//standard generators for PSL(2,25), a order 2, b order 3, order(ab)=12.
//standard generators for SL(2,25), a order 4, b order 3, order(ab)=24,
//                                           order(abab^-1ab) = 13.
_LR := rec < recformat< F: GrpFP, AI: SeqEnum, G: GrpMat > |
      F := FreeGroup(2) >;
_LR`AI := [ [a^-1, b^-1], //PSL(2,25).2_1 = PGL(2,25)
            [a, b^-1*a*b*a*b^-1*a*b*a*b^-1*a^-1],//PSL(2,25).2_1 = PSigmaL(2,25)
            [a^-1, a*b*a*b^-1*a*b*a*b^-1*a*b] ]
             where a is (_LR`F).1 where b is (_LR`F).2;
//six constituents (each twice) fixed by AI[1], interchanged in pairs by AI[2]
_LR`G :=
/*
Original group: c9Group("sl225p")
From DB /nb/reps/l2/2l225/d24.2l225.deg12.si2.M
Schur index: 2
Character: ( 24, -24, 0, 0, -1, -1, 0, 0, 0, 1, 1, 0, 0, -zeta(13)_13^9 - 
zeta(13)_13^4, -zeta(13)_13^8 - zeta(13)_13^5, -zeta(13)_13^10 - zeta(13)_13^3, 
-zeta(13)_13^11 - zeta(13)_13^2, -zeta(13)_13^7 - zeta(13)_13^6, zeta(13)_13^11 
+ zeta(13)_13^10 + zeta(13)_13^9 + zeta(13)_13^8 + zeta(13)_13^7 + zeta(13)_13^6
+ zeta(13)_13^5 + zeta(13)_13^4 + zeta(13)_13^3 + zeta(13)_13^2 + 1, 0, 0, 0, 0,
zeta(13)_13^10 + zeta(13)_13^3, zeta(13)_13^7 + zeta(13)_13^6, zeta(13)_13^11 + 
zeta(13)_13^2, -zeta(13)_13^11 - zeta(13)_13^10 - zeta(13)_13^9 - zeta(13)_13^8 
- zeta(13)_13^7 - zeta(13)_13^6 - zeta(13)_13^5 - zeta(13)_13^4 - zeta(13)_13^3 
- zeta(13)_13^2 - 1, zeta(13)_13^8 + zeta(13)_13^5, zeta(13)_13^9 + 
zeta(13)_13^4 )
*/
MatrixGroup<24, K | [
Matrix(K,24,24,
[[-109/100,77/50,-259/50,-108/25,-11/2,-55/4,-66/25,-553/50,
-7/10,-69/20,-2/25,-37/100],[22/25,-313/100,107/20,-37/4,
353/50,-383/50,17/4,-16/5,59/50,-73/100,3/25,-7/100],[43/50,
239/100,102/25,228/25,519/100,1081/100,87/50,263/50,1/50,
113/100,-1/25,9/100],[147/100,-223/25,-8/25,-1457/100,-166/25,
-467/100,-481/100,147/50,-51/50,179/100,-1/20,6/25],[-13/25,
17/2,-247/100,2419/100,122/25,2381/100,337/50,1217/100,249/100,
313/100,29/100,31/100],[-43/20,1/50,-861/100,-123/25,-206/25,
-577/50,-113/100,-831/100,73/100,-121/50,4/25,-1/4],[29/50,
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-41/100,-4/25,3/100],[-52/25,-191/100,-1907/100,-251/100,
-2037/50,-233/50,-3081/100,-97/25,-471/50,-123/100,-1,-13/100],
[33/20,423/50,607/50,926/25,703/50,5343/100,123/25,1621/50,
19/50,869/100,-1/25,17/20],[-101/50,-42/25,-236/25,-137/10,-8,
