//Standard generators of L3(8) are a, b where a has order 2,
//b has order 3 and ab has order 21.
_LR := rec < recformat< F: GrpFP, AI: SeqEnum, G: GrpMat > |
      F := FreeGroup(2) >;
_LR`AI:=[ [a, b^-1], //duality
     [a, b*a*b*a*b^-1*a*b^-1*a*b^-1*a*b^-1*a*b^-1*a*b^-1*a*b*a*b^-1]]//galois
              where a is (_LR`F).1 where b is (_LR`F).2;
//6 constituents
_LR`G :=
/*
Original group: c9Group("l38p")
Direct induction from degree 6
Schur index: 1
Character: ( 438, 54, 6, 6, -10, -10, -10, -10, -10, -10, 4, 4, 4, -3, -3, 6, 6,
6, -2, -2, -2, -2, -2, -2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 
-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 )
*/

MatrixGroup<438,IntegerRing() |
Matrix(SparseMatrix(438,438,\[
1,11,1,1,12,1,6,7,-1,8,-1,9,-1,10,-1,11,-1,12,-1,1,
7,1,1,8,1,1,9,1,1,4,1,1,5,1,1,6,1,6,1,-1,2,-1,
3,-1,4,-1,5,-1,6,-1,1,1,1,1,2,1,1,25,1,1,26,1,1,
27,1,1,28,1,1,29,1,1,30,1,1,37,1,1,38,1,1,39,1,1,
40,1,1,41,1,1,42,1,1,13,1,1,14,1,1,15,1,1,16,1,1,
17,1,1,18,1,6,55,-1,56,-1,57,-1,58,-1,59,-1,60,-1,1,
55,1,1,56,1,1,57,1,1,58,1,1,59,1,1,19,1,1,20,1,1,
21,1,1,22,1,1,23,1,1,24,1,1,67,1,1,68,1,1,69,1,1,
70,1,1,71,1,1,72,1,1,73,1,1,74,1,1,75,1,1,76,1,1,
77,1,1,78,1,1,32,1,1,33,1,1,34,1,1,35,1,1,36,1,6,
31,-1,32,-1,33,-1,34,-1,35,-1,36,-1,1,91,1,1,92,1,1,
93,1,1,94,1,1,95,1,1,96,1,1,43,1,1,44,1,1,45,1,1,
46,1,1,47,1,1,48,1,1,49,1,1,50,1,1,51,1,1,52,1,1,
53,1,1,54,1,1,85,1,1,86,1,1,87,1,1,88,1,1,89,1,1,
90,1,1,79,1,1,80,1,1,81,1,1,82,1,1,83,1,1,84,1,1,
61,1,1,62,1,1,63,1,1,64,1,1,65,1,1,66,1,1,127,1,
1,128,1,1,129,1,1,130,1,1,131,1,1,132,1,1,133,1,
1,134,1,1,135,1,1,136,1,1,137,1,1,138,1,1,109,1,
1,110,1,1,111,1,1,112,1,1,113,1,1,114,1,1,115,1,
1,116,1,1,117,1,1,118,1,1,119,1,1,120,1,1,145,1,1,
146,1,1,147,1,1,148,1,1,149,1,1,150,1,1,97,1,1,98,1,
1,99,1,1,100,1,1,101,1,1,102,1,1,103,1,1,104,1,1,
105,1,1,106,1,1,107,1,1,108,1,1,163,1,1,164,1,1,
165,1,1,166,1,1,167,1,1,168,1,1,121,1,1,122,1,1,
123,1,1,124,1,1,125,1,1,126,1,1,151,1,1,152,1,1,
153,1,1,154,1,1,155,1,1,156,1,6,175,-1,176,-1,177,-1,
178,-1,179,-1,180,-1,1,175,1,1,176,1,1,177,1,1,178,1,
1,179,1,1,139,1,1,140,1,1,141,1,1,142,1,1,143,1,
1,144,1,1,187,1,1,188,1,1,189,1,1,190,1,1,191,1,
1,192,1,1,158,1,1,159,1,1,160,1,1,161,1,1,162,1,
