/*
www-ATLAS of Group Representations.
3.M22 represented as 330 x 330 matrices over GF(121).
*/

F<w>:=GF(121);

x:=CambridgeMatrix(3,F,330,\[
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52,114,56,58,89,57,103,80,79,1,116,64,81,44,17,79,106,94,1,96,73,91,67,3,71,0,110,61,95,86,98,63,75,86,52,77,12,10,75,82,82,86,45,36,80,98,110,3,109,51,25,27,14,59,83,63,29,111,43,98,83,62,113,0,53,25,57,31,48,16,90,96,1,16,43,5,57,22,98,102,24,2,19,105,14,85,62,68,110,87,24,21,38,30,34,94,35,80,4,111,88,6,42,62,90,73,58,92,42,38,11,43,81,113,88,35,15,34,24,27,119,58,62,70,54,42,58,87,83,6,104,9,93,115,97,111,70,73,30,25,115,1,61,98,113,17,7,93,54,0,83,32,39,3,65,95,114,5,9,105,39,26,11,104,56,24,71,33,99,106,97,94,64,11,74,79,117,115,0,103,35,75,41,64,23,86,116,43,89,18,22,100,44,61,26,75,37,100,62,60,52,72,88,31,109,40,21,112,42,80,76,19,29,77,19,56,26,22,48,79,69,91,100,24,63,41,17,37,38,105,119,0,84,13,53,45,102,48,62,14,114,62,16,16,67,73,15,70,10,75,31,49,57,59,100,69,67,78,10,112,99,41,16,25,39,68,72,109,116,85,97,24,79,17,55,85,55,98,79,14,0,61,10,8,52,39,39,106,51,55,6,26,13,95,11,30,83,80,73,86,119,82,90,27,41,104,46,8,119,1,64,77,15,45,95,56,69,5,43,21,54,60,66,65,114,66,77,43,71,17,
11,104,59,31,93,23,32,69,114,101,34,108,119,35,82,38,70,8,10,75,41,54,36,104,11,120,87,117,11,27,62,60,37,33,97,8,41,82,26,95,82,60,12,40,96,31,33,119,56,73,39,19,11,27,38,89,88,110,71,116,5,75,36,88,42,120,7,84,93,52,34,80,3,37,103,36,17,110,61,15,43,102,113,21,24,55,96,78,28,17,40,96,120,55,108,40,120,77,22,43,47,120,25,85,29,75,90,93,12,97,50,93,16,95,71,38,76,101,55,48,2,6,48,85,4,58,69,112,96,100,119,27,24,82,13,96,108,84,23,81,118,60,22,29,114,116,93,17,77,22,113,62,76,108,98,50,38,22,111,106,111,52,81,59,49,19,66,21,108,97,31,43,97,12,35,111,57,115,20,75,83,83,53,93,49,71,77,60,41,59,11,84,116,112,23,96,83,33,70,29,97,106,78,98,40,60,11,65,71,7,10,103,24,8,15,3,66,87,38,118,90,51,74,3,116,88,70,50,2,59,16,3,65,17,16,101,13,0,88,113,101,36,93,40,1,97,21,45,75,56,40,7,49,91,49,68,17,116,109,5,42,46,37,105,111,8,23,66,91,66,86,63,58,34,15,108,22,110,38,97,86,101,3,53,87,77,82,12,63,60,31,35,80,35,82,106,20,52,81,92,51,26,65,65,96,39,41,37,118,96,93,28,40,8,39,23,34,36,94,31,100,1,24,79,93,101,35,29,91,59,
5,60,78,50,1,74,79,68,62,69,72,23,33,9,72,109,57,50,40,114,41,32,109,0,62,44,95,7,83,48,1,27,97,49,14,103,56,89,79,48,45,21,92,24,48,90,42,112,13,6,78,44,49,16,74,73,58,75,19,96,49,54,72,107,119,2,30,84,58,47,32,63,38,60,35,104,5,114,27,48,40,26,11,107,86,112,118,88,53,38,81,75,103,22,19,94,80,63,46,71,55,1,16,35,88,36,86,3,36,97,114,28,105,67,107,66,76,20,38,32,9,0,84,118,84,115,110,70,2,114,56,114,52,54,100,82,86,88,33,41,3,48,117,8,76,56,0,61,54,12,53,98,84,6,13,3,102,65,9,30,95,7,3,105,25,66,84,16,111,3,21,92,88,97,64,35,22,36,94,107,1,68,119,54,69,10,75,1,118,106,7,83,49,89,25,21,112,75,23,115,70,97,71,28,70,24,1,77,82,118,61,22,64,39,95,82,74,11,54,89,117,26,106,117,73,93,7,51,16,56,32,5,50,77,32,78,67,105,9,43,70,93,92,39,91,66,104,94,42,96,48,15,104,17,86,32,43,28,91,25,32,35,56,13,112,40,69,90,93,111,98,35,120,90,94,95,28,65,77,15,82,88,120,52,89,38,114,46,100,76,90,32,38,22,50,34,21,97,55,28,107,118,31,118,35,88,111,17,108,31,3,83,85,94,85,111,6,11,95,0,103,67,113,35,101,98,69,39,31,61,
