/*
www-ATLAS of Group Representations.
TE6(2):S3 represented as 78 x 78 matrices over GF(2).
*/

F:=GF(2);

x:=CambridgeMatrix(1,F,78,[
"010011110010100000001100000100001111010111100001001000001001001000111000000010",
"001001100111100110000111001111100110101101001100000111011011101001111000000011",
"111010000101010100011101100101110100111110010011111010000101100010110000100010",
"001100101111010010011001000010101101001100000000011110011101001001011101111100",
"100000011001100000001100101111011110010000111000111100111101000111011011010111",
"000011010010001110011111001001101101100010111111000101011000101101111111011000",
"000011010000000001101011011101101110011001001000101011000101100001101000001011",
"011000011101100100101010001101110111000010000100011011111110110101110100001101",
"011100011111010100111101101111000100010010011100111110100100101011001001111000",
"101011101011111000111000100011110111001010110110001000011001111001011111010011",
"001111000001111010111010010011100110001011011010011111110100010001011001100010",
"001001111001111010110001001110101111111000110110011110011001010110001111010100",
"011000111111101110000111000011111010001110101000001001100100110110011000011100",
"011010110100001001100010100001111110100111000010010110100111010011011100000011",
"101111001100000001101010100110000000000110101100100000010001110000000000100111",
"111101011111000001101101011101111000001001010100110001001101100001101010011010",
"111000010111010101110010010001111110100011001001110001101011110110000100000100",
"001101110111101111010100010000101111011001100011111101011100100000100111110111",
"110101010010100010111010010101001110001101100100100010000111000010100011011001",
"011110110011010111000011100111101111110001101000001011001001110101011010001010",
"100001111000100001010011011010100111001110001111001110111101110000111101100100",
"101001001100010010101100111011111110001101001001110101101011000011011001110100",
"010010000000000111011110101000111010010100111000011110100001011000101100100100",
"110100001001111000010000110110000111010010010111000010111011100110101111100010",
"010011101010111101110000111110000010001011101001110010110101110010000001011101",
"101100011010111100100110000101110010010000100100111011110100001010011101101110",
"111001001010100101010101110110010100111111111100010011011111000001111110100110",
"010001010110001100010010110000010000001010100000011001101111010110111011110010",
"111011101100111000101010010001001001010100000100001010110000000101101111110101",
"011100010010101001100101100100000100101011111101111000111100011101111000101110",
"001010001111010110100100110011110100100101111100100111000011101110001010111110",
"010110101110010101010011101100010100101011101111111110010101001000111101111000",
"000011001111101010011001100010100010110110100110111001111001011010111100101000",
"111010100010011010100100110000010111110111100110001000110110100101101010100101",
"111001111111011111000100101001100010001110110000101000011011011111110101010101",
"001001110101010100010001100111011101000001000000001101101010011101101111011111",
"101001100010000101001101011000101100000010011101000100001001110110110101100010",
"111001101101001011000001101000110011011001101101100000011001001101111001111001",
"000101000000001110001000100000101110011000111110110111010010000011011111101110",
"110100000100110110101111011001010101101010010001111000000100011111110000010101",
"011101111101110001011001001011001111010101001011010001100100100110000011101111",
"000111101011001100011000000000000101000110010101011111000110000111011011110000",
"000010011000110001010011100001111110010011010011111000000011010011101000011000",
"101100010001100001000110111001011110001001011011111100101001011110101101110001",
"000010100100010111110101010101011111101111000100110100111111111111111010101000",
"000011110110000011111011000010101111001011001111010001011101010011000010010110",
"010000011010010000100111000110011100011000000001000001101010011100010010000001",
"100011101010101010010101010000101101011001011101010000001011101101010100011011",
"100001011101010001110000101111001111001010000011011010111001000101110100001011",
"010101101001001101100001010001000010100111100010110110010000100111110000000110",
"010010100000110001011010100001111110010010100101101010110110100011110000010001",
