/* www-ATLAS of Group Representations. M12:2 represented as 120 x 120 matrices over GF(25). */ F:=GF(25); x:=CambridgeMatrix(3,F,120,\[ 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, 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, 0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 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5,22,18,14,8,9,13,23,9,24,8,12,10,20,9,11,5,8,24,4,13,19,3,4,19,1,8,5,12,4,5,11,24,21,12,2,16,16,16,12,17,5,2,0,24,21,14,15,24,23,16,8,4,2,24,24,5,2,23,19,24,22,3,12,20,2,14,8,12,21,19,3,0,14,13,15,15,7,8,0,0,21,20,12,4,8,1,17,1,7,16,8,9,4,5,7,0,3,21,18,10,20,15,3,8,0,16,19,6,17,3,23,23,19,22,24,15,14,3,13, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 8,3,19,19,17,8,18,15,14,19,23,10,0,0,6,10,10,3,6,7,22,22,22,13,14,15,17,13,4,12,11,6,17,17,24,13,19,14,10,0,16,24,15,8,24,11,10,14,16,8,4,15,11,21,6,15,0,2,21,1,22,17,7,24,16,21,17,23,20,9,8,9,24,12,23,19,19,5,22,1,9,4,24,1,6,0,14,17,15,19,3,11,0,6,15,22,8,2,3,9,5,19,8,13,19,5,20,14,3,3,22,13,12,17,18,24,1,5,17,18, 17,13,22,21,0,20,21,21,16,0,19,24,9,1,2,18,3,23,6,8,19,11,0,3,7,12,10,23,17,18,19,9,9,19,0,5,4,13,6,1,5,2,7,14,2,12,7,18,20,3,15,21,1,17,3,18,7,12,22,4,20,4,3,2,17,12,22,2,18,11,10,11,18,15,16,16,24,22,5,19,9,7,3,18,19,6,6,18,15,18,23,3,5,18,20,17,0,2,18,16,22,17,8,9,7,8,24,7,24,1,10,20,14,5,20,24,20,18,5,2, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 20,8,22,12,1,18,9,6,5,19,18,20,23,15,7,10,1,0,7,17,15,23,8,13,22,14,13,2,19,10,20,10,7,9,17,8,3,23,16,20,23,10,14,19,19,9,3,15,22,4,24,12,23,12,17,7,5,18,22,18,0,5,17,5,7,6,9,10,4,21,5,9,14,11,0,8,9,17,1,23,2,3,16,14,23,9,7,6,3,9,1,20,16,22,3,5,12,6,21,23,3,15,8,3,7,19,1,24,2,21,21,6,10,14,7,0,22,16,22,17, 24,17,22,18,21,6,21,23,21,20,4,15,10,19,17,2,1,1,18,2,8,0,13,7,20,14,23,13,12,4,3,19,4,22,11,13,22,5,16,3,16,22,24,6,22,10,1,22,16,7,5,14,14,6,23,0,23,15,20,20,19,2,15,21,11,13,19,17,16,5,19,0,1,12,21,16,12,18,7,5,24,11,9,6,22,20,17,8,5,14,5,17,23,16,20,24,0,14,16,1,11,4,0,3,13,5,1,24,5,8,22,9,21,10,2,2,11,16,17,5, 20,23,12,14,24,20,23,18,6,3,20,9,23,9,19,18,22,3,21,20,3,20,0,20,8,12,0,12,4,19,11,24,17,15,6,18,17,6,12,3,10,8,0,12,1,15,18,12,5,4,7,24,9,19,24,8,17,7,9,23,2,18,8,9,11,23,4,24,20,24,16,23,0,20,0,3,11,16,16,20,5,12,15,4,10,13,21,21,17,13,1,19,7,6,0,4,0,24,1,4,4,4,7,14,1,18,19,13,11,1,19,1,6,0,19,6,9,10,3,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 