/*
www-ATLAS of Group Representations.
3.M22 represented as 231 x 231 matrices over GF(121).
*/

F<w>:=GF(121);

x:=CambridgeMatrix(3,F,231,\[
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58,115,107,62,59,32,24,37,110,22,86,18,46,78,6,57,46,62,87,68,65,112,42,50,88,43,83,63,85,70,109,6,19,56,46,76,35,111,36,83,2,106,74,93,39,55,57,32,31,113,108,41,12,90,12,70,51,115,116,51,96,48,58,105,93,34,49,91,13,108,96,103,30,66,75,31,109,81,66,43,25,59,11,46,75,115,87,104,41,40,83,118,109,104,62,104,103,86,84,107,113,72,0,102,64,24,58,65,38,116,11,14,67,18,53,112,106,76,55,114,61,109,79,12,119,70,15,69,21,20,105,119,77,116,6,49,56,39,0,50,77,95,28,110,10,65,23,27,1,3,91,18,47,34,76,86,104,100,17,94,66,41,99,117,120,54,59,38,6,49,112,48,88,100,117,68,82,47,91,59,28,45,84,45,100,83,110,77,42,28,37,71,64,116,32,45,82,114,89,50,52,21,78,64,103,120,58,48,97,114,41,70,113,17,36,116,50,17,10,60,28,73,68,45,79,48,39,24,33,34,30,
27,23,88,32,95,111,33,28,99,116,86,71,104,80,78,39,110,37,49,90,113,7,77,120,26,53,29,3,38,86,99,60,27,63,105,69,15,39,79,115,51,9,62,28,79,91,19,15,41,60,14,9,26,14,7,104,38,60,27,6,114,37,86,41,46,3,40,93,86,51,32,98,32,3,53,106,65,115,9,37,36,56,115,7,85,99,40,97,20,8,2,33,93,40,28,70,91,12,77,113,48,27,108,50,18,94,66,19,118,18,85,76,111,58,78,42,83,54,45,103,0,104,22,80,65,104,115,116,34,101,102,6,18,97,51,80,27,60,17,24,76,20,97,6,99,39,19,113,12,10,42,39,68,39,1,86,79,82,111,47,38,36,43,26,105,60,24,112,44,71,16,3,7,3,38,74,85,13,49,31,7,64,107,88,57,84,8,68,83,4,53,93,69,33,68,86,39,6,109,88,33,112,118,101,54,94,58,105,30,120,70,15,115,46,119,25,104,120,107,118,8,88,42,77,65,61,37,54,14,99,58,
102,74,29,52,39,81,61,94,50,109,94,41,65,111,27,36,57,81,94,0,16,61,112,32,120,54,91,35,9,47,103,75,1,75,95,63,116,79,66,48,32,86,118,10,81,22,19,24,35,91,88,20,103,21,101,67,97,90,78,113,11,75,52,111,86,15,16,3,45,118,11,20,59,57,4,82,102,61,106,102,4,25,35,12,0,19,74,23,2,26,87,33,63,108,40,61,107,9,117,22,64,10,70,6,29,68,109,7,32,5,55,66,115,76,101,30,93,42,47,22,113,78,53,108,23,108,49,22,111,101,59,68,54,48,92,22,41,17,56,104,97,110,113,0,105,22,98,15,84,5,15,91,61,39,83,33,108,21,99,52,90,66,1,29,89,102,48,40,0,81,27,70,103,98,76,50,67,76,41,73,37,109,7,9,25,92,83,87,114,81,97,58,72,30,53,104,61,12,16,37,12,27,47,91,87,6,1,18,52,32,0,21,98,26,6,0,7,17,97,15,103,85,32,110,81,82,34,53,24,0,109,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
