/* www-ATLAS of Group Representations. 12b.L3(4):2a represented as 72 x 72 matrices over GF(25). */ F:=GF(25); x:=CambridgeMatrix(3,F,72,\[ 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, 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, 0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 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3,13,13,4,10,19,6,20,9,16,24,7,16,18,19,13,17,18,16,2,1,18,20,3,4,13,6,10,6,5,21,9,12,17,20,18,15,17,11,14,0,2,17,17,2,0,9,3,15,21,23,19,15,3,18,6,14,0,1,15,3,12,20,18,17,5,9,0,4,2,12,2, 15,3,13,17,15,3,0,23,23,4,20,9,6,5,7,8,23,7,2,14,23,4,18,1,20,16,16,13,16,21,4,22,17,7,5,6,16,19,20,20,15,8,0,17,20,9,2,19,4,21,3,9,16,15,17,17,24,2,21,15,0,4,20,10,3,22,0,2,16,22,2,3, 20,5,10,23,12,11,14,23,10,9,4,18,16,3,24,8,17,2,7,13,20,8,20,0,8,23,12,17,10,5,19,14,18,17,4,2,18,20,24,19,0,23,16,0,22,7,0,0,16,23,12,13,9,0,16,11,1,16,10,15,16,18,18,12,7,10,12,16,14,23,14,23, 12,22,15,7,13,17,14,6,23,11,13,15,5,15,23,17,5,4,23,17,7,4,2,3,1,19,3,5,2,18,8,20,9,5,3,22,0,0,9,5,1,16,14,8,1,20,24,23,16,9,22,9,12,2,0,15,20,18,6,1,17,17,23,5,20,23,20,17,19,3,16,16, 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, 19,9,11,1,11,21,6,17,23,19,2,2,10,0,14,0,11,22,9,20,6,23,23,4,22,6,18,5,6,11,7,1,16,3,1,22,0,17,10,0,2,3,13,0,14,11,22,15,3,15,14,6,3,4,15,6,5,8,8,6,20,19,22,8,10,21,13,6,9,11,9,14, 7,24,24,11,8,24,13,1,10,12,13,1,5,8,2,7,21,13,23,17,24,15,13,3,8,20,11,11,17,14,8,10,15,7,24,5,10,22,3,24,4,19,4,8,9,11,20,4,18,9,24,4,13,3,24,7,13,19,13,12,10,0,15,15,1,23,24,19,13,7,12,21, 15,1,2,22,2,16,19,8,15,13,21,22,23,21,18,15,9,1,3,2,2,1,16,13,17,15,13,21,3,20,20,15,15,3,4,1,12,5,24,10,24,15,4,16,23,12,14,21,10,14,9,0,24,15,9,0,0,22,13,7,17,7,5,8,23,17,22,13,18,7,11,9, 9,10,9,0,16,0,10,0,0,19,0,11,8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,19,0,0,0,0,0,0,0,0,0,10,0,0,0,0,0,0,0,0,0,11,0,0,0,19,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 5,24,1,7,10,5,8,4,24,12,22,0,1,1,3,4,13,22,10,19,9,10,21,8,19,10,22,10,17,22,5,12,2,14,7,6,7,2,18,5,15,9,22,18,10,10,10,0,0,11,0,23,1,18,20,2,4,10,14,20,10,6,17,3,17,20,13,23,11,1,10,22, 2,13,11,0,18,22,19,22,22,21,10,11,14,11,3,5,21,12,6,9,15,2,7,7,1,1,10,6,11,20,3,6,13,19,17,21,17,3,14,10,3,5,6,18,6,3,19,23,2,24,5,13,14,24,17,8,23,0,10,19,13,19,22,3,2,13,17,12,24,19,0,16, 3,1,1,14,8,11,1,14,24,4,2,2,13,2,7,13,4,21,17,19,1,15,6,19,17,2,5,15,10,15,0,7,7,4,12,16,12,8,22,21,0,13,23,20,19,19,4,4,16,19,15,0,18,10,17,0,12,19,9,8,14,1,12,22,3,3,22,21,9,2,3,20, 18,0,24,11,4,6,11,11,24,22,12,1,17,11,16,5,14,11,16,22,22,4,24,24,18,10,1,4,5,13,11,17,13,5,20,23,22,11,19,4,1,13,23,22,9,24,5,6,0,6,11,17,10,5,17,14,19,24,24,23,7,6,2,15,22,14,24,10,10,8,24,0, 6,4,24,7,6,5,5,1,15,0,0,4,2,15,14,6,22,1,2,12,13,21,22,5,22,12,1,22,2,16,12,7,12,10,18,14,8,15,19,1,13,21,12,14,23,19,0,3,3,19,4,19,0,13,13,3,20,3,16,20,14,3,3,17,23,6,17,3,8,21,13,8, 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, 23,4,18,3,1,19,24,15,3,4,2,10,20,13,3,10,16,12,7,7,12,23,7,7,7,2,10,1,6,10,4,16,7,7,19,14,8,22,2,12,19,12,12,19,19,17,3,5,7,12,3,7,24,1,14,7,5,7,17,10,23,19,17,4,4,24,16,17,20,3,6,10]); G:=MatrixGroup<72,F|x,y>; print "Group G is 12b.L3(4):2a < GL(72,GF(25))";