27,4,0,26,0,0,73,0,0,0,0,36,0,0,0,0,0,0,0,0,90,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,101,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,95,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,10,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
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17,33,97,66,37,24,82,18,99,83,20,89,98,57,38,99,96,52,22,103,38,102,25,61,103,112,113,11,82,46,29,40,108,30,36,108,72,69,120,88,114,107,67,66,81,15,69,4,83,86,48,111,5,22,84,80,40,78,101,97,7,56,104,58,1,27,118,76,2,113,72,120,99,11,85,28,49,23,64,31,42,87,74,43,69,95,106,34,20,95,22,15,78,17,13,48,79,61,28,28,57,83,25,31,100,83,57,41,4,72,18,58,52,11,100,76,78,88,107,52,71,24,93,69,44,81,99,5,96,117,61,72,115,98,94,91,108,44,106,0,42,6,33,23,21,8,25,116,93,14,16,33,35,75,0,43,81,16,57,80,77,73,24,120,86,116,105,60,0,24,8,79,45,3,53,116,93,74,35,17,85,99,116,67,43,59,39,105,117,47,81,31,85,0,76,67,115,77,59,35,62,4,119,50,20,28,79,6,30,31,38,25,4,77,7,28,2,94,84,36,20,39,14,27,116,39,45,8,83,39,3,17,89,41,61,39,111,54,92,28,38,92,111,28,91,80,11,115,11,115,103,68,33,67,39,65,84,6,26,90,14,49,35,99,108,48,43,80,47,1,56,120,10,73,33,47,37,79,97,84,13,79,91,53,65,85,60,91,60,38,29,51,23,119,74,13,6,60,18,1,6,33,69,55,42,79,95,108,93,114,26,21,9,1,14,93,49,66,32,103,96,91,44,105,28,84,83,120,75,108,
50,66,23,67,32,74,101,118,79,47,113,50,75,51,8,115,49,67,48,105,46,51,47,108,11,74,35,64,59,118,56,110,71,68,0,0,62,4,39,7,17,7,87,70,11,23,55,69,98,25,98,90,31,10,66,99,16,71,94,3,117,38,106,23,12,1,67,80,95,39,52,50,20,22,14,16,61,24,29,48,120,0,86,86,98,42,53,50,78,114,90,65,32,100,87,1,91,102,68,19,50,36,34,79,96,119,13,24,74,74,21,35,77,25,55,114,52,22,45,97,38,37,15,81,90,9,30,16,83,21,67,115,49,66,106,116,56,62,46,78,4,104,5,96,22,29,50,99,119,48,35,80,26,105,33,29,119,52,117,103,88,8,12,25,120,85,48,108,110,91,31,51,92,41,31,57,67,59,3,120,27,77,21,62,50,115,117,91,115,45,77,35,24,70,112,84,87,41,13,96,12,66,0,33,17,72,61,25,45,44,4,47,100,82,73,14,32,69,61,47,45,37,4,66,62,75,60,62,87,88,37,44,94,63,66,21,120,66,41,96,1,79,90,2,9,118,3,31,67,34,15,53,112,100,68,119,7,119,9,70,53,111,54,67,15,50,11,5,27,90,98,109,5,118,54,11,112,56,63,50,42,79,57,75,106,102,16,92,57,68,58,18,17,115,90,22,41,98,106,56,47,36,7,83,27,96,77,80,22,38,73,66,50,35,12,96,114,114,48,2,21,114,48,72,35,106,42,91,13,55,
