/* www-ATLAS of Group Representations. 6.M22 represented as 66 x 66 matrices over GF(121). */ F:=GF(121); x:=CambridgeMatrix(3,F,66,\[ 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, 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, 0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 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65,21,40,4,18,92,23,96,17,75,11,62,4,54,55,32,69,45,5,75,93,60,36,48,85,48,56,55,45,42,27,21,16,4,31,49,117,116,68,46,27,97,108,12,33,83,39,22,105,29,11,35,101,108,39,79,12,78,17,58,81,35,78,53,108,111, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 37,79,69,23,27,16,80,110,7,107,64,5,42,92,75,15,46,92,33,79,106,73,19,93,91,70,39,85,21,86,38,95,108,56,58,103,105,40,92,25,102,111,20,51,104,30,85,54,89,20,74,112,61,115,105,104,5,89,26,54,39,83,55,32,61,92, 4,107,40,76,80,108,81,106,100,60,20,33,6,52,52,4,15,90,52,5,15,29,93,50,33,2,110,5,41,53,40,85,57,58,117,31,15,90,23,44,92,41,109,98,5,74,19,118,110,104,84,107,43,105,13,7,105,11,34,57,5,4,3,64,92,51, 100,95,64,84,20,79,13,120,51,14,39,38,74,50,67,8,44,82,76,71,98,82,2,5,106,70,45,85,33,76,41,8,51,56,78,38,14,42,46,64,117,30,58,73,39,44,37,98,116,28,56,116,63,76,43,46,98,104,114,23,24,40,84,89,16,101, 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, 20,118,10,15,100,33,56,120,85,8,106,103,28,107,100,52,49,61,50,90,28,27,46,78,54,84,81,118,22,97,63,31,78,9,34,18,28,15,70,102,64,81,17,80,3,42,40,74,63,98,23,36,71,28,51,11,2,88,21,30,104,21,105,32,6,55, 43,4,93,110,98,9,0,71,14,44,98,84,11,104,78,17,88,53,54,82,116,76,107,58,3,48,70,67,4,100,50,87,108,104,21,66,51,29,23,21,54,91,10,18,104,22,43,42,89,89,114,56,86,6,21,114,12,26,20,30,97,3,72,106,10,34, 81,100,93,82,97,58,100,58,95,86,92,101,35,73,93,90,104,86,95,14,22,99,84,78,53,15,117,101,22,62,23,65,112,4,88,59,59,102,40,69,30,0,58,89,53,50,43,86,34,16,76,108,7,93,17,108,84,38,61,100,119,119,21,30,66,64, 45,43,93,48,16,81,15,37,86,75,100,113,1,88,120,105,118,88,112,86,30,82,106,31,14,108,118,67,26,91,30,9,43,17,53,57,72,81,15,73,119,54,28,99,39,22,83,1,51,93,82,96,92,23,20,86,74,59,57,46,73,41,15,1,85,34, 1,1,2,0,1,0,10,0,10,0,0,0,0,9,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,10,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 58,97,16,110,87,60,16,35,34,96,17,9,78,46,59,33,54,58,68,62,13,68,44,110,70,8,109,95,104,65,87,78,81,76,13,93,118,103,4,104,40,111,50,55,106,80,88,39,41,40,116,16,57,6,85,28,113,46,113,119,106,114,35,91,98,3, 8,40,3,70,65,22,74,8,23,112,41,119,114,80,63,22,36,118,111,7,11,61,10,105,48,11,76,43,23,18,68,21,94,40,13,52,48,110,113,52,35,62,101,107,4,102,106,81,106,110,72,71,40,16,119,90,74,16,8,5,23,2,73,12,107,25, 67,36,72,42,10,113,40,97,109,46,21,29,7,56,83,61,11,33,104,61,58,97,3,27,6,14,44,91,96,29,86,9,95,102,93,79,28,117,49,107,70,103,75,66,77,89,51,78,49,68,63,10,45,96,23,117,40,62,36,2,36,56,75,30,85,78, 89,84,108,99,91,106,101,76,108,42,33,29,63,80,41,91,32,65,30,17,82,20,26,117,20,105,80,60,110,110,87,99,45,24,19,24,4,111,50,63,17,20,81,78,2,66,39,105,63,93,66,18,73,108,57,42,15,117,9,16,113,22,85,119,25,118, 59,108,46,50,54,100,113,20,15,28,23,19,42,109,87,43,84,18,61,30,74,52,90,17,88,84,22,58,84,65,12,10,45,70,13,99,77,116,75,94,51,86,48,108,97,60,111,40,56,25,88,22,3,99,86,93,9,33,38,22,114,0,58,98,97,84]); G:=MatrixGroup<66,F|x,y>; print "Group G is 6.M22 < GL(66,GF(121))";