6,157,-1,158,-1,159,-1,160,-1,161,-1,162,-1,1,209,1,
1,210,1,6,205,-1,206,-1,207,-1,208,-1,209,-1,210,-1,
1,205,1,1,206,1,1,207,1,1,169,1,1,170,1,1,171,1,
1,172,1,1,173,1,1,174,1,1,221,1,1,222,1,6,217,-1,
218,-1,219,-1,220,-1,221,-1,222,-1,1,217,1,1,218,1,
1,219,1,1,199,1,1,200,1,1,201,1,1,202,1,1,203,1,1,
204,1,1,184,1,1,185,1,1,186,1,6,181,-1,182,-1,183,-1,
184,-1,185,-1,186,-1,1,181,1,1,182,1,1,235,1,1,236,1,
1,237,1,1,238,1,1,239,1,1,240,1,1,196,1,1,197,1,
1,198,1,6,193,-1,194,-1,195,-1,196,-1,197,-1,198,-1,
1,193,1,1,194,1,1,223,1,1,224,1,1,225,1,1,226,1,
1,227,1,1,228,1,1,247,1,1,248,1,1,249,1,1,250,1,
1,251,1,1,252,1,1,211,1,1,212,1,1,213,1,1,214,1,
1,215,1,1,216,1,1,265,1,1,266,1,1,267,1,1,268,1,
1,269,1,1,270,1,1,229,1,1,230,1,1,231,1,1,232,1,
1,233,1,1,234,1,1,283,1,1,284,1,1,285,1,1,286,1,
1,287,1,1,288,1,1,259,1,1,260,1,1,261,1,1,262,1,
1,263,1,1,264,1,1,241,1,1,242,1,1,243,1,1,244,1,1,
245,1,1,246,1,1,305,1,1,306,1,6,301,-1,302,-1,303,-1,
304,-1,305,-1,306,-1,1,301,1,1,302,1,1,303,1,1,307,1,
1,308,1,1,309,1,1,310,1,1,311,1,1,312,1,1,253,1,
1,254,1,1,255,1,1,256,1,1,257,1,1,258,1,1,319,1,
1,320,1,1,321,1,1,322,1,1,323,1,1,324,1,1,330,1,
6,325,-1,326,-1,327,-1,328,-1,329,-1,330,-1,1,325,1,
1,326,1,1,327,1,1,328,1,1,274,1,1,275,1,1,276,1,
6,271,-1,272,-1,273,-1,274,-1,275,-1,276,-1,1,271,1,
1,272,1,1,277,1,1,278,1,1,279,1,1,280,1,1,281,1,1,
282,1,1,343,1,1,344,1,1,345,1,1,346,1,1,347,1,1,348,1,
1,289,1,1,290,1,1,291,1,1,292,1,1,293,1,1,294,1,1,
297,1,1,298,1,1,299,1,1,300,1,6,295,-1,296,-1,297,-1,
298,-1,299,-1,300,-1,1,295,1,6,367,-1,368,-1,369,-1,
370,-1,371,-1,372,-1,1,367,1,1,368,1,1,369,1,1,370,1,
1,371,1,1,373,1,1,374,1,1,375,1,1,376,1,1,377,1,1,
378,1,1,313,1,1,314,1,1,315,1,1,316,1,1,317,1,1,318,1,
1,385,1,1,386,1,1,387,1,1,388,1,1,389,1,1,390,1,1,
355,1,1,356,1,1,357,1,1,358,1,1,359,1,1,360,1,1,361,1,
1,362,1,1,363,1,1,364,1,1,365,1,1,366,1,1,332,1,1,
333,1,1,334,1,1,335,1,1,336,1,6,331,-1,332,-1,333,-1,
334,-1,335,-1,336,-1,1,337,1,1,338,1,1,339,1,1,340,1,
1,341,1,1,342,1,1,409,1,1,410,1,1,411,1,1,412,1,
1,413,1,1,414,1,1,349,1,1,350,1,1,351,1,1,352,1,
1,353,1,1,354,1,1,421,1,1,422,1,1,423,1,1,424,1,
1,425,1,1,426,1,1,427,1,1,428,1,1,429,1,1,430,1,
1,431,1,1,432,1,1,415,1,1,416,1,1,417,1,1,418,1,
1,419,1,1,420,1,1,379,1,1,380,1,1,381,1,1,382,1,
