/*
www-ATLAS of Group Representations.
6.M22 represented as 174 x 174 matrices over GF(121).
*/

F<w>:=GF(121);

x:=CambridgeMatrix(3,F,174,\[
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63,96,26,0,52,56,2,23,50,94,80,108,32,83,79,100,90,42,25,77,31,69,16,81,103,60,104,77,80,107,61,46,109,41,77,39,30,56,58,113,62,114,45,69,95,14,92,10,36,6,103,62,52,2,49,110,97,12,108,103,8,92,49,83,60,27,90,56,79,85,113,2,113,116,109,100,116,13,45,41,6,87,58,56,59,3,13,112,87,8,46,51,49,89,67,113,18,91,114,5,65,70,68,29,22,114,109,97,84,29,115,93,29,18,70,56,94,32,27,105,63,21,55,60,114,53,119,115,42,54,88,85,97,74,115,21,14,67,13,111,57,51,90,118,25,62,37,30,83,0,104,83,104,73,85,34,119,120,87,20,14,47,101,34,91,20,111,75,38,79,13,64,82,95,
4,17,97,7,91,115,28,101,3,50,67,110,20,5,69,86,108,89,31,84,97,21,51,0,5,87,66,35,16,8,2,110,20,116,76,108,119,106,25,60,10,69,113,66,25,110,104,45,18,63,90,39,85,99,109,0,71,118,70,31,35,37,77,85,103,117,46,100,37,7,101,42,53,52,24,114,109,67,19,94,115,105,58,20,43,51,101,71,67,99,66,12,15,18,33,9,45,50,69,70,62,103,88,62,11,55,90,107,52,5,35,91,79,115,86,45,97,47,75,111,53,98,7,37,35,92,97,4,16,1,51,23,10,103,90,80,109,17,110,13,81,6,105,8,37,84,58,15,6,120,24,73,10,97,33,93,109,104,11,62,112,118,77,45,109,42,7,118,2,40,71,4,70,52,
29,82,3,25,96,32,34,27,116,95,106,109,15,43,85,113,78,84,104,57,4,68,32,59,35,11,102,30,71,11,11,35,47,27,68,48,88,23,13,102,27,3,97,59,109,103,49,16,69,105,39,51,80,79,31,117,40,49,47,85,98,111,64,74,45,50,58,101,60,35,24,68,61,1,56,66,110,110,57,14,80,82,42,52,46,112,110,34,50,34,98,39,15,48,83,14,117,92,17,10,110,21,114,89,1,67,48,63,107,101,7,69,30,119,41,44,87,67,112,111,29,117,6,55,73,66,94,74,106,99,75,66,88,45,101,36,79,68,89,55,34,118,110,31,4,79,54,110,92,105,60,35,81,27,29,47,43,88,62,29,115,109,29,54,72,7,20,66,117,81,21,4,63,58,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
24,2,56,39,68,5,108,82,18,79,88,0,120,40,104,15,115,4,22,41,116,16,36,15,52,110,73,28,27,44,87,70,35,45,9,0,57,21,81,22,7,110,41,33,92,57,81,40,15,104,52,0,51,32,40,2,24,110,72,61,62,61,42,14,94,53,31,75,107,93,32,50,89,54,76,81,114,22,94,81,45,74,24,96,119,30,98,80,105,9,106,54,27,91,118,4,88,25,61,17,15,11,77,33,95,79,112,64,56,0,14,84,9,95,19,63,90,9,44,31,108,52,11,46,102,57,63,82,48,105,43,36,101,18,9,19,53,37,63,16,61,109,93,99,17,99,8,40,4,38,21,101,45,27,49,60,67,54,28,13,89,68,30,20,81,44,57,35,47,114,21,89,100,40,
55,60,1,80,14,46,79,54,37,70,77,56,29,104,82,109,101,105,19,27,80,63,61,62,103,109,22,93,50,97,119,8,63,43,9,44,99,49,75,75,55,73,99,112,22,14,90,119,69,46,84,17,76,31,7,87,40,76,16,36,33,59,85,65,59,28,78,35,24,64,50,31,51,67,78,116,99,59,18,68,108,26,74,114,47,12,104,120,101,21,90,41,98,52,48,113,102,54,61,86,31,106,50,0,3,8,115,10,119,51,84,42,0,30,66,112,36,12,16,17,51,22,78,80,109,10,87,110,76,15,100,93,9,5,106,4,9,110,110,49,27,0,15,60,19,16,45,119,68,85,91,63,31,69,110,85,84,37,116,29,101,21,67,53,34,26,21,55,98,69,92,107,54,55,