-1233/50,-81/50,-17,1/5,-249/50,3/50,-13/25],[46/25,-14/25,
161/10,-19/50,752/25,233/50,107/5,223/50,317/50,69/50,33/50,
7/50],[29/50,126/25,227/50,397/25,198/25,71/5,231/50,227/50,
53/50,2/5,2/25,-1/50],[401/9275,-25857/9275,-1392/1325,
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488/9275,-50/371],[22/25,-313/100,107/20,-37/4,353/50,-383/50,
17/4,-16/5,59/50,-73/100,3/25,-7/100],[43/50,239/100,102/25,
228/25,519/100,1081/100,87/50,263/50,1/50,113/100,-1/25,9/100],
[-109/100,77/50,-259/50,-108/25,-11/2,-55/4,-66/25,-553/50,
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33/20,423/50,607/50,926/25,703/50,5343/100,123/25,1621/50,19/50,
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752/25,233/50,107/5,223/50,317/50,69/50,33/50,7/50],[29/50,
126/25,227/50,397/25,198/25,71/5,231/50,227/50,53/50,2/5,2/25,
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313/100,29/100,31/100],[-52/25,-191/100,-1907/100,-251/100,
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369/50,37/100,73/100],[-137/100,47/25,-359/100,447/100,-67/20,
479/100,-247/100,143/50,-1,87/100,-7/50,1/10],[52/25,-19/5,
507/50,-266/25,651/50,-184/25,577/100,-97/100,91/100,21/50,
3/100,9/100],[29/100,-57/25,-9/20,-1143/100,-617/100,-1773/100,
-123/20,-1109/100,-211/100,-299/100,-6/25,-29/100],[3/50,
131/50,59/25,593/50,333/50,462/25,269/50,589/50,42/25,81/25,
9/50,8/25],[-7/10,151/50,-151/50,407/50,-87/25,19/5,-29/25,
-69/50,-1/25,-11/10,1/50,-4/25],[6/25,-36/25,43/50,-12/5,
91/50,-99/50,47/25,-6/5,19/25,-11/25,1/10,-3/50],[372/1855,
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543/1855,-11742/9275,860/371,-20494/9275,4489/1855,321/265,
1028/1855,3634/1325,-18/265,416/371,-43/1855,1266/9275],[
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[3992/9275,-58/371,986/1855,4357/1855,-26366/9275,2383/371,
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577/100,-1499/100,53/100,-29/20],[-107/100,927/100,-2349/100,
772/25,-171/4,3981/100,-1371/50,1137/50,-73/10,583/100,-69/100,
11/20],[3/100,63/20,1889/100,-109/25,1003/25,-1979/100,1381/50,
-397/25,761/100,-477/100,73/100,-49/100],[-51/100,573/100,
-51/2,1459/50,-4697/100,3743/100,-156/5,1929/100,-881/100,
429/100,-89/100,17/50],[13/50,-71/50,459/25,167/50,889/25,
223/25,622/25,311/50,369/50,44/25,39/50,9/50],[-4/5,-291/50,
-483/25,-556/25,-2069/50,-134/5,-1443/50,-721/50,-201/25,-18/5,
