/* www-ATLAS of Group Representations. 3.McL represented as 126 x 126 matrices over GF(121). */ F:=GF(121); x:=CambridgeMatrix(3,F,126,\[ 0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 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53,119,36,101,22,97,49,0,92,46,27,66,12,8,14,23,56,38,112,95,56,62,14,93,92,92,91,66,73,68,50,32,50,107,67,58,96,10,75,46,103,92,10,117,52,74,80,119,65,51,73,88,49,49,61,112,16,73,83,44,101,60,33,38,31,115,56,74,80,45,50,68,104,64,120,119,17,45,32,85,108,52,23,27,66,6,41,34,72,42,83,39,105,46,26,118,4,45,22,19,31,53,61,11,87,86,56,31,28,28,88,14,52,43,92,37,16,51,31,80,19,117,66,39,54,34, 40,13,20,33,87,22,92,65,102,89,13,47,103,39,32,89,60,60,1,27,6,64,14,78,99,19,72,64,114,77,54,8,96,36,92,34,72,43,35,10,110,63,94,63,82,19,49,43,119,99,110,54,44,43,94,95,60,41,59,113,68,36,111,57,3,119,113,60,61,102,34,38,111,44,94,13,85,46,115,87,16,38,103,9,55,36,15,19,25,55,54,98,58,95,30,55,20,111,64,101,112,94,40,52,74,76,58,68,29,30,60,55,50,108,49,63,120,112,31,62,76,54,75,41,25,103, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 36,45,40,104,35,108,30,26,58,89,109,28,81,4,48,25,48,18,73,95,92,33,63,56,116,112,94,82,115,67,103,50,46,116,118,38,46,31,116,33,59,64,85,41,36,89,96,93,71,63,91,79,114,65,68,120,111,92,106,74,30,96,54,45,35,103,69,9,64,114,120,44,79,22,84,55,58,95,81,59,45,88,97,91,33,62,5,114,63,100,71,106,117,88,100,94,51,3,91,106,15,95,102,119,17,87,35,24,67,77,115,83,75,60,51,9,27,104,21,92,17,19,64,62,53,45, 118,81,22,3,4,16,23,54,71,103,57,33,80,52,105,79,9,12,26,81,42,17,56,83,9,79,40,29,99,48,59,47,6,89,72,16,112,73,53,84,64,43,58,12,89,99,69,16,98,100,32,93,5,95,118,61,88,45,71,98,59,25,3,13,85,67,82,89,57,62,37,110,91,67,102,110,68,35,23,97,44,74,95,67,1,97,19,36,33,108,90,23,55,90,64,82,70,55,76,7,2,25,86,120,97,2,41,25,55,28,24,15,90,91,21,92,38,102,9,46,64,108,111,46,1,85, 103,61,94,77,74,63,66,61,29,77,66,4,100,102,64,60,101,114,81,86,24,58,44,52,62,33,81,102,108,43,36,33,57,28,72,116,21,85,54,43,47,41,19,39,107,75,100,26,115,17,16,28,50,72,56,9,34,70,11,17,113,85,44,13,117,38,2,7,65,41,97,99,65,79,52,18,12,21,0,46,89,30,90,48,97,8,87,104,115,77,95,40,114,119,40,64,92,44,92,88,106,120,82,9,48,106,30,1,22,100,54,91,92,99,64,78,107,104,47,116,106,2,8,52,83,62, 50,24,35,98,73,52,117,75,82,79,9,118,35,74,24,14,59,50,70,119,42,102,99,97,20,27,43,16,35,88,41,5,89,77,1,19,47,104,56,14,66,92,60,61,65,53,40,81,94,26,43,107,91,86,60,111,18,70,111,113,38,85,71,112,118,58,60,1,59,69,37,9,82,18,34,8,23,95,115,69,96,109,74,7,73,100,88,42,93,56,50,74,113,74,15,8,42,2,109,92,48,89,41,98,107,24,102,26,69,120,52,3,30,110,112,86,79,70,59,103,6,30,3,31,16,81, 3,74,118,20,63,65,26,84,11,64,46,83,75,25,33,42,0,16,92,58,98,24,45,30,44,56,101,105,9,68,16,17,19,9,85,2,90,91,19,87,117,106,107,81,81,41,80,117,113,115,90,50,83,11,98,41,6,80,55,39,34,65,113,112,81,103,106,101,37,31,12,60,77,28,64,1,72,66,35,51,28,47,71,78,55,26,30,77,9,2,47,112,73,50,114,88,15,56,49,28,23,1,50,24,13,0,102,92,35,96,39,80,93,6,77,15,17,10,94,11,95,92,86,95,107,61, 