//Standard generators of L2(79) are a and b where a has order 2, b has order 3
//and ab has order 79.
//Standard generators of the double cover 2.L2(79) = SL2(79) are preimages A and
//B where B has order 3 and AB has order 79.
_LR := rec < recformat< F: GrpFP, AI: SeqEnum, G: GrpMat > |
      F := FreeGroup(2) >;
_LR`AI:=[[a^-1,b^-1 ]]
             where a is (_LR`F).1 where b is (_LR`F).2;
//two constituents, interchanged by auto
_LR`G :=
/*
Original group: c9Group("l279p")
From DB /nb/reps/l2/l279/d39.l279.deg2.X2.M
Schur index: 1
Character: ( 39, -1, 0, -1, -1, -1, 1, 1, -1, -1, 0, 0, 0, 0, 0, 0, -1, -1, -1, 
-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, zeta(79)_79^76 +
zeta(79)_79^73 + zeta(79)_79^72 + zeta(79)_79^67 + zeta(79)_79^65 + 
zeta(79)_79^64 + zeta(79)_79^62 + zeta(79)_79^55 + zeta(79)_79^52 + 
zeta(79)_79^51 + zeta(79)_79^50 + zeta(79)_79^49 + zeta(79)_79^46 + 
zeta(79)_79^45 + zeta(79)_79^44 + zeta(79)_79^42 + zeta(79)_79^40 + 
zeta(79)_79^38 + zeta(79)_79^36 + zeta(79)_79^32 + zeta(79)_79^31 + 
zeta(79)_79^26 + zeta(79)_79^25 + zeta(79)_79^23 + zeta(79)_79^22 + 
zeta(79)_79^21 + zeta(79)_79^20 + zeta(79)_79^19 + zeta(79)_79^18 + 
zeta(79)_79^16 + zeta(79)_79^13 + zeta(79)_79^11 + zeta(79)_79^10 + 
zeta(79)_79^9 + zeta(79)_79^8 + zeta(79)_79^5 + zeta(79)_79^4 + zeta(79)_79^2 + 
zeta(79)_79, -zeta(79)_79^76 - zeta(79)_79^73 - zeta(79)_79^72 - zeta(79)_79^67 
- zeta(79)_79^65 - zeta(79)_79^64 - zeta(79)_79^62 - zeta(79)_79^55 - 
zeta(79)_79^52 - zeta(79)_79^51 - zeta(79)_79^50 - zeta(79)_79^49 - 
zeta(79)_79^46 - zeta(79)_79^45 - zeta(79)_79^44 - zeta(79)_79^42 - 
zeta(79)_79^40 - zeta(79)_79^38 - zeta(79)_79^36 - zeta(79)_79^32 - 
zeta(79)_79^31 - zeta(79)_79^26 - zeta(79)_79^25 - zeta(79)_79^23 - 
zeta(79)_79^22 - zeta(79)_79^21 - zeta(79)_79^20 - zeta(79)_79^19 - 
zeta(79)_79^18 - zeta(79)_79^16 - zeta(79)_79^13 - zeta(79)_79^11 - 
zeta(79)_79^10 - zeta(79)_79^9 - zeta(79)_79^8 - zeta(79)_79^5 - zeta(79)_79^4 -
zeta(79)_79^2 - zeta(79)_79 - 1 )
*/

MatrixGroup<39,K | [
Matrix(K,39,39,
[[6282/79,951/79],[15430/79,-4295/79],[-27153/79,
-11172/79],[-97044/79,331/79],[-23846/79,27753/79],
[125871/79,18060/79],[74740/79,-23214/79],[-108451/79,
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[262019/79,-45315/79],[-210891/79,-67783/79],[-271075/79,
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[-92377/79,126980/79],[612573/79,47967/79],[181933/79,
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[394370/79,6166/79],[-85336/79,-100362/79],[-496915/79,
8522/79],[51163/79,112833/79],[454780/79,10382/79],
[19471/79,-82955/79],[-288149/79,-10105/79],[21538/79,
