/* www-ATLAS of Group Representations. L2(19) represented as 20 x 20 matrices over GF(125). */ F:=GF(125); x:=CambridgeMatrix(3,F,20,\[ 0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0, 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, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0, 0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0, 7,45,10,97,10,51,92,121,54,100,6,70,6,85,47,98,70,77,68,63, 0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0, 46,98,97,74,119,118,54,51,103,44,118,101,81,12,40,35,111,15,99,90, 93,45,111,105,15,5,111,22,1,70,108,97,124,100,110,40,56,25,44,64, 106,97,93,123,25,37,23,55,67,95,119,40,31,64,118,79,78,29,112,28]); y:=CambridgeMatrix(3,F,20,\[ 40,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 38,108,110,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 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, 0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0, 0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1, 0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0, 92,113,21,15,84,18,75,2,74,93,124,87,66,116,39,61,23,85,95,106, 0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0, 23,69,73,31,34,33,41,81,70,45,110,30,89,70,60,26,13,2,29,80, 36,45,34,70,83,13,23,42,75,37,83,40,39,93,98,112,111,115,13,107]); G:=MatrixGroup<20,F|x,y>; print "Group G is L2(19) < GL(20,GF(125))";