/*
www-ATLAS of Group Representations.
4.M22 represented as 160 x 160 matrices over GF(121).
*/

F<w>:=GF(121);

x:=CambridgeMatrix(3,F,160,\[
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112,116,74,3,117,83,101,69,54,49,46,6,115,55,29,4,46,13,46,44,51,16,108,38,109,27,3,89,16,35,25,83,84,25,0,113,94,42,93,106,114,83,24,86,68,28,29,47,67,73,3,70,109,76,83,73,63,68,96,71,40,86,80,87,17,77,91,16,118,105,105,7,50,36,93,29,108,7,85,43,0,1,49,48,60,96,39,1,50,84,58,46,66,67,44,7,97,47,72,120,4,108,69,66,11,120,70,33,45,6,44,16,2,113,13,104,51,13,69,113,82,2,95,51,33,100,26,104,27,38,33,89,74,27,73,113,107,0,100,109,17,7,42,67,59,47,56,95,98,1,26,17,82,68,116,23,96,94,27,93,
15,86,87,101,23,30,106,61,59,62,65,62,110,13,107,119,118,30,93,112,14,49,47,70,30,50,98,70,108,86,39,86,92,108,91,99,7,3,103,23,22,54,35,58,15,42,93,66,34,101,52,119,68,45,36,106,39,15,67,82,77,98,53,72,58,18,81,79,88,118,57,10,67,13,91,67,102,30,18,52,14,15,31,114,97,36,94,43,102,67,92,86,30,2,24,36,100,119,118,1,92,86,58,96,44,94,85,105,35,87,3,101,28,36,112,10,56,106,18,56,105,11,4,57,63,69,54,3,8,27,15,48,105,93,52,97,16,87,77,74,37,97,87,4,84,1,71,67,110,22,32,66,115,27,11,13,81,113,73,50,
94,16,41,11,17,21,5,8,88,98,97,1,108,12,1,83,26,95,63,57,5,2,98,11,71,41,83,110,12,31,76,1,62,86,5,39,29,102,34,58,46,113,47,53,119,27,63,94,33,101,50,83,77,14,44,25,32,105,63,80,96,89,75,6,20,37,9,74,102,61,70,32,49,14,4,89,13,24,5,30,42,108,64,77,23,3,56,76,40,19,108,75,116,40,67,45,42,3,61,62,33,94,55,69,85,9,109,78,58,25,1,33,118,2,20,13,0,31,35,98,72,81,69,96,8,56,114,28,71,61,13,96,78,115,105,89,41,120,42,55,63,12,118,85,73,30,31,29,51,31,71,76,10,115,54,84,58,101,24,61,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
105,91,18,77,119,56,109,38,115,79,94,31,15,75,88,1,13,82,62,110,101,38,2,68,111,29,21,7,103,118,83,37,83,93,105,74,91,109,57,29,43,91,72,17,89,41,49,75,67,33,109,112,35,83,0,32,86,10,97,45,75,29,63,76,24,103,114,30,67,17,62,26,111,62,51,120,53,7,71,13,53,34,40,15,20,18,100,89,68,31,50,65,117,29,68,20,13,39,99,2,52,88,54,57,33,118,73,88,41,86,77,20,4,92,98,80,42,105,79,53,59,106,119,120,29,80,53,61,86,24,21,16,86,83,82,95,49,75,17,56,79,19,46,84,66,32,69,5,0,92,20,92,105,69,38,15,21,16,67,58,
112,76,74,62,4,8,106,2,63,47,9,24,94,95,103,28,106,6,30,73,101,15,70,93,31,84,109,81,24,38,28,116,29,45,94,115,19,3,39,25,12,13,32,5,83,86,39,62,110,79,28,92,3,92,50,39,65,23,119,22,8,34,6,100,73,101,22,57,21,103,21,47,40,64,33,88,82,88,82,65,64,60,37,0,108,81,37,7,107,33,39,35,81,22,15,75,51,46,91,2,45,85,11,71,115,51,33,24,104,74,67,2,102,40,32,109,119,41,92,34,9,99,41,45,16,9,114,78,75,21,92,70,105,54,79,48,92,14,3,0,104,58,34,48,12,1,24,35,84,49,30,115,42,86,114,23,79,99,46,114,
76,12,66,51,84,80,70,34,42,15,94,40,83,40,75,50,110,119,78,29,66,98,45,82,2,94,36,99,18,28,38,30,44,83,84,68,6,43,6,8,28,80,0,65,27,2,93,50,35,100,81,109,77,33,34,32,7,93,105,89,73,35,51,71,84,54,30,50,73,58,90,63,105,90,12,114,1,119,53,73,73,87,111,4,43,106,89,111,6,117,120,73,43,113,7,104,111,114,113,107,75,5,76,28,13,50,107,0,79,50,13,95,22,71,17,38,108,77,110,119,84,15,59,110,26,22,118,76,5,62,85,27,58,51,81,23,73,69,119,99,56,11,34,63,40,119,77,6,38,80,111,15,102,27,89,119,14,70,2,40,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