"111101010111111001111100110001011011101010111000010001000011100110101100100001",
"110000011001000010110001101011111111110110100000000101101100110001110010111110",
"000001111100101111011101011001001011110110011001010001001000011011000111100110",
"111100111010000011001100010100111100101000100000010100110110111011011001010010",
"110100000101010101100111011011001011100111011100011111110100111000101010110101",
"011001001001111111100001011000110111011111000011100100000111110111101010000010",
"000000011110111101100101000000110110010010111010001100011110101110100111010100",
"011110010100101000111101100011000010010101100111011111000111010101011111000011",
"110111101010001100110100010110011011010101111001001101000111001010111001101010",
"101010010110001110111110100101100101000010010011011011101100010111011010011101",
"010101011011100110110100110101110011101101001000100001100000010111000101001010",
"101101001101001000011010110100001100010011010001010111001001111010010110001010",
"001111000100011111111101011110111111011011110000010011111011110101011011100101",
"010111001001000101101010000110010001111001010110111000111011101110011100011011",
"101011100010001111001010111001101111111010110011001011000111000010001110100010",
"111000011010110110000010000101100100100011110101100010101000000001011001011011",
"101110110011110001110101101111000010111100010100100000010101101111010010011101",
"010111101011101010111010000010101101010011110111001110010101000110001001100010",
"110001111001010001110000010010110111101001110000001011111111001000011110111110",
"011011000111111100011101110000101011101011011111010100101010011101000100011110",
"101110101011110000000010011100100110100001101110000010100110111111011011001000",
"111010110011001100111111111111111011101100000111011000000101101101000110000010",
"111011101111100000101101010100011101001001100001011001010100101110001010011100",
"000001001010111000001111101011000001111010100100000100000110000101100110100101",
"001011111001011001010010011111011111100010101010011001110000011100101111100111",
"100001100100010111111101110001101011110110000101101111101001000011011010000001",
"110011100110010000110100110001110001000101100010001101111010101000100001011010"]);

y:=CambridgeMatrix(1,F,78,[
"011000010110100100000000010010001000111000111001001111000111001101100011000000",
"100101110001100001001101111111111100110001101100010111001000111110110101001100",
"110101111100111010100010110110001011100000111110010100101110000101100100101001",
"101011101000001100101011111001100001100000011110111111110110100101100111000000",
"010011010000101011010110010011010010011101100111000101100100101011001111010100",
"010111010100100111001111100111101001100111100100110111111110000111010000011101",
"101111100010001000010101110101110110001111010001101000001000110000111001111000",
"101010110111010011011000010001001000111101101110101011100110010100000010110001",
"011001000001111111111110111110110110101100000101100010110111010110100010011110",
"000100011100000000001110101001101010000101110110001101001011101110010100011001",
"111101000000111001111011111010000110001101101101100011010011010110000010011110",
"010111001001110100111011100101100110111000000011011101011111010011111001000101",
"010101110110000001001001001001001011100011110101000001000101011101000010010101",
"100101011000110010011000000101000111110111001001100101010001101000100011001010",
"101111010101110100100110100010100111101011100111001000011100000011011011100111",
"100011110010101000010101101101111111010101100011000101100010000000101011101001",
"101101101011100101111110101101111010011011000011011011101011010000010110000100",
"010101010111000101010100101001011110011100100100110001110101001000100011001010",
"010000011000110011111101011100000111110011000000010001110010110000101101101011",
"101001101101011011000111101111101010000101111011001000110010001101111111110000",
"011100000010011100000101011001000001101011101100010100111111000110110011011000",
"000000110110101001001111111101001011011100001100011110101110110000110110000100",
"011110011010000111011000011010100110100101000100001101010000100111011000111110",
"101110001111110011101100101010100110100110011100010111101110001100101000000110",
"100010100011000111010100101010000010111010110111001111100010101110010011011000",
"010011001110101110011101110000111110111010001001011100010011001101111111110000",
