/*
www-ATLAS of Group Representations.
4.M22 represented as 176 x 176 matrices over GF(121).
*/

F<w>:=GF(121);

x:=CambridgeMatrix(3,F,176,\[
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12,85,87,22,119,93,52,90,77,11,94,83,82,24,54,10,72,90,108,27,11,53,42,5,8,56,49,18,84,120,66,94,40,82,67,80,82,46,59,59,52,89,39,87,24,117,71,86,97,96,21,47,8,102,99,17,71,61,104,81,28,36,33,80,84,70,105,104,92,9,83,5,61,76,29,42,102,24,102,17,46,67,85,11,47,64,7,105,107,24,27,116,23,12,49,79,40,21,77,65,56,4,116,73,108,78,1,10,114,118,45,49,52,110,72,57,32,53,27,4,2,53,11,72,23,107,70,2,16,75,36,37,37,13,28,54,98,1,67,47,49,110,13,6,51,65,91,47,17,14,75,3,99,44,108,101,56,41,71,120,50,72,22,81,20,16,31,13,41,52,94,48,45,118,57,37,
102,16,106,77,20,54,74,90,56,106,33,40,69,92,112,115,91,47,75,43,82,76,45,58,47,106,38,112,80,92,58,18,6,77,108,112,0,24,113,87,96,17,36,79,113,60,117,120,2,40,91,96,8,28,37,43,3,15,93,45,4,112,77,82,26,93,69,61,116,75,15,119,4,78,42,13,77,26,83,24,4,22,100,56,102,42,36,25,69,55,13,98,7,1,85,54,106,1,17,37,87,68,112,64,15,56,40,116,6,58,81,76,71,93,113,13,93,73,21,1,14,115,75,38,20,102,51,66,50,3,25,71,94,13,36,94,94,90,39,64,50,76,113,11,61,27,90,56,120,70,68,96,120,43,50,13,0,48,54,34,7,67,30,12,21,44,22,112,113,34,23,0,103,37,17,107,
83,55,3,66,16,38,36,61,71,101,57,66,10,92,92,46,47,97,21,14,109,64,118,28,80,65,81,97,110,10,21,53,43,15,41,110,55,37,16,91,90,101,108,47,22,55,50,37,29,37,92,91,89,45,54,92,8,113,81,73,58,19,31,95,8,116,32,15,72,27,23,88,69,32,81,58,57,80,85,105,81,116,71,16,94,7,91,65,98,16,13,52,8,34,41,117,39,30,21,12,100,7,68,14,86,119,42,38,115,52,112,50,72,55,108,51,6,68,60,63,66,85,119,108,94,74,35,47,102,81,18,1,85,28,35,53,97,101,107,50,26,52,42,5,99,34,20,117,120,26,114,75,107,13,58,115,100,105,63,31,11,20,21,72,70,4,4,42,84,67,56,87,1,99,54,59,
62,79,89,11,87,56,12,70,77,72,24,116,83,28,35,102,119,21,30,45,117,11,84,32,100,41,50,87,96,106,20,88,116,102,86,104,54,67,46,85,29,108,29,100,68,62,0,60,100,107,105,46,20,50,16,87,44,22,51,116,96,100,66,99,37,97,95,81,3,109,50,66,16,1,91,65,58,39,111,60,5,114,80,56,71,73,29,111,100,8,96,89,114,16,90,58,94,49,20,113,120,55,75,27,0,70,86,14,52,51,93,16,3,92,116,116,47,107,52,21,65,56,21,7,106,81,20,28,0,106,53,36,34,115,92,63,40,34,16,55,50,120,34,36,38,120,87,74,20,62,1,67,65,37,76,21,92,55,17,2,97,11,99,49,83,23,73,96,91,52,84,114,71,5,31,76,
90,61,1,52,9,84,60,43,82,47,17,31,73,119,36,118,21,35,9,83,86,84,62,65,90,117,62,0,80,106,69,82,96,5,15,105,94,106,64,100,74,12,4,74,96,60,100,70,7,35,32,32,35,44,74,69,97,52,91,37,44,21,97,93,52,0,77,6,30,2,88,101,43,84,73,57,102,1,84,108,34,54,108,103,27,92,46,55,88,73,62,97,106,108,31,96,44,38,23,39,31,73,106,91,58,25,109,97,92,120,87,51,52,107,33,54,70,84,50,66,59,47,76,103,56,30,60,67,27,54,69,15,47,119,16,2,84,62,47,53,117,111,25,29,37,57,118,30,76,16,26,57,77,43,15,106,31,30,97,65,119,99,106,77,40,78,53,12,13,5,27,22,61,64,102,63,