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58,103,33,77,16,35,10,59,52,70,105,106,103,99,21,50,45,69,80,68,95,52,86,66,27,54,82,90,60,18,5,99,53,112,118,44,108,66,68,110,18,90,71,62,106,37,28,113,30,44,78,65,17,7,58,87,98,43,96,54,101,83,116,18,18,113,99,111,100,51,52,13,77,42,11,97,108,104,42,5,79,113,85,32,114,32,94,43,3,17,33,8,82,94,30,19,31,72,95,80,34,91,103,54,19,35,106,39,116,35,60,36,82,8,66,28,16,32,46,70,66,47,81,90,83,82,40,8,105,105,5,22,64,14,10,91,54,2,92,10,46,29,3,115,103,120,29,0,52,88,54,109,61,5,79,29,45,25,33,76,51,84,79,63,48,46,78,23,16,91,94,44,43,120,96,111,9,29,53,50,13,57,14,22,21,46,8,53,20,48,119,18,70,52,47,59,48,34,100,116,31,98,81,70,8,70,22,87,98,113,1,51,22,107,1,107,29,97,44,21,101,2,85,57,89,23,5,86,66,62,58,59,114,79,96,41,61,107,18,0,65,116,102,57,94,9,60,111,98,45,86,85,19,6,42,24,120,39,17,92,59,62,67,112,79,28,23,11,52,19,5,99,54,50,20,13,33,28,36,65,111,91,17,73,111,81,48,61,21,0,15,2,106,74,98,16,53,49,63,11,92,29,54,62,6,74,103,119,46,35,95,15,112,93,68,63,17,117,42,15,95,106,10,11,108,14,9,31,46,41,
16,62,88,65,19,104,88,36,54,31,11,110,34,57,60,89,35,120,92,101,84,36,68,75,98,108,23,83,7,64,71,58,30,94,6,23,12,42,15,41,61,23,90,48,82,21,16,3,88,42,62,80,22,80,102,40,95,12,120,37,31,96,20,36,81,94,103,104,68,34,103,98,77,22,82,30,34,36,101,45,49,20,35,17,115,29,67,87,89,116,77,25,90,104,36,58,5,53,69,94,53,85,83,65,51,75,75,22,34,18,33,14,20,30,42,77,32,105,70,106,81,105,113,19,66,117,12,89,119,77,35,43,46,30,14,84,99,103,110,108,2,6,66,3,26,14,21,63,60,111,44,23,37,110,75,80,65,30,24,103,44,64,112,87,66,70,36,76,20,27,12,16,7,86,46,55,44,89,88,83,107,112,21,67,37,99,4,71,9,104,51,96,65,70,23,113,64,27,40,43,42,98,64,107,52,81,87,69,54,95,16,76,75,101,28,62,115,33,28,113,67,91,75,68,16,9,72,19,35,63,107,98,28,102,76,112,101,39,62,36,30,70,117,99,32,89,79,67,42,111,113,21,83,33,84,28,43,55,111,31,22,24,63,31,120,76,71,37,28,29,64,71,7,33,89,79,111,45,36,87,57,55,73,33,42,81,104,70,96,68,13,71,88,95,58,77,88,74,62,27,101,12,95,37,20,16,56,101,94,68,76,58,26,82,25,112,62,47,63,89,2,113,120,56,114,34,116,7,83,60,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
59,104,57,81,103,27,51,19,56,64,85,2,112,99,88,93,38,119,46,17,94,81,8,71,24,94,13,90,24,48,26,75,20,55,2,27,100,100,84,53,53,79,89,37,94,108,32,3,112,11,10,42,107,28,112,11,4,98,104,60,59,115,69,96,57,44,8,2,91,35,5,7,47,25,67,47,22,26,96,20,7,77,45,77,80,59,22,0,69,11,101,33,37,70,13,110,44,4,56,71,92,104,40,8,56,47,70,53,101,59,36,39,15,40,1,1,98,77,106,66,38,39,77,37,108,56,52,69,111,107,102,21,111,33,2,22,59,90,9,11,27,46,114,73,61,82,59,24,71,23,9,53,86,75,102,101,95,10,34,98,58,75,52,105,93,107,111,119,19,19,28,26,86,88,4,57,96,27,99,81,48,90,4,39,38,61,95,14,93,66,21,59,84,10,106,115,52,103,33,93,27,68,93,64,61,44,111,113,95,20,44,0,72,75,65,50,45,56,113,12,68,84,100,4,7,26,19,48,52,17,95,42,45,119,93,9,9,3,72,106,8,64,54,36,53,13,92,15,116,1,50,106,17,104,57,38,11,22,19,48,96,54,100,71,105,103,6,48,65,22,16,115,22,120,68,32,102,58,95,120,119,29,12,21,110,12,13,50,75,84,89,26,118,117,91,89,34,96,62,104,119,66,49,23,13,88,11,36,116,21,118,55,1,84,33,61,37,63,16,40,20,33,46,117,74,6,64,25,40,2,
