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