/* www-ATLAS of Group Representations. 6.L3(4):2a 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, 0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 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0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 20,6,12,8,9,6,3,6,1,13,10,13,7,5,5,18,7,19,9,0,5,22,3,9,21,7,9,18,15,2,18,21,6,6,3,23,1,12,14,12,13,12,5,21,13,5,22,16,20,13,1,5,24,7,20,12,5,14,13,12,9,16,9,16,13,23,19,18,9,3,10,10,2,4,9,0,16,6,8,1,8,19,4,18,3,16,16,7,4,15,14,20,4,22,1,8,6,11,6,19,5,0,22,17,19,8,4,14,19,15,2,13,6,11,1,20,21,24,5,8, 2,17,3,13,23,19,10,12,4,20,17,19,11,10,6,15,13,16,1,20,23,20,12,12,7,2,7,0,16,13,12,23,7,22,3,5,14,4,2,12,10,24,13,1,8,1,21,1,2,19,23,7,21,15,4,5,0,10,9,5,0,4,20,9,9,11,1,17,23,15,7,6,13,12,21,21,1,5,11,12,0,3,12,22,0,13,10,13,0,24,12,9,9,18,24,23,23,17,17,18,18,9,22,6,14,19,3,11,14,5,3,21,8,22,18,2,14,9,12,14, 9,6,24,14,3,9,7,20,19,22,11,6,20,19,8,17,17,0,6,24,1,13,13,6,0,10,16,9,21,0,17,23,22,1,4,23,19,3,2,21,23,20,19,6,18,21,19,9,12,2,9,2,11,18,11,23,4,22,14,23,10,8,22,16,18,10,23,14,18,6,16,22,1,17,18,19,11,21,11,20,24,22,1,23,14,5,7,24,11,5,15,7,9,9,4,1,18,21,6,20,10,19,17,21,12,2,15,19,9,8,2,8,0,9,10,11,0,12,6,12, 18,18,15,14,23,17,18,22,15,4,17,12,0,9,0,23,3,2,6,6,12,23,18,12,4,13,11,22,23,1,14,6,22,13,7,5,5,16,0,15,0,5,13,6,24,23,15,12,14,21,4,23,1,16,22,4,20,16,8,18,10,8,3,4,13,7,8,6,14,19,15,15,13,24,12,22,15,2,10,2,3,18,1,14,10,4,20,21,10,22,17,4,9,17,4,22,8,18,3,18,15,13,15,7,1,1,21,20,17,8,6,5,5,1,9,6,15,3,5,4, 9,11,16,16,5,14,18,15,8,24,17,23,5,4,17,7,6,5,8,12,14,2,11,19,13,2,8,15,17,3,0,15,3,0,19,20,10,1,0,10,15,7,3,13,12,11,10,3,0,20,9,4,16,15,23,2,5,16,17,11,3,23,21,15,11,21,1,19,24,3,10,23,9,1,1,5,22,18,2,13,3,9,1,0,16,10,9,24,1,21,15,16,0,10,11,10,21,23,12,3,0,24,19,12,15,13,19,2,18,11,7,9,13,19,10,23,3,16,13,0, 5,6,13,16,2,5,12,3,11,3,4,0,18,16,13,18,18,11,8,8,17,20,21,24,5,18,10,13,1,8,23,4,19,1,0,14,16,4,21,13,5,24,24,5,19,23,3,6,9,18,4,2,8,19,9,24,22,16,18,6,4,23,21,21,16,8,2,4,7,11,12,16,24,16,5,23,13,16,17,14,21,11,13,10,18,22,0,20,1,3,24,18,15,20,5,7,23,3,14,23,18,20,15,22,7,2,19,12,17,17,5,11,5,21,4,4,0,13,2,18, 10,13,9,0,7,16,4,21,22,8,0,13,11,2,5,13,7,5,12,15,23,4,22,14,22,1,21,21,0,12,0,9,0,2,16,0,11,5,6,18,11,24,12,8,9,13,7,23,9,6,7,9,24,9,1,4,5,11,18,15,14,24,12,9,5,8,15,2,3,15,10,6,19,13,6,16,13,9,4,16,20,1,9,7,1,12,20,5,2,8,7,20,0,22,4,18,8,13,13,9,19,7,18,13,0,23,14,5,5,1,16,13,6,13,23,16,19,20,17,6, 15,16,12,10,11,17,3,11,5,6,18,11,24,2,0,0,14,18,2,9,9,12,6,9,11,12,24,23,16,4,3,0,5,21,17,0,4,24,3,4,6,22,4,5,17,23,12,3,21,9,14,12,23,0,0,11,1,4,20,24,10,3,4,22,19,12,6,7,0,2,0,23,3,9,14,11,11,15,24,4,22,20,24,5,16,13,17,10,18,17,14,21,0,11,2,1,1,21,4,1,12,24,19,23,14,16,0,15,18,12,22,22,17,15,4,10,16,12,18,23, 