53,60,46,49,110,3,5,120,83,84,87,79,52,17,49,25,113,39,120,74,32,109,115,60,39,18,53,51,46,79,45,17,107,35,41,52,48,112,63,6,30,0,72,81,82,105,12,51,101,13,83,91,87,85,71,70,40,11,109,44,15,60,54,21,102,34,39,24,49,6,34,81,45,92,4,56,14,96,56,22,71,61,18,89,37,47,2,95,87,59,62,18,46,77,43,54,16,34,36,26,16,61,107,68,94,47,95,12,66,97,109,6,73,95,17,10,89,118,35,0,21,104,53,47,23,8,13,80,20,77,27,76,61,24,109,52,48,55,114,97,63,27,80,76,24,94,2,68,103,66,48,6,64,59,25,65,34,62,60,65,41,31,102,71,38,9,97,96,61,89,63,3,74,113,114,3,74,29,41,117,102,82,53,106,114,53,100,120,63,104,49,112,61,30,29,27,40,86,46,99,78,61,45,97,103,30,50,56,105,78,69,112,76,38,14,105,27,52,116,29,85,39,11,75,44,92,59,90,84,61,2,34,117,77,113,2,81,51,27,63,101,106,9,94,79,97,15,45,96,52,100,65,1,6,33,66,47,118,118,34,34,17,108,0,102,10,32,33,16,55,82,49,51,43,50,30,87,44,30,25,23,70,62,54,95,70,117,82,38,1,95,98,46,88,57,58,82,79,42,58,16,101,114,75,74,34,91,26,14,71,30,110,87,84,47,117,69,62,53,37,17,20,79,31,83,96,60,33,54,6,
5,7,42,53,6,87,104,116,54,76,99,63,66,44,18,93,63,104,27,50,20,74,44,1,65,83,75,45,106,101,34,46,31,2,36,39,82,116,23,1,84,72,29,39,23,15,78,39,7,5,78,109,8,70,119,4,0,99,61,11,8,57,91,31,93,17,27,97,71,78,44,7,47,71,60,57,13,77,62,18,72,7,107,91,45,117,107,4,70,36,108,55,8,78,30,120,2,94,90,8,50,6,59,91,61,27,96,76,39,42,71,39,19,37,18,44,45,95,27,68,6,67,42,110,45,116,91,20,17,88,86,29,34,6,6,92,34,22,61,12,6,30,113,112,6,97,73,87,120,5,66,30,61,101,27,43,69,36,12,107,24,105,72,53,64,115,118,66,47,78,115,72,53,120,86,93,76,99,20,43,99,59,68,64,108,83,19,106,72,66,62,49,41,110,116,3,97,0,78,26,6,52,79,34,41,53,103,42,60,81,96,38,58,104,36,59,42,44,105,70,116,15,6,54,43,50,15,3,3,81,114,67,65,21,60,50,60,0,103,22,56,23,31,16,33,58,68,76,89,18,31,61,61,15,78,111,88,84,70,76,36,28,23,12,81,107,89,25,2,96,102,59,92,97,4,10,38,3,101,62,20,76,96,106,19,111,73,107,84,36,38,52,39,113,97,37,98,116,6,77,8,57,69,114,103,36,63,19,43,92,61,81,47,49,97,77,106,59,38,22,39,54,67,8,115,1,84,42,38,7,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
51,108,29,70,111,27,59,52,61,97,0,87,106,119,24,58,80,41,116,6,111,112,23,95,102,102,109,97,111,102,118,49,68,1,97,9,99,33,6,75,38,97,30,4,120,80,90,110,9,47,49,49,101,1,51,43,66,111,18,111,28,118,8,118,60,13,60,60,84,102,10,50,78,103,43,43,91,89,55,93,47,64,57,88,114,51,95,99,61,99,91,116,71,96,8,30,87,80,80,58,86,36,6,75,51,73,54,38,43,104,3,6,71,85,110,10,44,59,10,112,58,46,99,20,93,90,117,113,43,97,87,120,63,76,14,30,62,38,34,54,2,50,14,73,109,51,3,94,51,54,51,61,97,103,85,16,41,62,64,29,15,49,47,80,78,99,37,37,105,107,41,102,113,8,9,23,93,23,24,112,81,112,61,47,55,44,55,48,21,84,24,105,38,11,93,4,102,38,55,117,0,68,63,46,62,63,90,99,67,71,63,71,43,34,101,28,103,117,20,94,69,114,77,15,23,83,32,97,17,94,89,105,22,36,9,68,100,96,65,25,108,72,62,22,32,7,13,88,4,37,84,9,18,39,69,103,119,19,78,2,28,95,74,32,39,60,75,1,95,107,66,41,24,106,11,31,117,14,114,32,53,81,79,90,26,92,91,92,101,39,1,84,31,107,108,31,53,88,97,51,45,62,40,73,89,113,36,59,45,28,1,34,62,40,43,102,118,62,10,104,95,22,73,120,74,77,66,6,104,3]);

G<x,y>:=MatrixGroup<330,F|x,y>;
print "Group G is 3.M22 < GL(330,GF(121))";