"100101011111010010111010000000100000101111000011110101011000101110010011111000",
"001011000110101011101011010101010111100001111011110110011101101010110011000011",
"111010010100000111110001010010000000011000111010001011111110111100111110001010",
"010100110010101111110010010111100011000011111000101001100100101111011100111110",
"010000011101010000111111011010010110001101011010001010110010011111011010101010",
"011110001011010101111100011110111100011101000111101001000011000000001011000001",
"101001010000101011111110000101001111000100100011011010110000101110110111111000",
"111001101001111111011111100110011001010011110101001110111101110111111010110111",
"011101110110111110111011010101111101110100111100011001111000101110111111010011",
"011000101011100001001000100110011111100010010010010011111000111110110110000110",
"000101011011100110010101101001010111100011111100111011010011011001000101001111",
"011011110001101000000000000111111100010111101101010110110000001111001000000110",
"000011011011101001000001111111010101101010011010101101000011001011101111011100",
"000001001000110001000110110000011010101001011100110011001111001110000000000010",
"111101011100110101000010001010011000110010000110100010001010001010011111000011",
"101010110101101101011001111111001100111000000010000000011100111011111001001101",
"110000100111010101010100110101000011111111101000001010001010110010100010100101",
"010010100100101011000011011111011100110011100100100110100010001100101000111011",
"001010111111111010010010011111111100001001101111011010111101000111011011011100",
"100101000011000010001001100111110011000000101110011111010011101101100000001010",
"001101111000001110000101001110101100110101110100010100110000111011001101110101",
"001110010110111101110011001000100101010000000011111111001111111110111101100100",
"010010000000100100111100101000011011010101110111010010110000011101100101001010",
"111101001101101010001001110000001000111001001001100001001101111000111001010000",
"101011100101001110101011000111011000011011110101000000011100110111000101001101",
"101111001100101111101001100010111000010100101000101111110010011001101101101111",
"011010000111111011010110001111101001001110100010011100111011010011000010011100",
"000111110000110101101000100000100111010001101001100100100001110000110110000111",
"010001000010110010000101000110110110000010110011010011010010000001010000001001",
"010000010100110101100011010001011111001001110111111001100100011111110101010110",
"111111110111000000001111000010101000101101000110001010011000011100100110010001",
"000010110010110110100000001000111101110111101000101111111110101111111011111100",
"010111100111011110100110111000000101101010000010101100100010111001111010110110",
"100000100101010011100100101010010001010010100011110000100001010011001001110101",
"011111111000001111100000011100001000010110011011010010010100100101001111101000",
"111001110100110110110111100001100110101111001011011011000111000101011010101101",
"010100010100010110101111011010101111100000000000011010001110101110110111000110",
"100000100001010111100111001111001110110110001111000011110100100101110011000000",
"100100111100010011001010110100100010110111100100000110111011011110001110000100",
"101001100000101001010100011001001100101110111011111100100010010110101010011001",
"000000111011110000110111011010010010101100111001011100111110101011100100001011",
"101010101110000000111100110001001100000110110110001100011011110010001110010101",
"110001100011010000100100001110111111000110001101101110011011101101100011111110",
"111101001001111011000111010111011010110111001000001100000001110111010101010110",
"001010111101100101001100000100100101101001000010001001110110001001000001011000",
"010101001110101101010111100110110011011101011010010010000001111000001011010100",
"000110001001101100100100111010011100010101101011110001001011001010001100011010",
"000100010110111001111100101000001111111110100011000111010010100110011111000000",
"011001100100101110001000111111101001101011100010000010111010000101110111111011",
"001101100111101101000100010100111011011111001111110101001000001000011111110101",
"010111011001110001100010001111010000101000000111110010101111011101111101110000",
"000110010000101011111001100011101010111101111010100111100010001011100011000000"]);

G<x,y>:=MatrixGroup<78,F|x,y>;
print "Group G is TE6(2):S3 < GL(78,GF(2))";