
//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;
//1 constituent
_LR`G :=
/*
Original group: c9Group("sl241p")
From DB /nb/reps/l2/2l241/d40.2l241.deg2.X6.M
Schur index: 2
Character: ( 40, -40, 1, 0, 0, 0, -1, -2, -2, -2, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 
0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, 1, 
1 )
*/

MatrixGroup<40,K | [
Matrix(K,40,40,
[[1159/7585,-812/7585],[-2383/7585,2384/7585],[314/7585,
-2032/7585],[928/7585,1351/7585],[-2204/7585,607/7585],
[-1696/7585,963/7585],[29/205,33/205],[-1023/7585,
1069/7585],[1031/7585,1177/7585],[20/1517,-83/1517],
[-25/1517,150/1517],[2421/7585,792/7585],[6/205,
-3/205],[2128/7585,-1039/7585],[-507/7585,711/7585],
[502/1517,-163/1517],[-3717/7585,1471/7585],[2217/7585,
-51/185],[439/7585,733/7585],[577/7585,-1501/7585],
[1139/7585,-62/185],[374/7585,753/7585],[30/1517,
190/1517],[-66/205,-22/205],[-269/7585,-273/7585],
[1346/7585,-1268/7585],[-653/7585,329/7585],[206/7585,
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[924/7585,-1622/7585],[43/185,-1254/7585],[-136/1517,
335/1517],[-284/7585,557/7585],[236/1517,27/1517],[
-187/7585,86/7585],[-1859/7585,-538/7585],[-1892/7585,
-229/7585],[-522/7585,431/7585],[-1011/7585,-2222/7585],
[120/1517,-276/1517],[-553/1517,-49/1517],[2577/7585,
559/7585],[-98/7585,1624/7585],[126/7585,317/7585],
[-563/7585,159/7585],[1024/7585,-187/7585],[1286/7585,
1867/7585],[64/7585,1688/7585],[-117/7585,1331/7585],
[1084/7585,1118/7585],[-1081/7585,1713/7585],[357/7585,
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[817/7585,-1461/7585],[-625/1517,457/1517],[2739/7585,
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[136/1517,-39/1517],[301/7585,932/7585],[-197/1517,
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[-479/7585,1357/7585],[293/7585,351/7585],[-60/1517,
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[-679/7585,2742/7585],[1158/7585,526/7585],[2469/7585,
208/7585],[1031/7585,1177/7585],[318/7585,756/7585],
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[1064/7585,-2092/7585],[-3632/7585,2071/7585],[543/1517,
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2472/7585],[-1719/7585,-2488/7585],[2284/7585,-532/7585],
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[-1018/7585,-996/7585],[773/7585,-4009/7585],[-3028/7585,
1814/7585],[1447/7585,-2096/7585],[-391/1517,459/1517],
[177/7585,-581/7585],[-1323/7585,1574/7585],[204/1517,
-299/1517],[1209/7585,923/7585],[-958/7585,3824/7585],
[1088/7585,1686/7585],[-483/7585,-136/7585],[303/7585,
-264/7585],[-97/7585,-454/7585],[2202/7585,-706/7585],
[282/7585,824/7585],[178/7585,-439/7585],[-1252/7585,
926/7585],[1317/7585,-1501/7585],[422/7585,-201/7585],