63,42,95,3,64,44,0,99,41,2,36,27,11,84,99,96,35,104,47,40,50,27,104,109,103,5,85,117,34,116,52,30,102,92,28,51,11,115,88,115,8,60,20,115,117,108,37,2,66,52,117,15,34,6,59,119,55,77,48,71,40,15,80,0,119,106,111,117,75,108,77,79,118,11,34,72,73,42,33,31,90,95,9,48,27,52,35,89,81,67,64,32,16,117,58,43,96,17,103,75,74,23,1,113,90,67,29,79,97,38,6,18,46,8,47,113,70,40,43,31,103,91,90,8,37,45,79,2,45,94,60,73,74,105,30,104,11,71,80,37,115,60,78,52,47,73,102,30,113,110,97,57,98,6,4,60,90,10,26,109,
39,9,12,59,29,10,109,93,68,44,105,12,63,8,21,3,37,53,8,55,116,50,83,89,23,74,62,95,69,78,76,41,24,38,90,119,94,73,16,28,30,93,94,44,41,7,112,84,60,42,2,117,5,97,26,27,82,72,59,14,93,63,68,30,75,32,97,97,35,62,5,23,42,95,28,58,104,8,91,115,56,82,25,89,42,18,36,81,69,84,15,108,82,30,29,35,12,30,21,113,87,98,30,110,53,69,62,69,42,55,59,93,15,1,33,85,5,59,80,68,74,61,20,60,97,70,9,88,109,65,58,11,22,82,68,90,102,28,19,54,117,59,57,32,68,14,63,23,29,56,36,91,72,87,107,54,82,60,80,98,
4,47,81,86,27,85,66,12,17,94,63,112,29,112,83,83,104,62,120,43,110,87,109,87,15,52,119,37,103,109,27,46,20,40,92,119,73,17,58,105,23,50,44,33,84,38,65,115,49,100,107,71,18,12,109,92,112,1,10,0,97,101,59,100,36,35,82,43,56,112,4,32,17,7,73,53,68,84,57,106,78,52,13,55,88,65,16,82,20,46,87,105,26,52,62,47,57,23,33,48,82,30,82,62,3,54,109,113,103,62,38,34,118,49,57,4,24,24,64,120,1,90,82,16,43,97,31,99,38,109,75,2,11,10,116,61,0,62,10,51,100,101,26,44,92,1,45,100,43,71,29,100,114,25,29,69,16,99,55,18,
95,31,87,101,10,116,94,60,72,99,68,120,62,76,31,111,11,98,0,17,50,94,92,108,84,119,44,51,103,105,104,79,34,6,42,93,83,26,77,9,45,106,85,15,103,36,10,5,71,45,111,48,116,86,74,65,22,92,23,89,114,17,1,40,88,42,117,116,9,114,50,97,10,40,44,76,72,113,111,94,94,119,22,2,110,102,40,44,29,67,15,85,65,98,72,43,29,106,92,17,111,67,91,58,13,82,40,119,24,36,64,38,61,64,79,118,67,0,63,98,41,88,3,67,82,100,31,53,4,118,114,17,55,82,107,105,111,26,92,13,46,63,9,22,22,97,38,75,72,29,80,13,81,39,103,83,77,80,66,51,
63,49,7,90,71,59,9,96,111,28,109,36,3,68,60,78,48,118,90,67,11,94,8,116,28,98,116,12,9,26,13,11,105,13,46,64,62,84,84,15,70,108,4,68,80,35,112,62,58,99,114,78,111,99,116,51,18,21,27,21,92,59,108,55,94,98,47,54,15,36,54,57,54,103,103,62,62,5,104,75,120,88,32,64,95,39,7,20,5,78,62,8,106,5,27,89,30,104,96,90,120,70,40,45,89,4,2,103,53,55,80,53,43,15,22,100,22,82,115,28,72,70,62,3,94,46,4,73,93,80,47,37,56,82,71,58,109,41,104,54,65,99,54,104,21,66,5,56,119,51,114,26,100,73,61,10,39,16,37,87,
68,18,118,25,90,47,8,18,45,72,97,41,10,70,88,20,49,19,44,63,0,115,111,96,8,23,32,53,70,14,17,40,83,54,42,100,104,76,64,53,118,90,55,98,3,7,9,73,33,13,28,67,60,13,103,101,75,19,85,53,37,5,111,83,61,119,7,86,103,13,52,8,66,98,119,64,24,24,7,0,40,10,56,43,15,15,85,81,51,37,106,47,95,57,60,74,28,49,44,20,13,82,24,37,119,38,49,47,119,19,29,114,50,112,57,114,60,84,29,78,119,79,84,2,39,44,74,33,2,64,17,53,94,17,48,109,41,60,79,34,19,80,15,37,44,7,78,15,40,58,27,35,58,10,65,83,32,16,43,41,