-39/50,-17/50],[-24/25,-283/50,134/25,-53/10,368/25,-3/25,
539/50,7/5,153/50,27/50,3/10,3/50],[-88/175,116/35,533/175,
286/35,203/25,57/7,949/175,136/35,34/25,32/35,4/35,3/35],[
-17/175,-109/35,-6/25,-361/35,-817/175,-477/35,-876/175,-291/35,
-311/175,-16/7,-36/175,-8/35],[34/35,-73/35,684/175,-166/35,
621/175,-29/35,107/175,15/7,-37/175,38/35,-9/175,1/7],[
-44/175,8/7,-18/35,1012/175,-54/25,1613/175,-82/35,1076/175,
-144/175,314/175,-16/175,33/175],[-88/175,-69/175,-799/175,
-531/175,-1382/175,-1082/175,-977/175,-743/175,-43/25,-206/175,
-33/175,-4/35],[21/25,-481/175,934/175,-1451/175,297/35,
-1256/175,992/175,-393/175,57/35,-33/175,29/175,2/175],[1/5,
-52/35,-51/35,-1016/175,-191/35,-1224/175,-157/35,-99/25,-48/35,
-187/175,-1/7,-19/175],[5/7,472/175,20/7,1543/175,22/7,
1901/175,3/5,1059/175,-8/35,268/175,-2/35,1/7],[-12/35,
-362/175,-101/35,-2362/175,-27/5,-546/25,-21/5,-2446/175,-10/7,
-671/175,-6/35,-66/175],[-166/175,-164/175,-174/25,-794/175,
-2064/175,-1469/175,-1439/175,-997/175,-432/175,-277/175,-46/175,
-27/175],[-6/175,-152/35,13/175,-2242/175,11/35,-1938/175,
169/175,-621/175,18/35,-59/175,13/175,2/175],[117/175,514/175,
152/35,2276/175,112/25,3362/175,11/7,2118/175,6/25,591/175,
3/175,12/35],[-143/100,-99/20,-1729/100,-649/25,-883/25,
-3809/100,-1251/50,-572/25,-721/100,-607/100,-73/100,-59/100],[
-173/100,-163/100,-611/100,262/25,-53/20,2351/100,51/50,807/50,
7/10,453/100,9/100,9/20],[-49/100,183/100,51/10,1109/50,
1137/100,3673/100,42/5,2239/100,261/100,579/100,29/100,27/50],[
61/25,157/20,487/25,1572/25,157/4,2623/25,2789/100,6649/100,
81/10,903/50,83/100,177/100],[108/25,-541/100,147/5,-5359/100,
2067/50,-2232/25,93/4,-1398/25,577/100,-1499/100,53/100,-29/20],
[79/100,-939/100,108/25,-7719/100,283/50,-2931/25,83/50,
-6847/100,-27/100,-861/50,-11/100,-157/100],[-51/100,573/100,
-51/2,1459/50,-4697/100,3743/100,-156/5,1929/100,-881/100,
429/100,-89/100,17/50],[-107/100,927/100,-2349/100,772/25,
-171/4,3981/100,-1371/50,1137/50,-73/10,583/100,-69/100,11/20],
[3/100,63/20,1889/100,-109/25,1003/25,-1979/100,1381/50,-397/25,
761/100,-477/100,73/100,-49/100],[-4/5,-291/50,-483/25,-556/25,
-2069/50,-134/5,-1443/50,-721/50,-201/25,-18/5,-39/50,-17/50],[
-24/25,-283/50,134/25,-53/10,368/25,-3/25,539/50,7/5,153/50,
27/50,3/10,3/50],[13/50,-71/50,459/25,167/50,889/25,223/25,