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101,90,29,54,21,77,10,59,92,23,43,13,101,102,47,59,1,97,46,75,46,42,64,92,68,95,50,1,68,61,51,3,17,120,53,50,106,58,116,0,70,116,20,93,40,23,48,60,7,87,115,62,72,69,28,86,116,44,67,46,12,37,13,24,70,13,103,63,103,74,68,21,117,40,92,100,3,75,91,58,88,32,14,36,38,46,118,5,92,4,49,76,30,1,35,12,3,109,2,74,110,53,76,41,63,74,36,86,98,119,93,25,73,101,55,64,87,114,5,58,50,104,37,95,104,86,74,33,16,0,14,105,79,19,23,6,63,55,23,82,4,20,65,70,71,23,31,67,69,106,96,72,35,85,40,117,22,56,39,108,44,102,71,34,10,73,33,0,101,113,54,119,0,94,44,55,
4,35,97,119,93,112,45,56,92,73,43,113,9,119,92,21,70,116,92,98,55,29,84,20,83,15,105,51,95,118,96,103,28,117,2,72,84,110,87,0,71,114,44,85,100,112,49,51,107,57,89,81,81,0,80,38,70,34,98,97,104,18,5,97,88,70,80,77,55,105,81,1,54,23,77,99,118,70,114,59,68,112,53,109,72,5,19,51,19,36,44,1,20,81,49,106,61,82,25,119,98,43,103,55,0,114,112,9,25,87,32,120,108,109,21,86,73,95,77,52,62,75,117,22,106,75,104,54,66,57,4,104,104,81,70,50,29,93,26,18,100,37,70,67,92,74,30,22,90,46,38,42,54,19,12,33,52,17,22,45,47,57,78,70,12,2,7,6,47,28,80,36,105,83,62,36,
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0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
101,88,64,12,110,89,50,39,26,71,111,103,82,19,16,47,79,98,37,40,53,42,2,71,62,15,104,41,65,38,19,52,53,36,111,40,53,0,51,19,9,54,8,56,96,69,69,0,33,38,17,16,62,19,20,53,81,64,53,66,11,28,94,5,82,92,0,74,100,71,27,61,93,100,76,83,37,94,68,30,30,32,74,65,9,73,27,65,2,39,7,98,116,17,110,20,52,8,81,44,100,78,60,97,116,12,98,88,68,36,56,45,0,34,70,14,73,103,1,7,34,90,90,64,120,14,34,119,20,84,55,113,86,119,82,88,21,90,52,38,107,85,61,9,3,17,50,70,87,111,19,84,34,84,118,66,11,10,66,40,19,57,94,58,39,89,56,104,48,61,79,60,105,62,94,103,
100,89,118,104,53,5,82,68,51,114,34,50,82,59,6,115,74,45,53,5,5,32,120,29,89,55,60,62,84,94,106,16,83,16,1,51,4,35,52,53,67,85,116,5,103,74,81,15,65,48,73,47,55,2,10,62,87,36,37,111,81,117,20,26,116,28,27,61,73,114,60,84,16,11,32,38,117,51,16,98,37,61,24,95,78,28,2,69,43,14,118,12,35,96,111,96,103,92,91,68,86,68,33,33,80,21,28,15,18,28,96,53,39,37,74,11,69,120,114,31,112,111,116,114,18,120,72,56,64,113,106,108,58,79,62,53,41,14,0,73,17,22,34,89,108,10,37,62,86,66,65,52,4,38,109,7,33,72,92,54,46,102,111,113,28,1,63,92,38,30,60,114,38,77,21,86,
89,118,62,10,92,61,88,0,99,28,48,116,27,116,39,51,51,49,75,84,106,111,51,47,12,32,25,118,116,106,21,2,84,109,59,58,108,4,95,120,37,76,109,15,91,78,98,53,12,38,112,120,35,74,101,47,88,7,100,23,103,17,106,26,17,50,111,76,26,60,14,29,43,59,84,72,2,109,79,101,46,89,97,12,84,25,94,63,13,91,5,89,54,82,87,55,114,33,110,95,22,98,39,98,70,103,97,98,55,47,17,74,62,54,65,104,109,114,52,98,96,23,72,15,49,96,5,48,79,14,95,96,8,71,11,26,73,75,66,39,101,85,107,25,97,31,77,42,16,29,91,101,24,106,84,73,69,85,113,101,8,50,35,8,119,49,21,61,64,109,15,3,74,103,30,64,