17,60,55,87,69,24,92,65,40,88,98,75,115,89,119,107,77,21,37,14,50,5,117,111,93,23,82,120,57,64,113,18,56,94,100,47,110,37,81,8,100,41,85,33,38,120,16,118,101,104,110,62,74,116,47,33,80,100,4,117,33,73,114,61,73,0,93,38,4,101,3,96,96,84,98,39,30,8,3,0,80,83,80,44,116,43,4,66,109,91,97,60,75,71,52,75,93,112,89,38,12,22,54,25,35,38,72,25,102,36,72,11,69,74,3,66,48,30,23,85,0,1,54,96,10,10, 70,20,63,96,107,34,117,102,47,114,0,112,91,19,113,39,42,22,37,49,63,33,86,29,33,85,50,91,116,120,53,67,77,4,34,85,1,14,45,92,82,83,39,111,118,116,73,91,118,51,23,49,39,86,62,104,1,28,97,32,52,86,4,26,107,103,64,47,44,34,79,34,24,37,102,21,97,105,19,92,64,64,50,45,56,49,58,117,69,32,109,45,3,75,16,115,75,116,7,87,56,29,12,72,80,105,7,47,68,96,97,81,72,68,38,53,28,6,116,85,103,120,32,83,47,16, 24,29,79,87,31,78,50,114,99,63,73,66,72,37,120,62,27,15,32,88,96,118,111,54,114,37,43,60,61,22,67,56,59,82,80,98,84,111,107,38,8,103,92,82,116,13,86,2,112,117,23,28,3,25,58,92,18,43,3,51,6,62,112,26,109,93,31,85,20,78,57,116,118,112,8,85,50,83,17,73,84,37,100,89,68,28,26,53,92,97,72,13,6,56,83,57,63,94,115,64,11,80,16,33,115,22,120,98,17,101,20,52,78,103,46,114,118,44,79,11,31,17,74,8,83,46, 40,118,4,90,51,58,26,98,90,46,92,11,29,117,119,75,118,112,12,90,13,47,28,109,32,95,40,31,34,37,20,11,48,53,100,9,50,111,34,59,41,24,87,7,35,37,119,109,3,45,93,113,116,44,21,81,39,58,97,54,84,115,13,66,54,87,8,52,30,73,112,15,23,72,20,76,96,74,13,30,104,65,54,12,41,57,65,16,108,8,92,61,55,88,102,18,20,114,70,17,18,31,115,65,75,54,109,16,71,11,73,55,80,11,75,28,31,38,71,64,2,84,1,81,49,69, 15,62,77,79,81,39,12,0,66,17,6,67,45,28,25,71,107,106,17,68,48,0,4,84,102,15,11,38,58,25,42,80,58,113,76,99,82,89,2,15,48,112,5,8,47,102,46,32,36,76,104,118,1,22,18,117,37,65,107,78,56,26,93,98,78,59,109,38,11,114,49,95,89,39,75,3,114,97,34,26,97,82,98,62,78,88,4,102,62,11,39,26,9,79,110,20,95,69,18,95,104,86,89,82,10,22,24,87,75,104,92,60,63,104,81,116,73,27,22,87,38,7,42,106,76,14, 74,38,112,31,107,48,43,99,85,4,70,89,45,63,115,68,78,58,104,35,93,31,33,47,58,99,27,14,35,113,7,34,42,68,73,92,4,14,6,96,1,70,48,88,77,105,49,56,102,100,89,111,114,28,49,52,79,118,97,86,38,18,109,107,85,30,60,77,69,36,22,69,40,87,77,105,90,70,63,6,116,26,23,15,64,3,71,85,74,53,22,104,39,65,17,6,86,46,45,26,58,40,9,70,119,8,58,110,33,73,68,113,58,75,40,21,104,92,98,107,27,102,36,84,114,40, 27,29,115,11,0,40,80,39,47,110,105,18,17,13,87,64,67,116,8,96,104,44,102,105,54,108,47,27,111,34,27,55,62,73,75,90,105,103,85,82,5,80,36,36,79,94,46,37,61,50,105,46,15,44,57,51,64,52,88,43,8,7,115,59,27,46,105,3,35,107,73,42,82,115,16,99,95,78,101,9,5,56,92,15,63,84,27,112,63,114,19,90,110,79,35,34,54,56,62,28,24,63,11,87,55,17,8,7,75,118,11,29,13,61,120,88,41,104,36,8,57,52,63,60,11,5, 