622/25,311/50,369/50,44/25,39/50,9/50],[-17/175,-109/35,-6/25,
-361/35,-817/175,-477/35,-876/175,-291/35,-311/175,-16/7,-36/175,
-8/35],[34/35,-73/35,684/175,-166/35,621/175,-29/35,107/175,
15/7,-37/175,38/35,-9/175,1/7],[-88/175,116/35,533/175,286/35,
203/25,57/7,949/175,136/35,34/25,32/35,4/35,3/35],[-88/175,
-69/175,-799/175,-531/175,-1382/175,-1082/175,-977/175,-743/175,
-43/25,-206/175,-33/175,-4/35],[21/25,-481/175,934/175,
-1451/175,297/35,-1256/175,992/175,-393/175,57/35,-33/175,29/175,
2/175],[-44/175,8/7,-18/35,1012/175,-54/25,1613/175,-82/35,
1076/175,-144/175,314/175,-16/175,33/175],[5/7,472/175,20/7,
1543/175,22/7,1901/175,3/5,1059/175,-8/35,268/175,-2/35,1/7],[
-12/35,-362/175,-101/35,-2362/175,-27/5,-546/25,-21/5,-2446/175,
-10/7,-671/175,-6/35,-66/175],[1/5,-52/35,-51/35,-1016/175,
-191/35,-1224/175,-157/35,-99/25,-48/35,-187/175,-1/7,-19/175],
[-6/175,-152/35,13/175,-2242/175,11/35,-1938/175,169/175,
-621/175,18/35,-59/175,13/175,2/175],[117/175,514/175,152/35,
2276/175,112/25,3362/175,11/7,2118/175,6/25,591/175,3/175,12/35
],[-166/175,-164/175,-174/25,-794/175,-2064/175,-1469/175,
-1439/175,-997/175,-432/175,-277/175,-46/175,-27/175]]),
Matrix(SparseMatrix(K,24,24,[
<1,3,1/4*(-2*w^11-24*w^9-108*w^7-220*w^5-186*w^3-40*w-3)>,<1,
6,1/4*(3*w^11+36*w^9+162*w^7+330*w^5+279*w^3+60*w+11)>,<1,7,
1/4*(2*w^11+24*w^9+108*w^7+220*w^5+186*w^3+40*w-9)>,<1,12,
1/2*(-w^11-12*w^9-54*w^7-110*w^5-93*w^3-20*w+3)>,<2,1,
1/4*(3*w^11+36*w^9+162*w^7+330*w^5+279*w^3+60*w+5)>,<2,4,
1/2*(-2*w^11-24*w^9-108*w^7-220*w^5-186*w^3-40*w-9)>,<2,9,
1/4*(-3*w^11-36*w^9-162*w^7-330*w^5-279*w^3-60*w+11)>,<2,10,
w^11+12*w^9+54*w^7+110*w^5+93*w^3+20*w-1>,<3,2,1/4*(3*w^11+
36*w^9+162*w^7+330*w^5+279*w^3+60*w+5)>,<3,5,1/2*(-2*w^11-
24*w^9-108*w^7-220*w^5-186*w^3-40*w-9)>,<3,8,1/4*(-3*w^11-
36*w^9-162*w^7-330*w^5-279*w^3-60*w+11)>,<3,11,w^11+12*w^9+
54*w^7+110*w^5+93*w^3+20*w-1>,<4,3,1/2>,<4,6,1/2*(w^11+
12*w^9+54*w^7+110*w^5+93*w^3+20*w-1)>,<4,7,-3/2>,<4,12,1>,
<5,1,1/4*(w^11+12*w^9+54*w^7+110*w^5+93*w^3+20*w)>,<5,4,
1/4*(-3*w^11-36*w^9-162*w^7-330*w^5-279*w^3-60*w-5)>,<5,9,
1/4*(-w^11-12*w^9-54*w^7-110*w^5-93*w^3-20*w+8)>,<5,10,
1/2*(w^11+12*w^9+54*w^7+110*w^5+93*w^3+20*w-3)>,<6,2,
1/4*(w^11+12*w^9+54*w^7+110*w^5+93*w^3+20*w)>,<6,5,1/4*(-3*w^11
-36*w^9-162*w^7-330*w^5-279*w^3-60*w-5)>,<6,8,1/4*(-w^11-
12*w^9-54*w^7-110*w^5-93*w^3-20*w+8)>,<6,11,1/2*(w^11+12*w^9