22,45,55,66,60,115,94,90,119,90,115,107,45,108,96,73,83,105,69,93,98,117,71,67,45,116,26,117,37,93,105,115,17,112,93,119,61,60,17,20,106,84,119,0,44,30,102,10,53,113,27,119,88,0,107,46,28,19,25,12,1,12,75,46,49,26,66,2,42,79,43,61,39,37,0,48,119,56,69,7,91,103,111,62,37,52,43,12,14,31,57,17,7,45,94,78,10,118,24,16,6,42,89,0,92,45,117,39,99,74,48,22,60,92,0,44,103,78,111,2,119,95,52,13,52,50,34,65,44,104,120,56,44,101,120,1,74,18,19,81,78,68,61,42,50,99,77,40,21,10,113,44,43,114,20,75,47,103,35,36,38,34,47,119,34,42,36,29,82,86,60,4,35,100,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
108,47,96,88,75,5,74,6,88,98,112,27,38,67,31,107,25,3,43,74,87,74,40,52,4,106,106,13,99,11,60,43,103,13,16,30,107,33,46,32,109,70,10,49,88,81,48,38,107,116,37,81,42,67,1,7,50,65,11,71,66,9,119,35,65,88,2,55,62,97,107,68,85,28,120,23,33,45,54,7,69,99,55,33,114,70,50,59,115,0,97,28,37,22,51,91,95,3,5,90,113,3,33,45,23,26,30,107,35,52,45,96,30,11,18,77,58,38,72,46,63,38,99,87,56,50,97,11,60,39,90,29,68,36,7,13,38,30,71,95,24,33,93,115,1,64,28,57,58,74,82,51,59,102,24,112,49,18,22,14,0,50,74,55,109,53,111,22,71,90,31,74,68,105,
51,25,65,87,104,57,57,60,20,106,24,16,89,39,91,16,69,0,58,20,105,7,5,8,3,44,89,76,83,114,95,90,0,105,74,32,109,117,51,94,110,54,28,52,104,14,66,48,112,41,107,93,20,106,48,93,60,32,36,41,57,81,18,90,75,115,8,29,30,79,73,33,114,90,108,68,100,57,120,52,25,94,50,79,66,13,113,13,26,0,37,108,76,120,5,34,8,101,92,6,72,28,85,104,28,4,65,97,87,94,106,115,61,85,7,2,18,89,19,17,29,114,80,48,4,54,74,110,26,81,51,0,41,68,19,9,101,80,102,44,35,28,89,103,19,41,71,106,60,17,8,105,10,87,119,64,27,24,41,73,57,84,32,30,53,21,6,104,120,36,22,47,105,67,
120,93,50,51,38,15,61,85,24,29,81,109,19,4,22,100,52,70,73,1,23,16,98,66,118,91,111,92,48,117,18,98,95,39,63,40,38,13,42,35,73,13,4,67,12,18,18,115,55,10,7,62,77,54,37,106,20,45,17,76,103,116,111,89,89,104,16,32,12,96,16,36,92,22,33,109,34,103,1,104,39,40,101,53,1,23,23,100,13,17,101,10,14,81,116,66,78,67,97,17,21,16,33,7,22,100,54,90,66,104,104,96,109,77,49,27,55,1,107,53,101,72,93,18,70,72,28,120,96,59,26,25,13,58,36,49,42,101,120,45,94,103,79,13,106,81,48,13,56,47,85,100,110,20,38,16,62,38,58,41,114,77,54,117,104,35,114,108,37,43,31,103,118,15,
98,107,23,78,64,21,39,120,43,4,3,63,69,54,41,18,109,111,19,14,110,78,112,117,77,62,79,10,79,96,95,88,17,53,41,106,58,6,76,11,63,81,74,92,35,9,93,15,81,72,43,15,106,78,39,18,7,118,24,61,54,83,99,68,117,101,38,103,71,21,116,109,1,99,104,78,17,54,119,102,77,66,56,63,74,85,48,13,59,55,37,96,57,116,65,37,81,77,84,81,20,30,33,119,44,110,41,45,92,7,0,104,79,89,49,92,118,72,111,42,77,24,88,15,1,65,7,16,57,90,12,12,60,46,30,93,1,19,7,55,36,55,41,107,94,111,57,30,83,105,79,0,110,66,24,17,37,21,35,72,40,63,37,116,90,59,108,113,82,1,119,28,61,4]);

G<x,y>:=MatrixGroup<174,F|x,y>;
print "Group G is 6.M22 < GL(174,GF(121))";