7,7,10,11,1,14,8,4,9,2,24,7,20,22,2,24,1,17,13,3,13,18,5,22,13,0,23,8,18,21,23,3,7,0,17,6,3,15,8,24,7,12,23,2,0,10,7,12,5,24,12,23,2,24,0,2,12,17,6,20,23,14,11,9,16,4,15,10,1,0,21,8,23,2,4,10,15,20,4,3,10,22,7,4,1,22,0,5,19,11,13,18,16,24,9,2,10,1,2,7,8,7,24,22,7,22,23,10,22,4,16,14,2,6,15,0,23,18,0,21, 13,15,7,16,8,2,3,6,4,0,22,2,13,12,8,18,10,15,8,18,2,1,2,1,20,18,24,2,16,16,9,7,7,19,11,17,18,12,11,1,9,15,22,12,18,6,1,3,24,6,4,4,4,20,5,9,5,14,17,17,22,22,7,12,2,22,20,12,0,13,4,20,9,22,2,24,8,22,15,22,14,19,19,2,1,8,2,7,23,23,22,0,12,0,15,14,11,14,3,11,24,2,1,7,3,13,3,19,1,14,4,10,7,11,24,21,21,10,13,18, 0,24,3,18,11,3,17,10,9,18,19,16,9,12,4,6,5,1,18,7,3,13,6,5,16,14,15,11,7,19,24,24,13,19,16,21,15,13,10,8,14,21,16,5,22,4,6,13,20,7,13,15,3,10,10,5,24,1,23,21,7,12,21,18,7,21,23,6,24,24,0,2,9,18,23,20,21,9,0,16,9,10,14,1,8,17,5,11,20,5,1,22,8,2,16,8,4,22,18,11,13,2,14,19,13,19,15,1,7,18,20,10,13,17,19,3,24,2,12,6, 12,1,6,3,1,15,12,22,7,18,11,19,13,18,23,1,23,24,5,18,10,22,6,20,1,19,18,13,20,0,10,6,21,4,14,2,14,24,18,16,23,4,1,8,21,0,18,12,17,16,3,18,2,10,6,20,2,4,18,10,1,15,7,24,14,0,5,10,11,1,24,6,1,24,20,21,24,22,20,8,8,5,19,4,12,8,18,14,24,14,19,20,17,23,21,0,1,15,16,17,19,4,12,22,16,5,17,12,6,4,23,10,10,14,24,20,23,3,19,22, 3,15,3,21,8,19,5,2,6,6,4,15,22,19,22,2,12,7,12,22,0,16,15,1,15,12,18,17,5,8,19,5,7,0,3,24,4,2,4,3,16,1,6,4,10,12,7,10,21,4,24,24,17,6,0,19,17,3,18,3,8,11,8,2,13,22,12,23,18,15,3,7,14,2,16,24,7,2,4,21,8,17,21,16,12,19,7,1,12,19,15,0,13,19,16,12,8,0,16,16,0,5,15,4,0,8,7,4,18,15,24,19,9,0,10,16,5,2,9,6, 19,15,3,3,15,19,10,19,11,17,15,17,20,8,11,4,13,7,13,12,9,3,17,13,10,10,6,21,23,7,21,8,22,20,4,17,7,18,19,22,15,24,12,17,20,0,24,20,14,16,19,20,7,1,12,15,19,11,13,14,18,12,6,8,7,10,9,13,2,5,8,11,22,3,22,23,23,0,11,16,11,18,4,19,14,2,1,10,14,2,19,22,20,3,5,16,23,20,16,0,10,19,11,10,2,11,12,22,16,5,0,1,10,5,14,18,4,10,22,19, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 20,16,6,23,4,14,22,13,20,21,17,2,6,24,7,11,13,14,6,1,14,18,21,21,4,8,19,23,8,12,12,2,8,6,8,17,6,1,18,23,0,14,6,0,12,3,23,10,15,22,13,11,13,12,5,10,20,3,5,16,21,11,14,4,15,15,11,4,11,3,14,14,4,14,9,0,22,15,20,10,15,11,21,23,17,3,24,13,7,8,6,24,5,15,3,17,18,1,16,12,24,21,14,6,10,1,11,5,2,11,6,19,10,21,7,16,7,2,5,3, 12,3,11,10,2,1,24,14,18,6,1,13,10,6,4,13,10,13,17,9,15,22,9,17,18,22,3,14,2,12,2,0,4,21,19,2,16,7,13,21,7,5,6,22,20,4,21,21,8,12,4,6,4,18,22,11,21,21,14,14,0,7,24,7,8,22,14,13,2,24,15,8,14,19,3,1,1,19,5,24,6,13,11,4,15,22,23,6,7,13,24,11,23,5,8,15,11,9,3,1,2,14,4,6,10,0,17,7,9,9,3,17,13,5,20,4,2,6,1,7, 13,6,12,8,16,9,1,23,20,4,15,4,7,23,9,6,13,13,4,6,22,12,4,0,7,4,16,13,21,4,17,10,24,9,8,1,7,6,20,1,7,16,12,6,8,15,1,9,9,23,22,17,6,10,0,16,17,1,22,11,14,3,17,14,23,9,10,23,16,1,15,7,14,15,0,18,9,1,2,2,21,3,13,10,3,19,19,0,13,15,19,10,3,24,23,15,8,21,8,11,15,1,21,15,5,22,4,17,24,22,1,24,1,24,13,15,12,19,20,19]); G:=MatrixGroup<120,F|x,y>; print "Group G is 6.L3(4):2a < GL(120,GF(25))";