[-651/7585,1168/7585],[-11/205,-47/205],[-2822/7585,
-384/7585],[-67/7585,-264/7585],[-688/1517,-127/1517],
[12/41,-4/41],[-7/7585,301/7585],[-988/7585,-621/7585],
[-512/7585,371/7585],[1286/7585,572/7585],[1039/7585,
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[2403/7585,1011/7585],[-1669/7585,172/7585],[2373/7585,
-1029/7585],[-448/7585,1319/7585],[707/7585,1974/7585],
[146/7585,-543/7585],[-66/1517,100/1517],[-736/7585,
-172/7585],[103/1517,-396/1517],[-3494/7585,1872/7585],
[894/7585,-2922/7585],[1532/7585,724/7585],[136/7585,
442/7585],[-1537/7585,2266/7585],[-818/7585,2059/7585],
[716/7585,-818/7585],[-958/7585,3824/7585],[-1864/7585,
2082/7585],[-177/7585,-1824/7585],[181/1517,-13/1517],
[-2814/7585,-1098/7585],[2194/7585,8/7585],[64/1517,
60/1517],[250/1517,-20/1517],[-2466/7585,1883/7585],[
2343/7585,-1219/7585],[301/7585,-1288/7585],[2118/7585,
-979/7585],[-91/1517,-157/1517],[467/1517,-101/1517],
[-723/7585,9/7585],[-768/1517,-276/1517],[8/205,-34/205
],[92/1517,77/1517],[636/7585,-893/7585],[577/7585,
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[-146/1517,-530/1517],[194/7585,-1497/7585],[340/1517,
106/1517],[486/7585,1487/7585],[2232/7585,-516/7585],
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[1707/7585,2079/7585],[-177/7585,396/7585],[-2328/7585,
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-953/7585],[2156/7585,-948/7585],[632/7585,-1276/7585],
[-3718/7585,1884/7585],[-186/1517,191/1517],[464/1517,
102/1517],[737/7585,129/7585],[523/7585,1006/7585],
[1226/7585,562/7585],[-1821/7585,603/7585],[147/7585,
894/7585],[576/7585,-718/7585],[17/185,2034/7585],
[28/1517,-94/1517],[-662/7585,-1134/7585],[6/41,-2/41
],[726/7585,1157/7585],[-727/7585,366/7585],[42/205,
-56/205],[868/7585,-1434/7585],[-618/7585,-991/7585],
[-166/7585,663/7585],[272/1517,-115/1517],[-31/185,
78/7585],[109/1517,-247/1517],[-1471/7585,538/7585],[
-229/7585,-1993/7585],[-1138/7585,-2311/7585],[572/7585,
-1101/7585],[-1289/7585,297/7585],[-2588/7585,-1936/7585
],[40/1517,-166/1517],[-1471/7585,-202/7585],[2/37,
285/1517],[-916/7585,-1497/7585],[-51/1517,158/1517],
[-4/41,-16/41],[1254/7585,2133/7585],[228/7585,186/7585
],[-3381/7585,158/7585],[372/7585,99/7585],[2371/7585,
-388/7585],[119/7585,-1232/7585],[-2031/7585,1123/7585],
[-1674/7585,572/7585],[279/1517,324/1517],[-1806/7585,
-1152/7585],[417/7585,199/7585],[94/1517,250/1517],[
-1711/7585,1238/7585],[704/7585,2473/7585],[-1736/7585,
-2312/7585],[3041/7585,1697/7585],[1364/7585,2213/7585],
[42/205,9/205],[-302/7585,36/7585],[992/7585,29/185],
[-883/7585,-881/7585],[1543/7585,-1414/7585],[-91/1517,
-305/1517],[-801/7585,-892/7585],[-724/7585,1532/7585],