101,115,28,74,12,1,21,118,111,47,73,35,69,6,27,42,53,26,63,106,25,97,6,3,97,53,15,67,2,79,21,79,87,0,25,104,98,57,22,61,63,0,98,109,71,115,50,109,27,15,76,87,17,110,83,43,101,60,25,106,70,22,112,68,98,1,49,49,119,30,88,90,25,102,102,99,80,98,94,19,52,120,105,32,15,108,80,104,39,22,119,20,111,24,99,74,100,30,39,99,78,45,2,115,119,40,83,111,75,63,74,115,0,22,42,28,13,42,51,44,57,7,5,44,97,82,102,14,76,97,85,51,56,82,3,73,107,82,86,104,93,54,75,51,43,8,115,51,22,86,78,78,89,45,35,18,63,31,78,41,90,51,83,64,70,11,57,73,13,99,27,87,39,102,63,42,
59,16,0,31,26,72,44,12,90,3,18,92,32,39,92,118,5,5,58,99,45,97,30,92,79,97,24,8,104,56,25,9,43,98,53,2,14,14,1,71,33,36,79,4,35,15,100,7,118,13,26,83,98,10,81,103,95,75,118,59,71,65,64,29,76,90,87,96,21,12,32,4,120,21,73,79,8,14,57,95,38,62,114,87,84,6,17,16,86,1,18,102,99,19,41,49,95,70,53,90,66,106,68,4,96,63,28,84,45,84,48,104,77,10,95,111,37,11,19,34,26,74,96,49,116,35,48,71,97,48,30,4,19,114,63,81,112,75,118,119,40,55,116,64,60,98,12,81,104,67,45,49,86,3,2,59,65,84,114,80,98,77,52,49,99,111,74,36,96,3,119,50,23,58,76,23,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
86,32,80,81,70,52,30,85,99,47,112,8,85,69,89,48,85,93,120,109,45,73,25,7,29,8,82,34,64,68,61,20,52,79,104,24,86,36,36,47,43,80,6,39,21,28,67,86,67,103,28,77,111,50,100,109,118,67,103,19,1,14,15,42,87,103,62,64,82,28,42,1,95,67,109,56,58,115,65,4,81,73,120,46,72,53,15,69,19,108,39,6,68,85,31,48,109,14,59,17,41,85,44,46,83,32,53,50,70,27,24,104,11,107,57,36,56,98,9,30,89,37,11,79,84,29,17,118,35,85,12,9,32,17,17,1,85,40,86,37,67,41,68,10,19,16,42,55,90,28,117,27,35,65,97,92,56,32,27,70,26,65,98,67,2,43,44,31,55,91,116,66,7,41,7,24,
49,57,45,23,58,17,67,3,117,79,42,2,59,71,2,86,72,79,52,96,81,74,24,20,95,3,7,33,44,12,5,120,120,108,68,102,68,113,37,2,113,26,18,3,18,120,32,116,90,92,12,9,5,50,25,8,14,45,44,32,87,42,65,44,22,72,49,109,96,24,75,44,44,97,4,15,31,58,77,99,112,84,65,1,1,119,4,17,82,108,34,72,66,67,62,9,72,6,53,93,50,116,35,40,116,91,93,56,84,9,25,81,46,102,55,11,35,11,22,74,48,28,79,10,58,56,43,20,97,87,108,96,36,56,44,6,88,87,45,106,13,113,97,95,36,57,117,36,60,6,42,44,36,95,40,49,104,44,24,98,1,113,6,35,5,3,40,100,35,35,111,80,77,71,31,45,
118,11,42,11,19,44,36,59,95,19,115,80,26,48,56,112,105,50,28,102,38,28,32,19,111,91,102,74,102,53,21,114,117,111,99,102,59,41,57,8,44,16,116,69,78,11,35,96,102,6,67,36,52,55,27,91,50,14,87,113,25,50,46,82,78,102,42,86,65,15,77,51,30,42,45,72,81,65,73,68,43,96,116,67,8,27,100,3,33,108,44,58,8,110,2,120,34,3,16,26,73,75,32,99,77,53,97,80,72,28,40,2,31,116,45,36,117,35,6,110,97,58,67,101,95,50,77,120,57,48,83,43,24,6,25,9,65,36,50,110,38,0,40,2,56,50,56,87,74,50,91,32,57,46,70,74,86,13,29,6,53,95,87,68,69,98,8,53,95,105,109,97,57,27,37,118,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
33,78,26,68,87,56,90,52,0,58,78,27,34,26,99,72,65,17,91,61,53,109,0,61,84,79,79,115,47,60,57,118,43,4,16,35,52,63,117,35,64,116,76,91,53,65,19,77,61,95,16,35,95,82,103,78,86,94,25,3,114,60,37,32,25,94,80,24,115,116,110,24,63,76,1,34,116,79,94,49,38,63,32,28,43,75,4,29,97,73,81,52,63,13,94,94,91,101,16,0,16,70,91,113,54,51,50,4,78,80,11,67,109,44,55,25,34,76,54,114,90,113,51,57,43,80,67,84,80,103,90,87,59,115,9,49,108,118,100,47,84,12,102,67,70,88,97,63,74,32,56,77,117,84,16,50,66,27,62,76,7,87,97,2,62,10,50,2,93,24,44,85,22,48,39,30,