62,27,23,96,29,54,10,104,15,118,10,84,45,14,24,31,3,85,77,39,82,97,59,8,73,31,120,2,57,82,72,112,38,81,46,9,114,93,52,103,43,75,17,30,83,42,69,96,27,67,16,79,41,41,6,37,9,31,82,12,91,114,89,49,115,110,12,15,108,12,14,44,42,73,34,96,120,100,53,60,20,32,40,53,110,95,81,31,15,2,23,109,33,85,33,107,90,89,5,116,24,98,47,63,43,34,29,43,7,8,114,53,73,9,5,89,35,118,22,79,53,34,98,32,93,60,85,52,38,46,0,76,18,116,89,69,48,111,58,93,52,99,90,68,96,49,105,111,82,59,19,40,12,89,0,65,77,30,25,19,67,23,96,21,7,10,42,63,64,106,91,24,96,102,5,32,17,8,69,12,20,12,10,34,94,80,11,65,21,25,38,28,87,102,20,74,89,13,103,81,74,34,2,119,11,63,7,2,9,96,84,50,31,66,0,92,108,30,7,19,120,109,75,32,21,81,66,54,8,73,82,
47,35,82,95,53,61,32,11,117,107,24,57,33,104,69,2,60,23,88,20,41,68,35,36,53,29,59,4,9,23,72,76,118,51,30,94,12,32,4,37,66,102,39,10,19,107,113,81,2,81,19,29,56,70,90,96,80,81,78,95,14,85,17,84,17,54,13,34,87,96,115,62,31,70,105,37,118,10,13,99,18,118,113,65,104,4,82,2,116,49,70,10,64,75,6,71,16,120,93,106,76,68,30,26,53,52,101,34,75,69,18,37,115,43,26,102,22,79,49,36,45,1,22,31,61,65,94,58,93,107,74,100,37,75,108,33,77,110,102,99,119,16,48,91,74,44,74,79,58,59,22,43,101,97,15,25,45,26,82,12,3,13,14,9,67,38,88,2,115,36,95,98,29,83,27,101,13,20,107,21,47,73,72,35,58,105,118,71,81,13,77,16,21,25,83,69,110,57,93,55,75,42,6,76,71,76,75,104,78,22,40,68,52,20,47,55,67,94,38,89,40,80,67,44,59,68,6,48,119,51,61,
112,116,108,55,18,41,80,64,74,16,31,15,115,80,101,29,53,52,90,79,68,99,120,28,35,69,23,22,102,66,7,19,115,8,109,72,73,90,66,66,6,83,75,53,64,70,29,11,113,5,105,8,79,77,52,44,108,5,22,102,100,19,104,77,105,47,58,19,49,35,62,116,28,83,79,38,40,119,3,72,32,83,19,49,90,5,48,4,27,96,4,74,104,60,23,99,112,37,53,67,113,39,110,92,95,66,12,70,41,28,86,62,108,26,34,72,113,42,61,63,67,75,69,84,64,2,105,18,103,5,104,34,26,6,73,52,74,111,54,41,102,74,7,103,91,101,14,102,43,25,118,119,106,82,0,109,47,102,11,88,70,113,22,22,94,109,4,38,21,40,65,40,35,76,110,33,7,93,119,111,3,62,42,37,80,118,42,7,66,66,1,99,72,87,94,30,102,37,74,92,29,96,81,77,64,78,100,47,81,88,93,77,110,35,114,103,108,51,65,2,103,104,37,1,5,46,60,113,67,107,57,
94,40,101,37,25,76,35,94,97,100,85,64,43,30,113,25,28,4,93,93,102,26,90,32,91,59,52,55,23,39,82,49,93,107,107,49,68,65,18,112,115,89,61,86,16,56,48,54,93,94,39,20,34,12,32,35,8,71,27,70,78,7,95,3,105,98,41,64,62,48,47,91,102,59,91,54,75,12,62,56,67,110,4,48,66,84,77,45,84,14,82,79,42,85,75,12,54,48,96,4,0,50,91,104,117,120,111,85,77,112,52,40,81,51,114,2,82,45,16,51,3,52,3,42,6,23,79,9,7,73,111,80,96,56,61,57,34,106,26,59,32,55,47,12,2,54,39,49,13,0,5,70,53,114,86,7,50,24,13,24,88,70,60,33,5,30,8,8,33,46,104,80,23,95,5,23,23,66,21,83,63,83,75,51,6,31,74,72,72,6,70,54,46,76,96,117,92,84,34,103,56,11,20,117,119,69,39,92,48,84,118,45,111,114,112,87,19,61,22,100,47,105,12,44,18,4,45,36,79,94,36,