[1413/7585,1401/7585],[-1296/7585,2078/7585],[442/7585,
-876/7585],[-2191/7585,788/7585],[-1527/7585,-2049/7585],
[248/7585,251/7585],[1339/7585,-3372/7585],[418/7585,
526/7585],[-2144/7585,-1418/7585],[-121/1517,-199/1517],
[-658/7585,-11/7585],[2978/7585,-404/7585],[1723/7585,
-3604/7585],[554/7585,1338/7585],[-352/1517,77/1517],
[-496/7585,-317/7585],[1839/7585,-822/7585],[-2421/7585,
-422/7585],[389/7585,-77/7585],[3953/7585,-889/7585],
[829/7585,-682/7585],[-1261/7585,2238/7585],[-1358/7585,
-991/7585],[961/7585,857/7585],[1614/7585,528/7585],
[971/7585,242/7585],[-1/7585,1153/7585],[-2528/7585,
1219/7585],[2616/7585,1657/7585],[-118/1517,-32/1517],
[368/1517,271/1517],[-1072/7585,-524/7585],[-133/7585,
1279/7585],[1397/7585,-2166/7585],[683/7585,-2544/7585],
[-12/41,0],[-197/1517,35/1517],[87/7585,-1706/7585
],[-188/7585,-241/7585],[-31/205,38/205],[722/7585,
-336/7585],[-2297/7585,166/7585],[-236/7585,-2247/7585],
[103/1517,455/1517],[71/1517,-241/1517],[1573/7585,
-114/7585],[-493/7585,-631/7585],[-31/185,263/7585],
[-1368/7585,-746/7585],[-403/7585,-6/185],[79/1517,
7/1517],[498/1517,194/1517],[1197/7585,-596/7585],
[-3/205,49/205],[-4/41,-16/41],[70/1517,172/1517],
[137/7585,-711/7585],[-2703/7585,1714/7585],[1459/7585,
348/7585],[2327/7585,-31/185],[463/7585,71/7585],[
-3067/7585,-209/7585],[-2324/7585,-708/7585],[763/7585,
-434/7585],[280/1517,96/1517],[1721/7585,-558/7585],
[314/7585,373/7585],[-324/1517,464/1517],[142/7585,
739/7585],[1519/7585,1653/7585],[681/7585,1427/7585],
[-942/7585,176/7585],[554/7585,-512/7585],[929/7585,
-2762/7585],[816/7585,432/7585],[-107/7585,-2429/7585],[
-623/7585,-1146/7585],[2576/7585,-1618/7585],[-1327/7585,
-474/7585],[-1329/7585,907/7585],[1883/7585,2466/7585],
[-562/7585,1781/7585],[-70/1517,-24/1517],[-596/7585,
1393/7585],[-1764/7585,-1293/7585],[4/41,0],[1178/7585,
-1814/7585],[-1456/7585,633/7585],[-2207/7585,-189/7585],
[-1701/7585,-302/7585],[-464/7585,712/7585],[1514/7585,
-352/7585],[843/7585,-1284/7585],[-1339/7585,-8/185],
[-394/7585,107/7585],[-1652/7585,551/7585],[366/1517,
-13/1517],[-3539/7585,1402/7585],[59/7585,-317/7585],
[2973/7585,-744/7585],[-463/7585,-1366/7585],[-4134/7585,
1087/7585],[-142/7585,-554/7585],[1444/7585,-1042/7585],
[-332/7585,401/7585],[2416/7585,-103/7585],[235/1517,
70/1517],[-374/1517,283/1517],[52/7585,2944/7585],[
-1067/7585,-924/7585],[858/7585,1401/7585],[-352/1517,
77/1517],[-389/7585,262/7585],[3/41,3/41],[-513/7585,
229/7585],[-1337/7585,2361/7585],[196/1517,45/1517],
[32/1517,-303/1517],[-158/7585,134/7585],[7/205,
24/205],[2373/7585,11/185],[-1839/7585,-843/7585],[
-147/7585,-1079/7585],[-787/7585,1281/7585],[-496/7585,
-1612/7585],[1223/7585,-1529/7585],[1481/7585,-783/7585],
