/*
www-ATLAS of Group Representations.
6.M22 represented as 210 x 210 matrices over GF(121).
*/

F<w>:=GF(121);

x:=CambridgeMatrix(3,F,210,\[
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96,37,46,25,44,61,15,62,113,62,32,98,69,83,106,49,64,113,64,85,60,22,34,108,117,78,53,55,106,69,64,16,94,118,98,5,68,87,93,7,59,75,37,116,3,70,46,113,120,38,4,78,119,118,57,95,102,20,84,118,86,89,24,66,51,80,74,36,97,5,40,26,85,66,19,44,66,117,58,16,66,10,81,2,4,51,114,60,56,120,80,0,74,11,19,45,43,118,120,7,21,33,117,46,23,113,25,32,63,11,70,59,73,38,67,69,32,16,21,63,78,68,43,79,91,82,96,41,72,95,45,44,63,111,44,31,38,9,41,33,65,86,119,70,70,1,6,50,75,0,35,63,88,63,54,117,64,16,19,22,62,109,113,99,24,41,56,63,20,53,1,20,86,56,89,120,112,38,112,72,94,87,35,85,116,120,111,96,65,57,61,108,59,87,106,13,102,22,47,92,44,83,39,113,36,90,100,27,40,5,
4,12,89,37,111,103,62,101,81,78,92,59,33,21,67,87,100,56,92,28,9,17,20,4,64,118,94,77,9,16,49,37,75,80,95,55,34,16,58,41,78,31,107,90,64,85,40,49,65,36,21,30,61,29,94,85,80,53,118,102,75,14,41,109,17,12,91,69,120,59,79,88,77,10,37,34,103,1,120,119,43,29,25,7,23,95,113,41,36,113,100,10,10,22,11,45,112,16,46,80,42,32,35,77,2,44,47,0,21,13,48,16,98,28,100,61,46,75,2,55,17,69,90,6,53,50,117,25,80,78,82,27,111,86,91,92,116,54,112,87,21,38,15,109,59,84,62,28,78,19,111,53,64,100,68,2,18,49,67,17,44,39,60,74,32,51,50,118,56,45,86,81,77,92,90,114,99,80,47,51,37,116,7,60,38,26,53,10,42,17,79,35,109,34,7,118,74,90,94,87,12,88,74,111,94,117,56,68,23,30,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
63,60,50,112,95,71,95,77,19,73,21,81,43,5,82,0,83,76,99,81,95,0,79,106,15,19,96,30,98,36,112,22,13,63,23,80,5,6,73,36,99,71,71,7,107,109,4,102,61,46,5,105,3,33,65,6,49,1,82,115,56,91,23,96,105,23,13,93,42,85,114,82,13,48,114,11,20,71,40,49,32,89,32,92,41,98,59,114,42,110,63,72,10,12,35,51,31,1,87,46,108,10,7,120,32,112,97,49,43,2,80,90,44,76,98,32,96,69,120,80,3,16,45,27,58,82,87,8,94,51,49,88,18,84,98,69,33,75,67,35,58,94,19,75,101,55,91,65,55,102,26,19,68,95,17,96,6,10,53,39,80,23,56,58,72,92,10,67,50,15,46,35,31,62,98,73,28,110,95,95,93,72,114,40,87,23,31,98,65,52,74,37,87,98,105,92,53,58,106,83,36,33,91,97,44,107,22,59,117,81,
106,15,82,86,78,106,64,40,34,95,73,80,102,28,106,37,43,89,116,20,13,97,115,102,60,81,96,21,25,22,56,16,26,20,55,50,116,103,40,62,117,59,1,47,114,37,35,63,46,33,6,20,113,28,70,26,106,65,33,77,119,83,68,93,65,16,110,70,40,100,4,58,63,119,21,11,1,25,65,81,72,21,36,108,50,32,119,48,93,72,83,9,51,80,63,32,100,84,43,42,55,73,32,60,64,110,94,49,94,22,48,20,102,25,116,102,64,56,85,58,43,117,5,23,45,118,100,111,114,38,75,51,67,11,3,69,88,82,33,24,85,61,96,68,118,102,92,91,114,6,102,8,85,102,100,60,60,35,95,119,88,2,83,100,68,22,57,23,27,94,70,119,112,9,34,58,57,119,65,41,78,48,106,65,74,67,6,49,93,70,103,38,82,108,65,5,78,72,4,72,120,91,41,76,57,105,26,88,65,27,
58,62,95,101,72,12,19,101,9,1,105,76,14,33,94,71,46,43,114,19,39,36,27,68,70,96,105,74,38,84,98,99,41,76,100,32,77,30,119,86,65,105,30,52,71,6,56,107,16,32,50,22,94,94,119,97,5,51,98,53,21,26,22,73,91,107,3,59,58,108,96,80,33,9,24,70,4,21,73,86,109,89,83,28,12,70,91,4,78,53,75,72,116,96,85,93,8,1,31,98,70,27,83,50,22,99,0,84,22,64,50,56,96,91,104,72,87,91,89,45,21,102,119,76,52,74,111,7,13,28,14,119,90,30,46,20,48,40,30,62,22,112,18,56,52,67,41,119,14,68,86,59,2,28,51,46,106,102,91,73,74,65,3,38,59,62,52,32,96,12,57,76,96,13,119,8,32,97,68,37,117,37,116,118,16,104,67,117,54,118,72,115,92,2,31,70,16,108,1,108,57,113,22,57,12,116,99,105,100,45,
