/* www-ATLAS of Group Representations. 2.A13 represented as 32 x 32 matrices over GF(25). */ F:=GF(25); x:=CambridgeMatrix(3,F,32,\[ 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, 4,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 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, 0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,4,0,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 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, 0,0,0,4,0,0,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 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, 0,0,0,0,0,4,0,0,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 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, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,4,0,0,0,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 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, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,4,0,0,0,0,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 22,12,15,21,8,9,8,0,0,6,9,0,2,9,22,8,0,0,0,0,0,12,7,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 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, 0,0,0,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,0,0,0,0, 8,21,18,22,22,2,22,0,0,16,18,0,9,22,0,6,0,0,0,5,0,21,8,8,0,12,7,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,0,0, 8,17,23,22,22,10,24,12,5,6,21,0,19,14,3,13,0,9,22,0,0,3,0,0,0,0,0,7,0,0,0,0, 0,14,15,14,0,21,0,21,0,20,12,0,3,16,0,3,22,3,0,0,22,18,21,0,0,0,0,18,0,0,0,0, 14,2,17,15,16,12,18,9,13,21,17,0,21,12,17,9,9,22,19,24,9,20,24,17,0,0,0,0,15,14,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,4,0,0,0,0,0,0,0, 22,13,9,19,8,8,13,24,2,3,12,0,2,18,20,18,0,22,0,13,0,2,0,22,0,1,0,8,0,22,7,0, 0,20,13,19,0,23,7,19,7,18,14,0,11,11,23,24,8,21,0,15,0,19,6,10,0,18,24,9,3,21,18,0, 0,17,19,8,3,7,3,20,0,6,17,5,12,22,0,17,8,8,0,0,3,8,17,0,22,0,0,1,0,0,0,0, 11,24,18,22,19,22,9,20,15,22,13,0,23,16,1,3,0,8,11,1,21,2,23,9,0,14,3,0,21,0,0,14, 2,13,6,0,21,0,13,22,12,18,4,11,18,7,15,3,0,12,21,6,19,18,7,21,21,6,0,24,10,12,0,10, 0,9,0,2,21,1,10,21,19,3,5,1,18,17,11,0,22,10,0,17,21,13,4,9,0,24,17,16,0,22,3,3, 19,2,7,16,4,3,3,23,18,21,19,12,21,18,24,15,0,12,14,11,22,5,12,21,9,2,0,23,17,21,3,8]); y:=CambridgeMatrix(3,F,32,\[ 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, 0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,4,4,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 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, 0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,23,6,4,0,24,11,17,11,13,0,0,4,13,19,19,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0, 0,0,5,7,11,2,0,21,19,3,7,19,0,11,11,0,0,4,0,0,11,0,19,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0, 18,6,8,15,12,17,7,24,18,20,16,0,14,7,12,19,4,16,7,22,4,3,7,6,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0, 7,20,14,8,23,5,13,14,0,14,10,0,15,18,18,23,18,20,15,21,18,7,15,10,0,0,0,0,7,4,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0, 19,23,5,23,11,0,14,15,5,13,19,0,23,5,13,24,1,0,0,21,0,14,3,5,0,20,24,0,6,0,0,0, 7,23,15,8,4,2,23,9,15,1,16,20,5,2,5,20,1,12,22,0,6,9,17,0,4,22,0,23,0,6,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1, 22,24,21,17,14,11,14,24,6,3,7,20,19,3,5,2,5,1,10,7,17,1,2,6,4,10,20,23,3,7,0,0, 1,24,5,10,4,16,5,13,21,12,1,0,0,6,5,3,12,0,0,12,0,9,6,15,0,8,22,0,9,1,0,1, 23,1,16,14,0,22,10,19,21,12,17,6,7,13,9,10,4,21,19,11,23,10,9,0,0,7,6,2,0,5,6,6, 7,12,5,7,24,11,3,12,15,19,13,4,22,16,9,7,19,9,14,10,20,5,17,22,1,11,7,8,5,15,24,23]); G:=MatrixGroup<32,F|x,y>; print "Group G is 2.A13 < GL(32,GF(25))";