],[22/1517,263/1517,428/1517,-612/1517,
643/1517,760/1517,-725/1517,189/1517,165/1517,27/1517,
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7/41,989/1517,-447/1517,103/1517,-107/1517,-614/1517,
298/1517,464/1517,374/1517,-375/1517,988/1517,-358/1517
],[-778/1517,435/1517,500/1517,-442/1517,-341/1517,
345/1517,-620/1517,-122/1517,472/1517,189/1517,-485/1517,
166/1517],[1040/1517,-810/1517,-855/1517,1512/1517,-31/37,
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0,8/41,355/1517,25/41,-357/1517,-711/1517,132/1517],
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372/1517,175/1517,-1448/1517,1015/1517,981/1517,-291/1517],
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790/1517,990/1517,-1033/1517,-157/1517,948/1517,-1284/1517],
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[-808/1517,-1/37,1020/1517,-1541/1517,-292/1517,1128/1517,
291/1517,-628/1517,391/1517,-178/1517,-1586/1517,422/1517],
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[-502/1517,-375/1517,830/1517,256/1517,-119/1517,9/41,
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-1186/1517,-543/1517,2000/1517,-37/41,-23/41,538/1517],
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249/1517,892/1517,-81/1517,-1320/1517,1273/1517,207/1517],
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-551/1517,-488/1517,440/1517,-400/1517,-302/1517,210/1517
],[68/1517,-2/41,-531/1517,161/1517,546/1517,382/1517,
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376/1517,233/1517,280/1517,-298/1517,-235/1517,-239/1517],
[-326/1517,1020/1517,-1356/1517,-501/1517,67/1517,318/1517,
-261/1517,798/1517,811/1517,-1094/1517,-227/1517,-167/1517],
[311/1517,-1431/1517,857/1517,650/1517,-838/1517,-392/1517,
631/1517,-352/1517,-771/1517,1607/1517,-486/1517,-337/1517
],[92/1517,806/1517,510/1517,-713/1517,1/1517,461/1517,
-311/1517,-256/1517,15/37,139/1517,-13/1517,1006/1517],
[-31/37,511/1517,108/1517,-884/1517,721/1517,1007/1517,
-17/37,-513/1517,855/1517,-1333/1517,-1090/1517,864/1517],
[-421/1517,-989/1517,619/1517,204/1517,131/1517,170/1517,
109/1517,-398/1517,-485/1517,394/1517,-950/1517,266/1517],
[18/41,110/1517,-1523/1517,499/1517,-447/1517,329/1517,
219/1517,11/37,-845/1517,242/1517,234/1517,-1158/1517]])
]> where w := K.1 where K := ext<K|Polynomial(K,[1,-1,0,1,-1,0,
1,0,-1,1,0,-1,1])> where K is RationalField();

return _LR;