45367/79],[152702/79,-11702/79],[-116624/79,-37328/79],
[-173521/79,20150/79],[48905/79,41483/79],[143452/79,
5032/79],[33714/79,-15364/79],[-25613/79,-7223/79],
[-9202/79,1188/79],[-1614/79,327/79],[5705/79,1535/79
],[16620/79,-888/79],[1700/79,-7107/79],[-40532/79,
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[21800/79,-6802/79],[-44522/79,-3724/79],[-5634/79,
14407/79],[85924/79,3499/79],[13658/79,-22770/79],[
-114583/79,-8519/79],[-36047/79,24286/79],[101772/79,
10073/79],[17924/79,-19926/79],[-97840/79,-945/79],
[26069/79,26068/79],[134018/79,-2460/79],[-17070/79,
-33034/79],[-139504/79,-2271/79],[-1532/79,26956/79],
[100882/79,235/79],[-32587/79,-19986/79],[-89773/79,
9343/79],[60219/79,23979/79],[106658/79,-8911/79],
[-38068/79,-23443/79],[-86027/79,3642/79],[20026/79,
15325/79],[44901/79,-3418/79],[-26347/79,-7190/79],
[-25153/79,7601/79],[38524/79,7370/79],[35804/79,
-5022/79],[-11532/79,-7659/79],[-20177/79,-696/79],
[-4685/79,1848/79],[2403/79,461/79],[1544/79,1982/79
],[31242/79,390/79],[23359/79,-12769/79],[-83648/79,
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[156809/79,-328/79],[-44427/79,-29999/79],[-131287/79,
18824/79],[168459/79,40194/79],[209156/79,-44075/79],
[-252965/79,-66137/79],[-323044/79,48164/79],[225845/79,
82207/79],[308643/79,-36913/79],[-213960/79,-59306/79],
[-191840/79,59194/79],[372747/79,49504/79],[225842/79,
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[-4181,139],[869,733],[2133,-160],[-1312,-352],
[-1311,371],[1799,384],[1806,-209],[-416,-362],
[-904,-48],[-235,78],[103,20],[6,11],[155,
1],[108,-62],[-428,-91],[-600,73],[236,177],
[751,-24],[-298,-146],[-622,110],[910,185],
[934,-239],[-1360,-300],[-1437,271],[1283,374],
[1366,-225],[-1206,-268],[-800,323],[1911,204],
[900,-458],[-2234,-300],[-1168,415],[1720,282],
[696,-331],[-1585,-104],[-77,401],[1999,67],
[230,-433],[-1752,-121],[-369,308],[1108,85],
[55,-178],[-673,16],[315,165],[742,-40],[-36,
-160],[-526,-41],[-175,50],[77,30],[37,-3],
[171,10],[169,-127],[-969,-209],[-2031,179],
[461,668],[3245,188],[705,-649],[-2667,-76],[
995,706],[4096,-355],[-2724,-1253],[-6642,478],[
2527,1761],[7845,-218],[-1623,-1593],[-5836,370],[
4053,1296],[5772,-1121],[-6316,-1704],[-7941,1163],
[5130,1877],[6965,-746],[-4174,-1277],[-3719,1031],
[6349,899],[3783,-1486],[-6746,-1141],[-4477,1150],
[4451,995],[3019,-686],[-2699,-452],[-632,557],
[3067,94],[359,-713],[-2730,-334],[-1521,338],
[552,270],[615,14],[22,-38],[15,0],[9,-11],
[-93,-17],[-165,19],[55,59],[290,12],[56,-57],
[-233,-6],[100,58],[336,-35],[-267,-106],[-559,
49],[253,152],[673,-26],[-154,-138],[-495,35],