1,383,1,1,384,1,1,403,1,1,404,1,1,405,1,1,406,1,1,
407,1,1,408,1,1,391,1,1,392,1,1,393,1,1,394,1,1,395,1,
1,396,1,1,397,1,1,398,1,1,399,1,1,400,1,1,401,1,1,
402,1,1,433,1,1,434,1,1,435,1,1,436,1,1,437,1,1,438,1
])),Matrix(SparseMatrix(438,438,\[
1,13,1,1,14,1,1,15,1,1,16,1,1,17,1,1,18,1,1,19,1,1,
20,1,1,21,1,1,22,1,1,23,1,1,24,1,1,31,1,1,32,1,1,
33,1,1,34,1,1,35,1,1,36,1,1,43,1,1,44,1,1,45,1,1,
46,1,1,47,1,1,48,1,1,49,1,1,50,1,1,51,1,1,52,1,1,
53,1,1,54,1,1,1,1,1,2,1,1,3,1,1,4,1,1,5,1,1,6,1,
1,61,1,1,62,1,1,63,1,1,64,1,1,65,1,1,66,1,1,7,1,
1,8,1,1,9,1,1,10,1,1,11,1,1,12,1,1,79,1,1,80,1,
1,81,1,1,82,1,1,83,1,1,84,1,1,85,1,1,86,1,1,87,1,
1,88,1,1,89,1,1,90,1,1,97,1,1,98,1,1,99,1,1,100,1,
1,101,1,1,102,1,1,103,1,1,104,1,1,105,1,1,106,1,1,
107,1,1,108,1,1,109,1,1,110,1,1,111,1,1,112,1,1,113,1,
1,114,1,1,25,1,1,26,1,1,27,1,1,28,1,1,29,1,1,30,1,
1,115,1,1,116,1,1,117,1,1,118,1,1,119,1,1,120,1,1,
122,1,1,123,1,1,124,1,1,125,1,1,126,1,6,121,-1,122,-1,
123,-1,124,-1,125,-1,126,-1,1,37,1,1,38,1,1,39,1,1,
40,1,1,41,1,1,42,1,1,139,1,1,140,1,1,141,1,1,142,1,
1,143,1,1,144,1,1,133,1,1,134,1,1,135,1,1,136,1,1,
137,1,1,138,1,1,55,1,1,56,1,1,57,1,1,58,1,1,59,1,
1,60,1,6,151,-1,152,-1,153,-1,154,-1,155,-1,156,-1,
1,151,1,1,152,1,1,153,1,1,154,1,1,155,1,1,158,1,1,
159,1,1,160,1,1,161,1,1,162,1,6,157,-1,158,-1,159,-1,
160,-1,161,-1,162,-1,1,73,1,1,74,1,1,75,1,1,76,1,1,
77,1,1,78,1,1,67,1,1,68,1,1,69,1,1,70,1,1,71,1,1,
72,1,1,169,1,1,170,1,1,171,1,1,172,1,1,173,1,1,174,1,
1,91,1,1,92,1,1,93,1,1,94,1,1,95,1,1,96,1,1,181,1,
1,182,1,1,183,1,1,184,1,1,185,1,1,186,1,1,187,1,1,
188,1,1,189,1,1,190,1,1,191,1,1,192,1,1,193,1,1,194,1,
1,195,1,1,196,1,1,197,1,1,198,1,1,199,1,1,200,1,1,
201,1,1,202,1,1,203,1,1,204,1,6,127,-1,128,-1,129,-1,
130,-1,131,-1,132,-1,1,127,1,1,128,1,1,129,1,1,130,1,
1,131,1,1,211,1,1,212,1,1,213,1,1,214,1,1,215,1,1,
216,1,1,145,1,1,146,1,1,147,1,1,148,1,1,149,1,1,150,1,
1,223,1,1,224,1,1,225,1,1,226,1,1,227,1,1,228,1,1,
231,1,1,232,1,1,233,1,1,234,1,6,229,-1,230,-1,231,-1,
232,-1,233,-1,234,-1,1,229,1,1,163,1,1,164,1,1,165,1,
1,166,1,1,167,1,1,168,1,1,241,1,1,242,1,1,243,1,
1,244,1,1,245,1,1,246,1,1,175,1,1,176,1,1,177,1,
1,178,1,1,179,1,1,180,1,1,253,1,1,254,1,1,255,1,1,
256,1,1,257,1,1,258,1,1,259,1,1,260,1,1,261,1,1,262,1,