+54*w^7+110*w^5+93*w^3+20*w-3)>,<7,5,1>,<7,11,-1>,<8,4,
1>,<8,10,-1>,<9,3,7/4>,<9,6,1/4*(3*w^11+36*w^9+162*w^7+
330*w^5+279*w^3+60*w-17)>,<9,7,1/4*(-4*w^11-48*w^9-216*w^7-
440*w^5-372*w^3-80*w-7)>,<9,12,1/2*(w^11+12*w^9+54*w^7+
110*w^5+93*w^3+20*w+5)>,<10,3,1/4*(w^11+12*w^9+54*w^7+
110*w^5+93*w^3+20*w+13)>,<10,6,1/2*(w^11+12*w^9+54*w^7+
110*w^5+93*w^3+20*w-12)>,<10,7,1/4*(-5*w^11-60*w^9-270*w^7-
550*w^5-465*w^3-100*w-1)>,<10,12,w^11+12*w^9+54*w^7+110*w^5+
93*w^3+20*w+2>,<11,1,-1>,<11,4,1>,<11,10,-1>,<12,2,-1>,
<12,5,1>,<12,11,-1>,<13,15,1/7*(w^11+12*w^9+54*w^7+110*w^5+
93*w^3+20*w+5)>,<13,18,1/7*(-3*w^11-36*w^9-162*w^7-330*w^5-
279*w^3-60*w+4)>,<13,20,1/7*(w^11+12*w^9+54*w^7+110*w^5+
93*w^3+20*w-1)>,<13,23,1/7*(-3*w^11-36*w^9-162*w^7-330*w^5-
279*w^3-60*w-1)>,<14,13,1>,<15,14,1/7*(-2*w^11-24*w^9-
108*w^7-220*w^5-186*w^3-40*w+6)>,<15,17,1/7*(-2*w^11-24*w^9-
108*w^7-220*w^5-186*w^3-40*w-2)>,<15,19,1/7*(2*w^11+24*w^9+
108*w^7+220*w^5+186*w^3+40*w+12)>,<15,22,1/7*(-w^11-12*w^9-
54*w^7-110*w^5-93*w^3-20*w-4)>,<16,15,1/7*(w^11+12*w^9+
54*w^7+110*w^5+93*w^3+20*w+5)>,<16,18,1/7*(-3*w^11-36*w^9-
162*w^7-330*w^5-279*w^3-60*w+4)>,<16,20,1/7*(w^11+12*w^9+
54*w^7+110*w^5+93*w^3+20*w+6)>,<16,23,1/7*(-3*w^11-36*w^9-
162*w^7-330*w^5-279*w^3-60*w+6)>,<17,16,1>,<18,14,
1/7*(2*w^11+24*w^9+108*w^7+220*w^5+186*w^3+40*w+3)>,<18,17,
1/7*(w^11+12*w^9+54*w^7+110*w^5+93*w^3+20*w+1)>,<18,19,
1/7*(2*w^11+24*w^9+108*w^7+220*w^5+186*w^3+40*w-2)>,<18,22,
1/7*(w^11+12*w^9+54*w^7+110*w^5+93*w^3+20*w+5)>,<19,21,1>,
<20,14,1/7*(2*w^11+24*w^9+108*w^7+220*w^5+186*w^3+40*w-4)>,
<20,17,1/7*(w^11+12*w^9+54*w^7+110*w^5+93*w^3+20*w+8)>,<20,
19,1/7*(2*w^11+24*w^9+108*w^7+220*w^5+186*w^3+40*w-9)>,<20,
22,1/7*(w^11+12*w^9+54*w^7+110*w^5+93*w^3+20*w+5)>,<21,18,
1>,<21,23,1>,<22,24,1>,<23,14,1/7*(-2*w^11-24*w^9-108*w^7-
220*w^5-186*w^3-40*w-3)>,<23,17,1/7*(-w^11-12*w^9-54*w^7-
110*w^5-93*w^3-20*w-1)>,<23,19,1/7*(-2*w^11-24*w^9-108*w^7-
220*w^5-186*w^3-40*w+9)>,<23,22,1/7*(-w^11-12*w^9-54*w^7-
110*w^5-93*w^3-20*w-5)>,<24,15,1/7*(-3*w^11-36*w^9-162*w^7-
330*w^5-279*w^3-60*w-4)>,<24,18,-2>,<24,20,1/7*(-2*w^11-24*w^9
-108*w^7-220*w^5-186*w^3-40*w+2)>,<24,23,1/7*(2*w^11+24*w^9+
108*w^7+220*w^5+186*w^3+40*w-16)>]))
]> where w := K.1 where K := ext<K|Polynomial(K, [1, 0, 21, 0, 70, 0, 84, 0, 45,
0, 11, 0, 1])> where K is RationalField();

return _LR;
