/* www-ATLAS of Group Representations. L2(16):4 represented as 60 x 60 matrices over GF(25). */ F:=GF(25); x:=CambridgeMatrix(3,F,60,\[ 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, 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, 0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 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14,13,12,15,19,23,4,3,17,15,7,4,17,23,20,21,10,13,2,5,12,21,11,11,3,17,14,0,20,5,19,21,3,10,22,22,7,10,6,18,12,1,0,23,24,18,9,0,10,17,13,5,11,14,11,0,1,5,11,20, 5,16,8,18,21,1,13,20,10,4,14,8,9,4,0,22,2,13,2,10,9,22,10,13,5,14,17,16,16,7,11,7,7,2,24,23,18,13,10,4,24,23,23,3,2,1,18,24,12,13,17,17,18,11,2,4,4,1,7,16, 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, 1,12,19,17,23,13,2,18,10,16,10,3,22,18,12,13,14,24,5,15,3,23,2,17,5,13,20,23,1,9,2,14,0,2,10,3,4,5,10,16,18,5,16,6,24,4,13,19,5,11,1,23,16,14,1,3,6,22,14,7, 4,24,0,4,13,16,24,23,20,4,8,16,6,9,0,18,3,18,12,6,24,0,21,13,7,2,6,14,7,16,23,12,2,4,9,18,24,9,14,20,14,4,7,18,16,6,6,3,9,4,1,13,21,20,24,2,9,4,20,10, 17,2,19,23,9,19,14,23,10,15,22,15,4,9,18,24,0,24,11,2,18,9,3,11,22,2,18,21,21,7,2,16,21,3,18,18,3,3,17,17,9,23,7,6,12,4,5,5,21,10,21,22,22,12,16,1,20,10,7,18, 21,21,19,17,2,11,14,15,1,15,24,6,13,14,21,15,12,6,0,4,7,23,21,16,13,2,23,22,12,20,9,14,11,23,10,17,9,4,17,9,8,17,9,3,0,18,21,6,11,2,16,0,11,2,2,17,15,23,11,19, 15,1,4,4,16,0,3,24,8,10,3,19,11,4,7,0,16,24,22,17,6,22,0,3,12,5,13,5,10,6,4,18,20,5,20,7,24,3,12,7,20,19,21,5,7,10,3,15,6,11,15,9,19,22,21,2,5,16,17,6, 16,15,18,8,24,18,3,19,13,23,6,20,7,2,6,7,13,14,5,5,9,12,4,2,8,11,0,1,18,3,10,9,4,22,23,12,5,21,16,0,18,16,2,17,10,10,18,10,1,9,0,16,8,21,18,16,15,24,23,13, 21,21,9,8,10,19,8,22,21,22,22,8,13,21,13,21,10,15,0,9,13,14,11,14,11,3,14,20,11,10,4,24,10,4,5,23,2,7,13,1,3,17,10,13,21,9,24,21,0,19,5,7,21,20,2,6,24,4,15,24, 17,20,23,21,23,6,12,24,19,4,17,24,14,18,0,8,23,12,3,12,6,0,20,2,24,9,19,18,15,9,18,23,9,5,0,4,11,3,18,21,20,17,9,14,5,3,4,8,19,1,3,13,20,0,12,6,2,1,7,18, 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, 11,24,5,11,15,15,10,17,4,18,5,13,20,24,12,14,0,1,23,8,22,14,24,8,8,9,23,5,24,12,6,20,23,24,22,9,10,1,24,14,11,24,18,22,10,12,20,9,3,22,14,9,15,0,18,10,19,18,10,12, 4,7,21,19,22,10,7,1,7,24,24,1,12,10,14,20,7,13,8,11,5,9,4,3,9,21,21,14,14,3,17,5,4,0,12,3,2,16,7,23,3,23,11,14,22,21,21,19,7,14,8,24,18,17,2,21,16,19,0,9, 21,7,2,0,0,14,5,2,16,16,0,17,9,3,12,13,5,11,17,17,22,15,10,13,16,4,1,8,15,1,3,18,10,6,14,3,11,6,10,4,2,0,18,8,21,1,3,5,23,23,12,15,13,11,9,19,16,14,1,0]); G:=MatrixGroup<60,F|x,y>; print "Group G is L2(16):4 < GL(60,GF(25))";