[889/7585,1548/7585],[-2443/7585,-956/7585],[1028/7585,
-2394/7585],[-308/7585,-446/7585],[2634/7585,-967/7585],
[321/1517,-113/1517],[-229/1517,153/1517],[-394/7585,
107/7585],[13/185,-4/185],[-138/1517,-23/1517],[
-2529/7585,522/7585],[-1644/7585,-13/185],[649/1517,
-46/1517],[-468/7585,-1521/7585],[-2936/7585,1928/7585],
[-1376/7585,1263/7585],[1557/7585,1314/7585],[231/7585,
-313/7585],[489/1517,-196/1517],[307/7585,119/7585],
[-549/7585,-813/7585],[-339/7585,1442/7585],[-220/1517,
-160/1517],[2443/7585,1881/7585],[-1798/7585,354/7585],
[187/7585,-456/7585],[-13/185,-576/7585],[1993/7585,
511/7585],[-831/7585,768/7585],[1574/7585,-897/7585],
[953/7585,-1389/7585],[470/1517,436/1517],[-1578/7585,
1254/7585],[78/1517,198/1517],[-2998/7585,1264/7585],[
-401/7585,-3292/7585],[-1094/7585,3752/7585],[-1544/7585,
-3168/7585],[2434/7585,-1247/7585],[416/7585,-1053/7585],
[-16/1517,-274/1517],[-1094/7585,52/7585],[986/7585,
-958/7585],[13/185,-4/185],[953/7585,1201/7585],[
1236/7585,-2643/7585],[-163/7585,719/7585],[-352/1517,
77/1517],[883/7585,1251/7585],[506/7585,-2888/7585],
[-1826/7585,1003/7585],[1229/7585,618/7585],[31/185,
-78/7585],[607/7585,-1311/7585],[-2248/7585,1019/7585],
[114/1517,278/1517],[2399/7585,-1407/7585],[-189/1517,
98/1517],[-1422/7585,-1014/7585],[277/7585,-256/7585],
[-396/1517,267/1517],[-412/7585,1251/7585],[-154/1517,
-112/1517],[998/7585,2226/7585],[-1542/7585,1371/7585],
[664/7585,308/7585],[759/7585,108/7585],[587/7585,
1029/7585],[-2796/7585,718/7585],[2554/7585,-1042/7585
],[59/1517,-317/1517],[38/1517,179/1517],[-92/1517,
-114/1517],[301/7585,-178/7585],[-1842/7585,396/7585],
[-859/7585,-2283/7585],[-1977/7585,1391/7585],[349/7585,
-1502/7585],[783/7585,-2034/7585],[1718/7585,-59/7585],
[-1296/7585,-1807/7585],[-1502/7585,21/7585],[842/7585,
979/7585],[542/7585,-921/7585],[3517/7585,-86/7585],
[753/7585,-744/7585],[-447/7585,721/7585],[-828/7585,
1564/7585],[-1614/7585,-898/7585],[1708/7585,741/7585],
[-1573/7585,854/7585],[398/7585,646/7585],[1266/7585,
-973/7585],[363/7585,-1179/7585],[-2707/7585,2256/7585],
[-2042/7585,-624/7585],[1204/7585,-712/7585],[-564/7585,
-1278/7585],[1723/7585,96/7585],[136/1517,-224/1517],
[-1179/7585,2042/7585],[1208/7585,966/7585],[158/1517,
-23/1517],[2252/7585,2879/7585],[-192/1517,-32/1517],
[-283/7585,2179/7585],[372/1517,-86/1517],[818/7585,
1086/7585],[-944/7585,262/7585],[-1352/7585,-2914/7585
],[1356/7585,-1513/7585],[-989/7585,-1873/7585],[
-2209/7585,1192/7585],[2221/7585,1067/7585],[-56/1517,
373/1517],[352/7585,-2741/7585],[-614/7585,1057/7585],
[-634/7585,-2153/7585],[1106/7585,-1493/7585],[1538/7585,
651/7585],[-754/7585,-1988/7585],[-1141/7585,38/7585],
