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