1,117,4,51,75,98,48,44,79,77,97,48,30,26,104,5,35,32,47,113,67,75,106,77,31,43,108,64,69,16,28,111,86,46,118,80,7,116,8,2,29,10,35,17,118,77,87,44,99,117,92,69,37,27,13,30,118,53,3,101,115,104,1,68,91,94,23,94,23,39,28,8,120,31,14,5,102,116,40,108,68,34,32,62,29,58,75,92,93,86,78,59,69,87,53,82,24,50,27,8,34,93,66,101,55,9,54,37,116,45,112,60,36,90,113,32,120,25,25,21,96,41,15,31,15,46,17,110,9,60,8,90,32,114,112,31,59,63,109,84,108,78,83,65,115,96,51,30,4,87,47,47,24,116,8,92,109,62,69,93,12,52,99,72,71,10,70,39,3,86,10,46,38,29,101,68,
94,75,115,100,33,102,38,42,98,99,24,96,9,49,22,111,74,19,7,96,29,44,47,26,64,41,8,46,94,103,31,39,11,2,27,86,107,88,35,94,50,51,105,80,48,67,8,19,51,34,89,93,113,41,86,117,73,102,42,5,10,86,70,42,59,15,37,118,24,23,27,94,65,78,50,0,46,67,80,62,71,70,109,68,70,98,68,22,21,4,49,81,105,88,85,99,106,11,64,80,68,4,16,55,78,27,33,115,65,56,78,23,119,70,13,109,2,74,116,110,4,35,76,13,19,58,47,93,80,98,35,17,96,60,94,105,89,21,70,28,77,16,107,36,44,59,97,114,83,59,96,112,77,43,99,116,96,44,31,69,89,29,76,7,37,87,104,82,93,58,81,1,5,20,20,46,
16,74,22,50,81,82,41,107,92,98,79,55,18,84,17,53,19,7,46,26,45,60,110,10,10,11,30,34,10,98,51,20,64,35,17,45,93,57,101,44,88,16,64,88,68,101,7,56,57,8,4,38,47,72,15,78,74,120,11,15,2,12,97,57,41,53,120,26,108,26,63,86,11,96,55,58,6,109,89,28,102,10,60,55,71,3,69,16,109,86,0,21,25,15,20,7,46,30,76,98,80,39,78,108,51,87,96,54,114,89,20,14,80,27,61,26,0,39,86,73,34,105,14,99,88,82,3,119,32,32,34,18,43,30,112,93,98,43,101,14,61,100,27,40,12,82,23,77,20,69,116,110,20,54,90,53,87,62,105,58,46,6,85,79,112,95,11,100,42,118,49,79,28,72,52,103,
12,112,55,82,92,15,64,58,35,86,44,67,115,43,31,37,56,51,45,74,16,71,103,92,73,91,56,42,39,81,30,45,38,47,76,5,52,94,7,52,22,20,68,44,63,15,116,16,84,79,78,49,36,36,51,46,25,94,17,100,109,0,8,13,56,106,102,38,113,96,102,78,87,54,23,3,5,29,106,64,66,20,98,52,91,76,95,52,109,62,60,94,6,39,3,72,118,6,63,81,7,45,112,4,116,21,5,39,53,92,107,93,92,80,69,45,112,52,67,47,82,64,20,79,88,69,73,91,52,24,107,2,23,97,80,7,92,38,75,68,60,64,97,116,22,3,24,18,20,36,85,88,103,42,3,18,115,28,76,42,100,115,98,20,103,32,99,24,99,103,70,86,14,70,19,6,
68,56,66,115,34,86,62,39,75,13,64,74,57,96,98,97,16,89,15,51,7,77,106,106,82,78,38,60,59,80,91,10,109,108,62,46,0,36,114,46,25,89,104,8,4,13,67,118,30,118,68,66,99,22,20,39,34,25,30,53,74,91,100,2,120,10,35,105,31,70,29,94,4,120,39,99,78,120,17,2,38,83,107,86,109,53,65,61,108,110,61,106,114,68,77,87,49,87,72,34,56,47,42,64,64,5,26,47,25,80,101,7,111,4,70,115,104,43,11,69,49,74,24,68,5,62,8,44,96,61,83,90,112,105,26,63,100,120,75,43,31,56,6,21,73,28,66,41,81,99,37,111,91,31,115,103,54,71,7,42,72,45,64,113,104,25,82,60,10,106,15,14,80,11,13,116]);

G<x,y>:=MatrixGroup<176,F|x,y>;
print "Group G is 4.M22 < GL(176,GF(121))";