[355,105],[471,-101],[-583,-141],[-665,107],[
473,163],[593,-69],[-358,-109],[-305,90],[550,
70],[299,-132],[-606,-94],[-379,103],[397,86],
[259,-59],[-229,-40],[-48,47],[253,6],[23,-63],
[-247,-27],[-139,31],[56,26],[59,2],[5,-4],
[161,-10],[-140,-133],[-1209,-85],[-1211,373],
[1756,538],[2878,-177],[-850,-635],[-2179,226],
[2304,510],[2388,-753],[-4774,-805],[-4082,1124],
[5662,1267],[5514,-1017],[-4610,-1202],[-3615,948
],[5900,692],[2031,-1597],[-8452,-818],[-3612,
1851],[7859,1085],[3697,-1380],[-5889,-653],[
-600,1297],[6786,107],[-249,-1695],[-7544,-280],
[-986,1466],[5467,391],[837,-908],[-2989,-100],
[723,551],[2561,-244],[-1212,-659],[-2778,-9],
[-456,448],[966,174],[489,-52],[-65,-34],[-5,
-11],[-180,-3],[-123,74],[500,111],[760,-88],
[-266,-220],[-968,14],[310,187],[786,-117],[
-1042,-237],[-1202,278],[1593,384],[1864,-316],
[-1492,-484],[-1833,254],[1387,356],[1129,-368],
[-2293,-281],[-1227,547],[2702,408],[1611,-505],
[-2067,-385],[-1063,394],[1922,162],[242,-482],
[-2474,-114],[-416,535],[2192,183],[585,-383],
[-1387,-135],[-175,225],[838,-2],[-312,-206],
[-955,42],[14,202],[692,62],[243,-67],[-95,
-43],[-61,4],[-109,-18],[-277,71],[417,193],
[1641,9],[471,-454],[-2051,-312],[-1247,380],
[1806,205],[143,-519],[-3322,-15],[427,970],
[5242,86],[298,-1282],[-5767,-318],[-698,1124],
[4563,100],[-1339,-1083],[-5396,382],[2420,1471],
[6947,-284],[-1416,-1506],[-5769,78],[1482,1071],
[3845,-451],[-3414,-958],[-4406,735],[3400,1128],
[4478,-481],[-1974,-898],[-2912,270],[1391,447],
[1103,-325],[-2055,-243],[-1085,435],[1514,373],
[1443,-130],[-77,-203],[-415,-43],[-55,23],
[-139,-13],[-198,101],[733,189],[1776,-111],
[-179,-562],[-2697,-208],[-820,537],[2274,113],
[-570,-607],[-3613,220],[1870,1091],[5814,-281],
[-1545,-1511],[-6770,49],[848,1368],[5154,-202],
[-2954,-1162],[-5319,827],[4762,1529],[7179,-834],
[-3753,-1659],[-6234,506],[3130,1155],[3584,-791],
[-5058,-867],[-3742,1171],[5362,1069],[4228,-888],
[-3471,-914],[-2846,525],[2169,433],[777,-453],
[-2571,-139],[-547,587],[2217,323],[1412,-264],[
-408,-238],[-540,-21],[-31,34],[-22,3],[40,18],
[177,5],[112,-60],[-285,-62],[-341,41],[191,
73],[222,-47],[-384,-49],[-183,120],[721,73],
[349,-178],[-871,-127],[-530,168],[711,117],[276,
-149],[-840,-40],[-15,225],[1170,49],[186,-263],
[-1086,-87],[-243,199],[781,34],[-141,-172],[
-858,39],[265,218],[953,-14],[-76,-190],[-694,
-13],[30,116],[347,-10],[-181,-64],[-276,52],
[225,78],[341,-14],[11,-56],[-125,-17],[-47,
8],[8,3],[-3,35],[533,30],[592,-191],[-1140,
-380],[-2405,117],[78,619],[2627,90],[-401,-516],
[-2474,229],[2345,765],[4111,-582],[-3408,-1235],
[-6043,569],[2740,1465],[5600,-405],[-2887,-1088],