96,44,35,26,90,9,120,39,35,93,29,44,98,15,35,97,10,4,1,68,51,78,17,81,4,64,40,2,73,92,44,5,105,68,28,82,102,77,40,75,119,96,33,29,75,69,70,53,13,88,110,34,59,104,38,21,79,108,55,72,84,97,100,12,65,26,32,61,62,34,19,91,75,103,105,22,64,11,22,57,80,94,15,37,69,15,103,58,91,12,56,47,34,37,102,48,119,9,79,95,69,40,111,7,102,73,10,65,19,89,46,71,42,33,28,32,18,16,114,59,9,64,21,35,74,4,9,20,114,96,42,62,7,83,119,19,71,94,87,2,82,53,86,41,23,21,84,59,117,90,86,5,55,38,48,112,11,59,80,104,39,74,45,105,46,77,91,84,49,10,59,108,4,20,60,33,112,106,11,84,67,92,88,31,71,66,7,63,35,10,67,5,82,16,45,42,48,44,74,102,76,115,106,19,14,15,48,114,47,81,
6,76,20,113,111,60,98,10,59,102,103,11,58,8,81,53,71,120,45,22,57,57,38,10,53,29,56,19,85,1,62,82,10,94,55,52,106,39,6,18,92,0,89,45,85,40,47,10,57,101,35,84,17,60,104,13,42,119,60,73,95,12,111,75,84,100,63,39,66,40,67,14,97,98,5,103,80,74,118,43,5,82,23,59,16,99,71,53,51,96,23,43,63,116,1,82,17,47,10,7,82,48,3,26,101,114,119,112,95,11,109,21,87,3,91,58,99,98,100,27,119,63,57,52,51,82,77,83,95,102,79,87,18,41,108,50,50,0,85,78,57,36,45,84,12,47,73,120,5,44,41,5,113,90,20,104,65,103,52,16,3,28,47,99,34,107,93,114,108,24,64,85,35,18,24,82,91,80,28,27,42,93,73,50,17,27,1,111,90,69,107,67,20,71,6,13,65,10,110,99,77,14,78,88,5,101,28,65,108,13,
15,31,20,8,1,10,115,55,60,114,30,110,47,87,55,72,80,87,44,53,18,52,39,22,25,113,110,41,24,107,42,118,108,46,46,119,68,0,5,6,7,112,67,64,2,0,17,57,84,46,46,97,108,98,41,72,119,7,56,47,64,28,79,49,57,99,74,93,4,10,105,90,70,59,107,53,45,44,76,71,13,19,44,21,53,67,28,2,93,83,32,68,87,38,45,43,118,22,118,63,65,57,94,114,40,105,68,32,9,13,33,98,3,75,43,61,87,84,25,87,19,67,97,56,116,86,20,84,16,36,81,62,52,91,109,80,11,83,114,28,110,0,92,25,120,42,105,96,42,33,36,74,25,93,118,48,25,25,55,81,61,67,75,74,14,26,102,3,50,88,30,25,28,13,58,59,107,83,39,30,61,73,92,88,100,14,75,54,99,116,16,119,106,94,41,110,71,12,47,10,35,29,76,84,108,6,97,10,63,19,
101,16,66,93,26,93,80,54,61,85,15,29,25,78,2,68,62,1,115,86,107,119,53,39,27,99,16,111,67,72,108,0,116,48,95,9,24,28,105,119,94,117,83,84,24,104,105,17,36,84,75,16,104,2,7,65,35,68,57,47,120,47,103,62,52,19,0,65,51,97,7,18,35,102,9,19,95,60,110,77,3,79,55,63,18,60,29,38,32,55,106,103,71,110,70,66,62,91,18,54,120,22,48,26,64,66,2,74,61,117,38,15,98,46,79,70,94,90,39,84,42,46,68,62,20,12,41,85,66,74,59,107,13,40,36,18,2,100,87,22,103,90,26,47,62,109,46,99,94,90,39,117,0,59,102,45,32,55,58,69,22,47,116,69,47,63,65,101,50,118,108,39,3,65,63,24,69,20,87,99,26,79,82,16,26,88,12,53,72,90,51,39,41,27,116,0,49,104,70,31,56,96,1,63,99,43,58,94,61,71,
11,95,79,40,1,79,62,15,102,88,73,100,32,50,95,92,13,53,68,7,65,96,2,71,47,105,103,110,58,54,98,101,65,0,86,33,113,104,1,3,97,7,105,63,72,30,17,86,11,83,20,99,79,21,85,37,68,108,18,41,97,66,80,59,100,1,85,29,68,15,42,63,107,105,108,57,91,8,31,109,40,93,50,84,43,94,57,16,7,120,112,88,53,83,5,32,37,39,39,65,89,42,93,90,86,62,66,72,106,103,84,47,0,38,85,15,37,45,33,52,112,101,52,1,66,12,36,47,51,97,1,84,20,88,53,26,39,72,115,8,66,7,32,44,18,74,38,1,65,80,2,6,0,26,67,42,49,49,93,100,1,80,9,0,50,72,50,87,34,19,67,83,119,68,112,95,53,76,40,16,72,5,53,44,96,3,103,81,9,62,78,3,99,15,10,74,9,48,34,41,110,88,71,46,119,23,96,108,29,57,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]);

G<x,y>:=MatrixGroup<210,F|x,y>;
print "Group G is 6.M22 < GL(210,GF(121))";