8,24,13,18,22,14,9,11,14,13,14,23,22,11,14,24,2,3,2,13,17,23,5,14,20,21,15,24,5,14,20,4,5,3,16,4,23,9,17,14,1,4,9,2,7,22,20,6,10,8,10,10,21,8,23,2,23,1,14,4,17,4,22,13,0,15,1,0,15,22,12,19,7,12,15,19,22,3,3,19,0,21,3,3,14,23,12,14,24,24,7,13,16,13,20,12,2,21,15,4,24,11,14,3,4,21,19,15,10,19,15,1,22,6,7,5,18,18,0,13, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 3,12,3,0,20,11,19,5,19,2,19,20,4,13,17,13,13,2,4,22,21,0,16,3,5,12,6,11,12,16,5,16,23,12,16,15,20,14,23,21,23,13,4,15,4,21,17,12,6,12,1,6,1,5,4,14,18,6,21,1,13,11,23,2,0,23,10,15,5,21,16,6,23,2,20,5,17,4,13,23,23,22,19,21,24,23,4,6,0,9,5,4,22,9,14,19,2,16,10,2,13,21,10,1,14,1,0,24,10,18,10,2,3,9,8,11,21,18,19,24, 17,21,19,1,17,6,0,11,0,23,15,14,3,7,6,11,24,11,0,18,19,11,5,6,12,23,24,19,8,15,8,7,8,14,9,1,15,6,0,12,14,18,12,16,6,5,8,10,24,11,4,1,24,3,9,24,6,13,2,7,19,14,15,5,12,3,20,20,24,13,19,8,6,13,12,17,15,19,0,4,8,14,7,3,7,12,14,16,15,15,5,7,16,1,11,3,14,4,20,5,24,24,4,2,1,10,14,20,11,21,24,11,13,10,9,23,17,21,10,9, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 11,8,13,11,9,24,6,11,18,23,22,6,2,19,5,11,21,15,4,14,16,21,0,4,10,5,7,23,21,6,0,13,11,15,2,8,21,21,2,9,17,14,11,4,3,0,5,2,14,20,21,19,10,22,9,23,5,23,13,8,15,2,0,21,9,24,16,23,2,0,13,4,22,21,17,9,24,17,6,5,0,8,0,14,11,23,0,24,4,8,18,7,4,6,2,11,21,20,9,5,23,1,10,4,9,5,20,24,1,23,15,21,24,14,21,23,8,7,22,13, 13,12,17,1,4,12,18,17,6,4,7,4,0,7,8,1,5,20,15,16,10,21,8,11,14,15,22,5,4,11,13,3,23,11,14,23,4,0,9,3,21,14,7,13,22,6,10,17,2,4,2,22,11,15,24,24,22,2,13,10,5,13,0,10,24,21,19,1,2,9,15,0,0,2,15,13,6,10,21,5,22,1,14,23,8,1,21,10,24,21,1,7,0,16,19,21,9,9,19,11,15,4,11,7,1,1,20,10,6,24,18,1,21,19,13,6,18,7,20,24, 10,6,5,5,12,10,5,6,12,10,11,20,14,21,12,12,17,1,14,15,15,12,10,19,10,1,15,23,20,9,19,23,19,8,15,3,22,0,13,9,6,2,9,8,12,8,20,4,5,21,6,23,8,4,24,20,0,16,3,6,14,0,10,23,15,0,22,2,11,6,4,18,7,11,2,23,21,12,13,0,12,2,1,6,8,5,14,10,11,11,5,11,3,15,20,11,7,15,23,22,12,11,23,15,1,5,3,23,2,12,15,2,7,24,17,18,14,8,18,18, 1,7,21,15,14,0,18,5,12,6,1,19,22,23,17,5,7,9,12,2,22,23,2,7,5,4,11,8,20,6,13,24,1,10,2,10,10,9,2,21,17,9,16,24,9,19,10,21,11,11,17,22,0,1,20,9,20,20,5,14,7,0,24,1,17,8,19,3,10,17,9,2,5,12,18,7,9,13,6,11,5,23,12,17,5,22,7,22,6,8,8,8,5,17,11,3,3,3,24,23,4,20,4,7,4,24,15,16,19,13,13,11,5,4,1,5,12,3,20,17]); G:=MatrixGroup<120,F|x,y>; print "Group G is M12:2 < GL(120,GF(25))";