/* www-ATLAS of Group Representations. 4.M22 represented as 56 x 56 matrices over GF(121). */ F:=GF(121); x:=CambridgeMatrix(3,F,56,\[ 0,85,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 47,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,85,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,47,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,85,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,85,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,47,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 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97,35,110,42,24,60,67,112,33,15,63,58,29,91,92,63,67,54,116,91,62,119,58,93,85,111,4,3,64,65,7,39,87,8,107,37,10,18,41,25,51,72,12,85,77,19,57,114,119,68,107,104,62,25,74,54, 41,13,5,12,39,52,20,46,83,12,33,50,51,26,86,21,115,112,31,80,64,42,103,71,7,115,90,14,110,32,87,109,106,57,56,83,17,112,24,48,27,99,23,34,29,57,42,88,53,24,95,87,63,110,89,52, 117,29,80,30,81,95,101,82,32,10,109,113,71,24,100,20,56,9,22,102,84,8,44,10,38,76,89,28,101,79,67,106,32,0,59,87,29,105,82,110,120,100,17,96,56,30,97,51,62,119,56,79,16,74,20,80, 20,61,61,26,49,82,100,56,113,66,1,35,26,11,86,20,50,61,86,21,66,97,92,68,12,1,51,11,31,34,63,37,3,36,64,30,27,89,36,26,85,88,22,7,15,2,116,28,19,25,62,3,29,54,118,52, 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, 71,81,107,88,58,112,85,97,57,85,17,116,77,99,98,35,12,87,17,14,39,24,79,33,5,12,49,113,53,86,53,63,45,88,46,105,78,56,67,62,100,14,63,116,73,114,116,110,6,49,1,100,93,87,66,87, 115,3,67,106,108,15,59,102,85,109,81,58,57,89,40,115,33,52,95,15,14,17,119,78,60,39,48,83,8,71,63,49,77,70,100,38,5,57,34,83,67,103,21,112,80,26,35,107,21,22,19,65,22,116,41,57, 40,11,104,116,5,108,67,112,37,110,9,25,67,57,56,62,91,111,95,94,9,119,85,47,108,76,84,57,118,84,21,7,26,91,56,65,119,8,76,53,18,19,89,96,14,1,120,28,85,24,89,119,79,21,97,69, 70,114,20,65,100,36,43,96,23,7,26,25,43,93,48,67,33,67,93,52,118,72,85,77,47,63,7,120,24,84,3,55,32,111,86,69,84,83,31,30,11,118,82,36,49,24,5,16,40,104,86,71,27,40,19,110, 47,43,54,57,85,108,67,94,90,34,46,9,0,15,90,36,26,44,27,117,87,75,19,106,33,80,9,93,59,116,105,109,66,104,41,82,85,1,68,49,43,71,28,103,28,30,45,26,100,65,0,1,37,71,11,39, 112,115,50,42,24,26,21,79,118,16,117,103,43,33,7,91,14,97,84,47,40,83,66,92,39,119,51,56,53,62,28,18,45,118,27,73,15,28,27,55,2,117,61,44,118,30,79,65,30,94,78,55,7,28,76,22, 37,29,28,102,86,42,81,10,56,109,82,70,41,57,24,19,89,19,0,104,27,39,24,72,91,48,19,40,86,85,32,77,11,11,51,85,22,78,46,76,37,71,2,53,30,65,11,0,40,22,19,20,47,69,103,4, 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, 7,34,1,69,30,26,38,108,19,80,63,90,78,4,98,74,70,73,114,87,83,111,120,85,117,98,51,52,17,78,96,40,110,8,68,50,15,57,29,78,46,19,52,100,4,113,31,5,17,18,27,48,36,51,120,53, 95,53,106,48,120,100,79,5,71,118,72,110,20,20,57,31,31,29,93,25,96,103,26,90,0,117,31,94,76,115,98,6,17,6,80,89,75,61,26,109,61,54,23,13,52,25,69,18,113,67,71,96,52,64,4,102]); G:=MatrixGroup<56,F|x,y>; print "Group G is 4.M22 < GL(56,GF(121))";