[-154/1517,406/1517],[-160/1517,-76/1517],[1414/7585,
-1602/7585],[-377/7585,-1179/7585],[-1444/7585,1597/7585
],[-1174/7585,-1503/7585],[-89/1517,-21/1517],[-54/7585,
7/185],[-1793/7585,2729/7585],[-104/1517,-79/1517],
[4369/7585,-92/7585],[924/7585,-2732/7585],[-389/1517,
299/1517],[394/7585,-107/7585],[133/7585,2421/7585],
[-747/7585,-254/7585],[546/7585,17/7585],[-1014/7585,
127/7585],[-1973/7585,294/7585],[19/1517,145/1517],[
-1407/7585,-364/7585],[3079/7585,2283/7585],[-462/7585,
-2519/7585],[441/7585,-1018/7585],[-827/7585,226/7585],
[94/7585,1508/7585],[-577/7585,206/7585],[1267/7585,
-461/7585],[963/7585,-154/7585],[504/7585,-397/7585],
[-176/1517,5/37],[-1456/7585,-1587/7585],[-1228/7585,
-106/7585],[-1024/7585,-18/185],[242/7585,879/7585],[
-808/7585,-961/7585],[1113/7585,-1239/7585],[1407/7585,
-1486/7585],[-19/205,32/205],[-132/1517,-133/1517],
[692/7585,-156/7585],[234/7585,668/7585],[469/1517,
-2/1517],[1246/7585,-1408/7585],[1038/7585,1061/7585
],[-4/41,-16/41],[-442/7585,1616/7585],[163/1517,
169/1517],[-2879/7585,957/7585],[459/7585,-497/7585],
[3103/7585,-2819/7585],[-169/7585,-1983/7585],[188/7585,
3756/7585],[-570/1517,-58/1517],[140/1517,159/1517],
[-474/7585,587/7585],[373/1517,93/1517],[-336/7585,
-907/7585],[-2182/7585,586/7585],[-954/7585,1432/7585
],[-787/7585,-384/7585],[12/205,59/205],[29/1517,
85/1517],[-482/7585,-1844/7585],[49/7585,-442/7585],
[202/1517,231/1517],[-268/7585,-871/7585],[972/7585,
-541/7585],[1112/7585,-1566/7585],[1879/7585,1158/7585
],[-284/1517,2/1517],[979/7585,1193/7585],[-92/7585,
2846/7585],[142/7585,-371/7585],[-128/1517,102/1517],
[-92/1517,-10/37],[1474/7585,-297/7585],[-988/7585,
-1546/7585],[-1612/7585,-244/7585],[-976/7585,-2987/7585
],[266/1517,-79/1517],[-1069/7585,87/7585],[321/1517,
146/1517],[1187/7585,19/7585],[563/7585,1876/7585],
[-1568/7585,-1396/7585],[53/1517,52/1517],[1032/7585,
1319/7585],[-1129/7585,3037/7585],[-242/7585,1156/7585],
[1411/7585,-548/7585],[295/1517,-549/1517],[-595/1517,
277/1517],[-568/7585,-921/7585],[2809/7585,18/7585],
[83/1517,-17/1517],[-1156/7585,1053/7585],[822/7585,
-1491/7585],[-1348/7585,59/7585],[1908/7585,1761/7585],
[-198/7585,-1661/7585],[832/7585,2889/7585],[12/7585,
-701/7585],[564/1517,-128/1517],[906/7585,1002/7585],
[358/7585,-964/7585],[-97/1517,-47/1517],[-1164/7585,
842/7585],[281/1517,-391/1517],[-1081/7585,973/7585],
[-1171/7585,2253/7585],[-17/205,21/205],[-616/7585,
958/7585],[-122/7585,-2154/7585],[-1401/7585,673/7585],
[181/7585,-1308/7585],[-506/7585,-1737/7585],[1056/7585,
-1193/7585],[-1196/7585,-372/7585],[-3323/7585,624/7585],
[-1746/7585,-957/7585],[213/1517,17/1517],[2601/7585,
-1583/7585],[953/7585,-1574/7585],[-24/1517,884/1517],