1,263,1,1,264,1,1,271,1,1,272,1,1,273,1,1,274,1,1,
275,1,1,276,1,1,281,1,1,282,1,6,277,-1,278,-1,279,-1,
280,-1,281,-1,282,-1,1,277,1,1,278,1,1,279,1,1,210,1,
6,205,-1,206,-1,207,-1,208,-1,209,-1,210,-1,1,205,1,
1,206,1,1,207,1,1,208,1,1,289,1,1,290,1,1,291,1,
1,292,1,1,293,1,1,294,1,1,297,1,1,298,1,1,299,1,
1,300,1,6,295,-1,296,-1,297,-1,298,-1,299,-1,300,-1,
1,295,1,1,217,1,1,218,1,1,219,1,1,220,1,1,221,1,1,
222,1,1,310,1,1,311,1,1,312,1,6,307,-1,308,-1,309,-1,
310,-1,311,-1,312,-1,1,307,1,1,308,1,6,313,-1,314,-1,
315,-1,316,-1,317,-1,318,-1,1,313,1,1,314,1,1,315,1,
1,316,1,1,317,1,1,235,1,1,236,1,1,237,1,1,238,1,
1,239,1,1,240,1,1,331,1,1,332,1,1,333,1,1,334,1,
1,335,1,1,336,1,1,338,1,1,339,1,1,340,1,1,341,1,
1,342,1,6,337,-1,338,-1,339,-1,340,-1,341,-1,342,-1,
1,247,1,1,248,1,1,249,1,1,250,1,1,251,1,1,252,1,
1,349,1,1,350,1,1,351,1,1,352,1,1,353,1,1,354,1,
1,355,1,1,356,1,1,357,1,1,358,1,1,359,1,1,360,1,1,
361,1,1,362,1,1,363,1,1,364,1,1,365,1,1,366,1,1,270,1,
6,265,-1,266,-1,267,-1,268,-1,269,-1,270,-1,1,265,1,1,
266,1,1,267,1,1,268,1,1,383,1,1,384,1,6,379,-1,380,-1,
381,-1,382,-1,383,-1,384,-1,1,379,1,1,380,1,1,381,1,1,
369,1,1,370,1,1,371,1,1,372,1,6,367,-1,368,-1,369,-1,
370,-1,371,-1,372,-1,1,367,1,1,284,1,1,285,1,1,286,1,
1,287,1,1,288,1,6,283,-1,284,-1,285,-1,286,-1,287,-1,
288,-1,1,391,1,1,392,1,1,393,1,1,394,1,1,395,1,
1,396,1,1,399,1,1,400,1,1,401,1,1,402,1,6,397,-1,
398,-1,399,-1,400,-1,401,-1,402,-1,1,397,1,6,403,-1,
404,-1,405,-1,406,-1,407,-1,408,-1,1,403,1,1,404,1,1,
405,1,1,406,1,1,407,1,1,414,1,6,409,-1,410,-1,411,-1,
412,-1,413,-1,414,-1,1,409,1,1,410,1,1,411,1,1,412,1,1,
303,1,1,304,1,1,305,1,1,306,1,6,301,-1,302,-1,303,-1,
304,-1,305,-1,306,-1,1,301,1,1,415,1,1,416,1,1,417,1,
1,418,1,1,419,1,1,420,1,1,319,1,1,320,1,1,321,1,1,
322,1,1,323,1,1,324,1,1,330,1,6,325,-1,326,-1,327,-1,
328,-1,329,-1,330,-1,1,325,1,1,326,1,1,327,1,1,328,1,
6,343,-1,344,-1,345,-1,346,-1,347,-1,348,-1,1,343,1,
1,344,1,1,345,1,1,346,1,1,347,1,1,435,1,1,436,1,1,
437,1,1,438,1,6,433,-1,434,-1,435,-1,436,-1,437,-1,
438,-1,1,433,1,1,421,1,1,422,1,1,423,1,1,424,1,1,
425,1,1,426,1,1,385,1,1,386,1,1,387,1,1,388,1,1,389,1,
1,390,1,1,427,1,1,428,1,1,429,1,1,430,1,1,431,1,1,
432,1,1,373,1,1,374,1,1,375,1,1,376,1,1,377,1,1,378,1
]))>;

return _LR;