8,106,55,54,33,78,100,78,14,109,57,49,56,1,53,38,75,39,64,102,32,1,44,33,33,83,69,119,33,36,64,17,45,60,108,32,117,107,15,22,73,119,104,10,50,31,120,52,10,48,36,86,33,31,52,103,67,69,76,62,114,25,53,8,81,113,118,5,67,54,67,30,47,74,10,33,67,84,51,82,1,34,3,116,71,52,52,23,81,73,16,85,120,45,50,44,61,12,93,111,65,69,88,109,102,64,78,111,4,16,106,55,54,116,56,109,112,114,53,15,120,88,13,20,74,33,81,75,13,110,23,56,101,84,46,47,80,58,101,90,95,40,111,26,78,87,25,94,81,30,69,93,8,80,67,6,28,87,24,99,69,77,120,90,66,119,64,32,78,40,48,21,19,98,40,12,38,55,44,38,66,44,38,119,95,40,2,41,68,35,70,110,97,49,100,78,67,113,118,36,84,44,60,53,10,68,46,67,86,100,116,22,54,101,90,89,58,98,41,76,17,113,57,10,94,60,16,2,46,26,29,
40,26,62,95,103,28,94,113,96,46,86,67,40,34,42,73,41,60,19,107,71,105,42,85,2,80,70,13,103,14,78,85,33,82,9,97,31,47,60,96,112,3,120,40,12,104,51,41,80,0,6,15,92,63,79,52,44,62,59,21,100,93,59,19,9,52,116,35,86,30,17,61,105,37,107,86,106,23,28,34,88,12,83,61,22,11,119,115,10,30,43,7,1,4,48,74,70,100,44,113,3,21,77,67,9,66,14,103,82,104,36,31,82,13,19,20,6,4,117,116,51,116,34,12,51,73,76,54,77,54,13,96,15,26,67,59,22,54,83,11,104,21,79,0,79,83,74,78,87,96,43,110,54,102,70,70,70,117,25,75,3,91,106,45,65,38,83,55,79,45,99,24,25,109,100,64,13,16,72,112,104,95,18,13,48,26,69,13,15,59,73,70,44,96,103,113,81,2,53,40,120,8,104,67,12,117,22,47,8,14,95,111,33,101,41,62,97,87,70,4,75,14,12,20,1,0,87,90,69,30,76,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
33,43,105,70,47,63,26,27,40,10,95,5,111,3,103,45,0,31,9,28,88,46,100,37,19,22,114,33,45,97,90,82,42,63,25,20,92,75,17,1,77,45,119,19,103,98,19,24,36,16,84,55,75,27,86,117,36,63,11,45,119,103,105,78,10,53,50,35,0,42,95,45,95,119,64,62,50,91,58,103,103,85,100,15,116,90,110,115,112,5,40,51,15,78,23,94,96,101,88,47,117,84,10,41,71,43,69,95,85,33,11,100,71,12,96,79,98,119,13,1,20,75,61,63,38,39,94,90,45,73,28,20,110,16,95,104,104,79,94,107,7,97,51,5,109,49,0,75,87,30,29,16,19,113,75,78,90,110,12,14,120,51,81,110,28,74,96,54,48,41,77,72,54,74,26,82,32,47,10,3,24,35,54,6,64,99,73,31,16,105,23,30,23,82,43,6,76,38,40,119,36,77,56,65,10,65,36,46,111,73,24,25,20,46,64,83,69,43,10,88,65,29,0,52,19,47,78,78,40,53,101]);

G<x,y>:=MatrixGroup<231,F|x,y>;
print "Group G is 3.M22 < GL(231,GF(121))";