[-3968,847],[5653,1042],[4937,-1281],[-6315,-1437],
[-5808,1072],[4546,1267],[3788,-875],[-4867,-652],
[-1896,1253],[6525,639],[2659,-1332],[-5424,-777],
[-2648,896],[3337,526],[1021,-541],[-2295,-90],
[365,589],[2763,34],[599,-526],[-1633,-262],[
-856,121],[113,116],[151,0],[-13,7],[114,17],
[215,-31],[-116,-107],[-638,-25],[-250,137],
[592,80],[133,-120],[-677,-5],[223,216],[1229,
-38],[-277,-343],[-1708,-8],[2,382],[1539,40],
[-193,-300],[-1322,92],[897,352],[1746,-171],
[-882,-457],[-1893,107],[517,381],[1322,-102],
[-869,-250],[-1011,229],[1292,286],[1240,-233],
[-967,-295],[-1055,138],[568,195],[508,-95],
[-505,-72],[-181,137],[667,69],[383,-104],[
-290,-97],[-266,9],[-25,29],[40,3],[87,25],
[374,-49],[-175,-207],[-1630,-109],[-1007,399],
[1684,413],[1696,-288],[-1586,-301],[-769,482],
[3317,214],[733,-940],[-5143,-395],[-1826,1188],
[5395,641],[2026,-1021],[-4474,-367],[29,1105],
[5871,-34],[-654,-1528],[-7297,-148],[-363,1503],
[5878,268],[-215,-1104],[-4413,194],[2253,1108],
[5291,-426],[-2055,-1264],[-5061,186],[907,965],
[3250,-81],[-869,-508],[-1515,239],[1757,356],
[1607,-343],[-1066,-440],[-1602,39],[-151,197],[
374,65],[83,-20],[88,-12],[-194,-82],[-821,-4],
[-449,302],[1592,292],[1712,-243],[-1067,-411],
[-1262,237],[1848,260],[942,-604],[-3705,-358],
[-1727,934],[4701,642],[2782,-929],[-3994,-659],
[-1669,794],[4337,256],[56,-1173],[-6119,-221],
[-857,1428],[6044,435],[1348,-1113],[-4403,-236],
[574,917],[4469,-189],[-1526,-1159],[-5160,113],
[543,1066],[3937,54],[-158,-676],[-2087,42],
[869,356],[1473,-266],[-1345,-406],[-1830,114],
[92,340],[814,81],[291,-60],[-78,-23],[28,-18],
[-260,-34],[-455,69],[307,224],[1293,33],[404,
-290],[-1240,-126],[-115,254],[1423,-30],[-687,
-444],[-2481,134],[874,698],[3415,-58],[-371,-772
],[-3025,5],[753,599],[2558,-277],[-2159,-681],
[-3371,430],[2181,883],[3593,-297],[-1413,-734],
[-2414,289],[2033,461],[1797,-530],[-2835,-520],
[-2231,525],[2155,539],[1895,-322],[-1296,-348],
[-827,216],[1098,114],[204,-292],[-1347,-113],
[-677,219],[603,173],[488,-22],[21,-54],[-65,
-4],[22,-38],[-589,-50],[-811,193],[1025,465],
[2859,-31],[449,-684],[-2879,-216],[1,567],[
2939,-150],[-2035,-924],[-5122,467],[2840,1491],
[7356,-364],[-1815,-1721],[-6694,184],[2267,1297],
[5144,-750],[-5531,-1368],[-6694,1193],[5935,1846],
[7565,-911],[-3992,-1585],[-5039,770],[4892,909],
[3185,-1285],[-6869,-979],[-4211,1340],[5470,1095],
[3837,-856],[-3293,-729],[-1661,534],[2489,196],
[72,-659],[-3145,-158],[-1171,557],[1632,368],
[1111,-90],[-10,-132],[-167,-8]])
]> where w := K.1 where K := ext<K|Polynomial(K,[20,1,1])> where K
is RationalField();

return _LR;
