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