[192/7585,-1781/7585],[453/7585,501/7585],[3784/7585,
1198/7585],[-2969/7585,1682/7585],[-757/7585,-1119/7585],
[2483/7585,-24/7585],[1388/7585,-1039/7585],[-151/1517,
277/1517],[-2141/7585,-807/7585],[319/7585,-952/7585],
[-307/7585,251/7585],[253/1517,295/1517],[1058/7585,
756/7585],[-2177/7585,741/7585],[947/7585,904/7585],
[59/1517,-206/1517],[1979/7585,1483/7585],[997/7585,
-876/7585],[-1133/7585,249/7585],[-342/1517,-131/1517
],[3/7585,241/7585],[-874/7585,-158/7585],[97/7585,
-1396/7585],[8/7585,211/7585],[1216/7585,807/7585],
[-345/1517,183/1517],[729/7585,1768/7585],[-3/37,
-39/1517],[-1736/7585,-2682/7585],[-811/7585,833/7585],
[-1658/7585,-486/7585],[153/1517,-400/1517],[29/185,
-2472/7585],[-140/1517,-11/1517],[-159/1517,-119/1517],
[-378/7585,-211/7585],[94/7585,-157/7585],[1404/7585,
-987/7585],[1356/7585,-1328/7585],[-603/7585,1879/7585],
[-1174/7585,-1503/7585],[118/7585,-819/7585],[1531/7585,
767/7585],[-2841/7585,1173/7585],[-248/7585,119/7585],
[2666/7585,-308/7585],[-757/7585,-564/7585],[-602/1517,
245/1517],[-153/1517,400/1517],[1454/7585,193/7585],
[1438/7585,-969/7585],[3052/7585,299/7585],[197/7585,
409/7585],[-372/1517,530/1517],[1444/7585,1733/7585],
[-813/7585,-1486/7585],[559/7585,2233/7585],[-769/7585,
-48/7585],[947/7585,-2611/7585],[-869/7585,1662/7585],[
3/185,631/7585],[-1/7585,-512/7585],[1234/7585,-337/7585
],[594/7585,-2232/7585],[-1479/7585,142/7585],[-8/37,
377/1517],[1052/7585,459/7585],[-2462/7585,1711/7585],
[-1993/7585,-3656/7585],[204/7585,848/7585],[202/7585,
-1841/7585],[49/1517,-294/1517],[521/1517,-129/1517
],[-957/7585,-1029/7585],[-1051/7585,-2167/7585],[
-396/7585,-1287/7585],[428/7585,1761/7585],[468/1517,
-33/1517],[2039/7585,-1282/7585],[-429/7585,687/7585],
[-828/7585,1564/7585],[26/185,1152/7585],[497/7585,
-281/7585],[-834/1517,268/1517],[1949/7585,368/7585],
[47/7585,-2761/7585],[386/1517,-244/1517],[-2092/7585,
2266/7585],[-816/7585,-1172/7585],[-169/7585,422/7585],
[-998/7585,-1486/7585],[445/1517,179/1517],[76/1517,
-3/37],[-1467/7585,1291/7585],[513/7585,141/7585],[
-1537/7585,1711/7585],[1556/7585,1357/7585],[-1531/7585,
713/7585],[449/7585,-252/7585],[202/7585,-1471/7585],
[377/1517,217/1517],[-857/7585,-334/7585],[867/7585,
-281/7585],[1707/7585,-1991/7585],[43/1517,-221/1517],
[-916/7585,1463/7585],[209/1517,1/37],[-1086/7585,
-292/7585],[1684/7585,-1002/7585],[67/1517,597/1517],
[-47/7585,-1494/7585],[-924/7585,-2263/7585],[-498/7585,
-1526/7585],[-490/1517,-501/1517],[-1612/7585,-614/7585
],[398/7585,461/7585],[648/7585,-114/7585],[878/7585,
2021/7585],[38/185,-579/7585]])
]> where w := K.1 where K := ext<K|Polynomial(K,[1,0,1])> where K
is RationalField();

return _LR;