48,6,71,72,57,28,30,72,46,67,63,34,117,10,45,89,1,54,73,115,6,4,120,45,22,28,100,31,11,39,80,27,102,105,93,109,34,82,24,51,102,23,17,1,31,115,75,44,119,118,74,87,51,118,62,59,111,39,3,118,82,112,98,93,69,84,43,30,77,44,84,98,120,29,101,41,99,118,90,20,67,119,61,100,16,46,51,105,25,53,18,105,42,118,20,62,5,120,61,66,103,59,84,69,22,81,109,18,45,44,67,103,87,31,27,98,99,110,100,109,51,78,111,19,93,111, 118,22,55,73,42,60,86,5,61,65,87,112,39,0,64,74,42,112,20,88,53,57,15,80,27,14,110,114,85,119,10,65,51,13,47,2,60,74,43,78,57,117,68,64,21,110,112,47,19,108,33,36,46,45,116,30,49,92,52,33,11,20,44,106,23,51,42,66,97,92,59,56,68,109,78,102,20,53,70,65,49,3,81,62,73,57,9,16,17,13,65,59,45,29,12,120,37,43,58,71,101,48,21,43,96,88,15,36,89,31,79,8,84,107,21,50,10,120,36,14,98,25,83,86,109,76, 98,60,84,15,46,70,91,97,58,27,26,84,111,1,86,49,47,109,99,0,73,106,79,106,44,96,29,46,104,78,113,96,94,50,52,9,19,59,88,37,3,53,98,97,32,40,97,74,78,70,41,14,95,89,41,43,84,100,80,104,111,55,96,82,65,13,118,65,32,10,3,101,42,47,66,74,32,94,9,37,0,42,53,27,43,16,26,2,115,23,58,17,114,10,20,15,48,67,66,80,98,103,37,46,65,96,44,97,82,58,85,20,58,9,0,32,96,42,57,84,88,38,46,84,40,86, 7,56,81,47,19,103,42,54,39,100,108,6,84,5,45,40,16,93,119,49,76,92,32,31,59,103,54,13,44,1,11,27,87,103,109,87,80,108,10,22,2,30,98,65,74,80,60,65,9,50,54,11,57,40,34,42,104,54,8,16,51,72,26,70,51,38,4,92,84,107,29,70,50,115,115,1,58,48,57,71,117,109,5,27,13,120,69,115,89,2,30,18,91,38,42,5,62,44,60,78,35,16,91,84,120,90,8,83,81,11,90,99,40,114,53,75,55,17,36,8,1,55,116,19,99,88, 18,9,104,32,119,62,85,117,88,33,75,95,5,54,16,98,103,54,26,110,21,9,88,108,47,112,34,24,33,15,52,112,61,23,23,32,28,13,65,14,74,5,92,62,75,17,50,38,62,75,6,112,84,20,5,111,93,106,31,61,108,115,22,24,56,35,79,17,50,88,73,96,1,8,44,114,53,19,43,31,94,6,17,29,22,103,21,76,0,9,63,97,32,57,28,113,40,101,79,49,38,105,62,94,25,3,17,63,53,56,15,8,76,0,100,61,70,64,77,11,114,83,35,61,112,101, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 106,42,44,69,19,22,17,109,40,46,114,109,35,71,67,118,63,36,71,94,22,103,37,39,72,62,87,116,47,10,38,103,21,90,21,96,10,110,55,58,23,114,20,35,87,94,118,25,112,101,27,110,89,85,69,39,100,104,81,11,85,20,47,7,117,117,71,84,84,33,50,65,95,83,37,0,114,73,93,48,52,54,56,100,48,116,41,47,117,64,102,33,120,99,115,2,58,105,103,71,120,102,77,29,95,62,117,81,47,119,25,6,28,112,100,41,19,16,70,85,82,62,38,103,94,7, 34,69,85,100,5,101,120,112,110,20,35,33,102,61,87,82,35,118,111,56,117,9,116,46,78,2,74,4,58,35,89,27,33,7,45,40,107,113,109,36,43,33,40,10,41,70,35,36,23,23,119,60,42,30,24,79,83,8,8,30,25,14,64,40,105,9,0,46,40,117,7,42,103,102,36,34,69,35,105,34,97,87,21,105,119,39,26,34,57,79,69,24,98,53,4,34,22,31,19,7,77,83,11,15,104,101,18,81,67,12,18,96,113,47,107,70,28,7,13,68,75,27,118,78,68,115]); G:=MatrixGroup<126,F|x,y>; print "Group G is 3.McL < GL(126,GF(121))";