/*
www-ATLAS of Group Representations.
E6(2) represented as 27 x 27 matrices over GF(2).
*/

F:=GF(2);

x:=CambridgeMatrix(1,F,27,[
"000000010010100111000011100",
"100011100110001111101111000",
"011100111001001101100100010",
"110010010010101001110110000",
"101111110111110000010100011",
"101101100110001100011011011",
"111100110111011101111010010",
"100011011101000011011000010",
"111100011010100011100010010",
"001111011101101010011110001",
"010011101100110101111010111",
"000110001011111011110001011",
"111110011101100010101111100",
"000111001101110101001000110",
"111001011011001010011100110",
"101101010100101001100100100",
"101110101101101000010111101",
"110001010010001011000111000",
"011101001011100101011000101",
"110110011000110101000100100",
"111100111001000110111011011",
"011001111100011010011101000",
"111100001001000111101111001",
"111101110010100111101011000",
"011101111100111110111101001",
"000001011100111010110110100",
"111100010000000111100001001"]);

y:=CambridgeMatrix(1,F,27,[
"001000000000000000000000000",
"011000000000000000000000000",
"101000000000000000000000000",
"000010000000000000000000000",
"000000100000000000000000000",
"000000010000000000000000000",
"000100000000000000000000000",
"000000000010000000000000000",
"000000000001000000000000000",
"000000000000100000000000000",
"000001000000000000000000000",
"000000000000000100000000000",
"000000000000000010000000000",
"000000000000000001000000000",
"000000000000000000100000000",
"000000001000000000000000000",
"000000000100000000000000000",
"000000000000000000000100000",
"000000000000000000000001000",
"000000000000000000000000100",
"000000000000000000000000010",
"000000000000010000000000000",
"010111001001101111001000000",
"000000000000001000000000000",
"000000000000000000000000001",
"110100101111110100000011000",
"000000000000000000010000000"]);

G<x,y>:=MatrixGroup<27,F|x,y>;
print "Group G is E6(2) < GL(27,GF(2))";