3,84,113,111,85,79,107,80,93,13,35,8,120,67,75,110,99,46,90,85,93,3,55,26,27,91,61,16,113,104,82,66,85,38,16,59,19,61,24,21,2,67,89,94,120,5,21,67,117,10,4,47,62,37,61,27,109,42,27,1,119,2,80,99,69,89,57,96,102,2,72,10,33,89,19,35,118,14,75,6,37,20,33,83,25,4,47,73,100,75,46,103,60,63,21,96,26,18,116,89,78,28,81,106,50,108,72,100,50,84,8,2,88,97,65,108,96,11,111,23,70,54,93,32,71,76,96,1,40,110,2,36,22,98,113,48,9,24,1,114,109,22,89,77,31,67,117,99,60,43,81,71,76,84,40,71,27,5,57,26,
23,39,58,53,17,84,115,36,6,26,88,93,1,45,53,8,116,94,10,42,118,83,19,95,49,87,72,35,71,60,111,5,16,88,20,36,61,16,113,106,15,48,29,11,21,0,12,26,52,101,54,18,89,66,8,61,4,37,105,83,44,83,33,34,35,46,74,38,114,58,100,59,96,26,95,88,94,22,6,102,46,18,73,54,71,79,55,100,67,99,117,28,90,69,95,60,49,73,89,61,21,98,115,63,41,41,108,7,9,92,26,33,77,75,43,52,48,19,90,21,5,28,86,100,74,81,19,47,90,21,111,18,35,6,53,118,35,90,16,117,58,20,21,34,90,34,102,44,68,16,98,8,64,24,8,53,34,71,101,52,
110,34,23,22,18,103,4,90,46,102,46,67,9,96,8,94,48,83,29,43,104,46,117,56,13,73,39,29,91,60,116,70,18,71,22,83,26,83,38,24,63,27,6,15,76,56,101,93,53,108,64,106,24,96,90,15,72,26,106,62,44,12,54,35,96,17,43,30,58,5,79,116,28,36,49,105,79,89,56,44,6,39,89,71,76,29,73,93,5,66,64,79,67,40,99,84,117,78,1,14,37,120,0,73,94,67,34,8,10,59,77,29,107,71,25,37,11,65,11,34,4,100,81,107,12,32,119,107,41,57,0,89,16,45,95,11,26,4,90,93,52,6,96,88,7,70,71,14,97,119,59,61,65,67,90,22,73,2,32,105,
98,100,29,22,34,120,52,13,96,25,89,93,20,11,52,89,71,58,31,103,38,42,75,101,93,2,23,48,31,21,55,114,90,99,9,10,14,11,71,48,45,94,63,78,94,53,83,90,64,92,60,6,8,89,73,22,112,43,118,48,57,29,93,94,92,92,36,74,29,113,25,79,30,19,75,2,71,54,50,48,7,71,11,7,96,79,29,42,16,99,73,107,12,45,87,23,31,112,25,46,106,75,120,57,57,77,16,18,73,7,40,24,109,56,93,55,59,83,18,109,15,44,37,26,16,102,31,116,41,92,45,59,50,25,61,22,52,40,120,117,75,56,37,113,84,5,104,32,17,65,63,36,78,78,115,67,72,119,65,69,
62,37,60,84,119,5,112,27,28,93,97,35,114,81,85,52,35,79,84,22,71,91,85,11,113,60,28,40,113,12,118,29,118,14,113,114,6,85,37,49,88,93,46,53,105,96,62,53,94,5,111,1,96,56,88,18,92,38,9,114,30,53,41,19,82,8,110,81,37,61,14,77,0,61,51,67,90,72,77,105,53,15,102,70,87,107,58,48,46,99,112,70,15,57,24,102,69,52,42,50,84,39,96,0,116,87,82,69,13,114,53,69,99,104,48,46,78,96,5,22,97,118,27,108,90,37,97,114,81,0,91,56,61,106,47,69,82,9,0,115,37,36,108,19,27,65,34,73,78,18,37,84,28,84,89,117,102,120,14,12,
60,63,50,69,11,86,102,109,55,7,1,118,12,86,16,45,44,44,111,99,106,52,79,56,58,109,60,7,30,72,23,31,88,79,78,26,101,40,36,35,4,52,100,97,41,106,88,1,28,114,82,20,35,83,50,120,57,81,74,101,119,40,79,35,61,32,84,27,78,39,44,106,77,43,80,58,47,10,106,65,72,91,109,37,98,50,63,53,19,14,52,75,91,22,58,27,56,23,86,41,100,13,74,104,7,86,50,49,25,52,113,118,51,10,73,21,42,107,65,68,108,61,36,101,64,77,116,28,48,12,120,61,11,21,71,27,116,118,93,44,68,56,94,15,94,105,112,116,70,75,35,43,50,96,16,73,58,82,70,85,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]);

G<x,y>:=MatrixGroup<160,F|x,y>;
print "Group G is 4.M22 < GL(160,GF(121))";