/* www-ATLAS of Group Representations. 2.A8 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, 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, 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, 0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 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, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 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, 0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0, 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, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0, 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, 0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1, 4,9,15,6,12,19,1,8,2,11,20,4,18,9,22,17,19,20,14,16,5,15,13,18,20,7,24,15,22,10,0,4, 9,16,16,0,17,16,13,0,7,4,17,15,24,15,1,2,9,16,13,7,22,17,10,6,14,8,3,16,6,2,17,19, 2,7,13,14,2,18,18,13,19,22,2,22,12,5,10,9,5,4,20,21,6,17,6,21,7,5,15,6,9,0,2,24, 19,20,8,5,17,12,6,23,13,9,13,2,24,3,1,19,22,10,15,14,22,5,21,7,17,13,14,0,11,0,4,4, 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, 1,4,24,21,1,3,23,7,0,21,22,7,0,10,12,4,7,19,0,16,13,24,5,21,3,14,5,16,2,19,8,23, 14,15,18,16,7,3,1,16,14,4,13,10,17,24,4,19,15,8,13,1,8,17,17,3,12,20,19,2,14,10,9,4, 7,7,3,10,18,7,13,19,19,13,17,15,1,6,7,5,2,24,11,24,5,8,24,21,21,1,15,15,21,11,18,8, 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, 10,14,2,5,17,15,6,0,7,19,5,22,10,4,17,18,17,17,17,5,1,13,9,0,23,19,22,22,12,7,1,0, 24,5,2,5,22,24,16,24,16,22,1,10,3,5,6,14,4,9,15,17,1,8,5,6,11,5,13,22,14,3,13,8, 14,23,20,10,21,19,21,23,5,13,18,17,19,4,11,11,14,12,0,3,8,4,1,1,3,13,11,11,24,10,10,14, 6,9,0,17,14,6,1,22,9,21,6,23,2,4,23,24,5,0,11,9,23,15,1,11,6,1,23,14,16,17,2,2, 17,7,24,3,18,6,14,12,17,12,13,6,18,0,11,20,0,5,14,22,18,13,5,23,24,13,14,23,8,17,1,8]); 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, 0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 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, 0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 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, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 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, 0,4,0,0,0,4,4,0,0,0,0,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0, 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, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0, 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, 7,4,8,5,23,24,10,8,10,8,16,12,20,13,11,14,12,20,24,17,16,10,13,5,3,20,18,5,11,9,22,23, 3,15,10,1,24,2,5,12,1,0,6,5,0,8,11,24,22,7,7,8,17,0,6,16,15,0,14,2,19,22,0,9, 5,19,15,10,14,5,18,15,10,21,17,2,23,7,0,7,3,21,23,3,13,21,22,18,2,6,8,6,12,17,2,7, 22,16,19,3,9,6,9,16,13,15,3,21,1,12,0,7,4,19,23,14,17,22,16,23,13,10,7,6,17,5,9,13, 2,13,11,7,23,22,6,4,7,23,9,18,7,19,14,24,9,14,20,8,10,11,20,13,11,13,3,23,20,14,7,18, 23,8,7,17,20,16,1,20,11,18,10,1,10,1,16,16,15,1,12,0,17,15,18,23,22,7,22,6,19,8,1,24, 19,18,23,9,10,21,16,0,16,15,11,6,14,16,7,1,2,21,24,16,19,23,11,4,7,13,22,21,0,23,17,2, 16,10,4,8,13,21,4,23,9,18,6,6,21,9,18,11,24,19,3,0,16,1,17,14,5,16,16,12,2,24,21,3, 23,20,6,1,14,18,3,20,17,8,13,3,19,22,17,18,14,14,18,23,6,4,19,19,13,2,3,13,14,2,12,14, 18,12,17,17,17,0,23,11,3,5,23,23,1,3,3,21,3,9,14,4,3,10,9,3,22,23,13,16,2,11,2,6, 21,1,4,6,12,18,7,1,6,4,18,16,17,14,21,5,1,12,2,4,12,11,4,23,4,16,19,24,19,5,24,12, 6,15,20,21,15,0,13,15,7,24,6,15,4,21,23,7,6,12,24,0,18,21,8,5,21,3,5,21,5,1,12,20, 21,6,1,3,16,1,7,0,24,6,13,23,4,19,0,18,5,10,2,15,7,5,19,16,15,14,20,11,18,17,19,0, 23,16,12,21,22,2,5,11,9,13,21,6,2,23,21,4,2,9,3,10,21,8,14,8,7,0,19,11,20,6,12,6, 3,11,24,4,5,9,4,14,7,17,16,11,19,8,2,19,2,5,12,13,16,24,22,7,7,22,21,1,18,23,11,3]); G:=MatrixGroup<32,F|x,y>; print "Group G is 2.A8 < GL(32,GF(25))";