/*
S14 as permutations on 39916800 points.
Matrix group is the 64-dimensional spin rep of S14.
Vector v9 has 39916800 images undex G.
The vector permute code has been commented out.
*/

F:=FiniteField(2);

x:=CambridgeMatrix(1,F,64,[
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"0001000000000000000000000000000000000000000000000000000000000000",
"0010000000000000000000000000000000000000000000000000000000000000",
"0000001000000000000000000000000000000000000000000000000000000000",
"0000000010000000000000000000000000000000000000000000000000000000",
"0000100000000000000000000000000000000000000000000000000000000000",
"0000000000010000000000000000000000000000000000000000000000000000",
"0000010000000000000000000000000000000000000000000000000000000000",
"0000000000000010000000000000000000000000000000000000000000000000",
"0000000000000000100000000000000000000000000000000000000000000000",
"0000000100000000000000000000000000000000000000000000000000000000",
"0000000000000000000100000000000000000000000000000000000000000000",
"0000000000000000000001000000000000000000000000000000000000000000",
"0000000001000000000000000000000000000000000000000000000000000000",
"0000000000000000000000001000000000000000000000000000000000000000",
"0000000000100000000000000000000000000000000000000000000000000000",
"0000000000000000000000000010000000000000000000000000000000000000",
"0000000000000000000000000000100000000000000000000000000000000000",
"0000000000001000000000000000000000000000000000000000000000000000",
"0000000000000000000000000000000100000000000000000000000000000000",
"0000000000000100000000000000000000000000000000000000000000000000",
"0000000000000000000000000000000001000000000000000000000000000000",
"0000000000000000000000000000000000010000000000000000000000000000",
"0000000000000001000000000000000000000000000000000000000000000000",
"0000000000000000000000000000000000000010000000000000000000000000",
"0000000000000000010000000000000000000000000000000000000000000000",
"0000000000000000000000000000000000000000010000000000000000000000",
"0000000000000000001000000000000000000000000000000000000000000000",
"0000000000000000000000000000000000000000000010000000000000000000",
"0000000000000000000000000000000000000000000000100000000000000000",
"0000000000000000000010000000000000000000000000000000000000000000",
"0000000000000000000000000000000000000000000000000100000000000000",
"0000000000000000000000100000000000000000000000000000000000000000",
"0000000000000000000000000000000000000000000000000000100000000000",
"0000000000000000000000010000000000000000000000000000000000000000",
"0000000000000000000000000000000000000000000000000000000100000000",
"0000000000000000000000000000000000000000000000000000000001000000",
"0000000000000000000000000100000000000000000000000000000000000000",
"0000000000000000000000000000000000000000000000000000000000001000",
"1111000000101001110110011010001100111100100000100000100101000000",
"0000000000000000000000000001000000000000000000000000000000000000",
"0100111001101101001100010010010110101000000010000100010010001000",
"1101001001101010011000111001110000110110000100100000101000000000",
"0000000000000000000000000000010000000000000000000000000000000000",
"1000001000011010000000000100010000001001000000000100010000000000",
"0000000000000000000000000000001000000000000000000000000000000000",
"0000000000000000000000000000000000000000000000000000000000000001",
"1010101110111000010110010110100000100111110110110101000101010011",
"0000000000000000000000000000000010000000000000000000000000000000",
"0100010000001110011100010000111111001100100001001001000101000011",
"1001101000000000110100001000011100111000100010000001000001000000",
"0000000000000000000000000000000000100000000000000000000000000000",
"0100100101000000000100000000000010000010000011000000000100001000",
"0011101000101001110100101111011001000110010010100000001001000000",
"0000000000000000000000000000000000001000000000000000000000000000",
"1100001111001010110011001000110000010011001001000100100000001000",
"0000000000000000000000000000000000000100000000000000000000000000",
"1100011010000110101101111101011010101111000011111100100100010101",
"0010010000011000111101001110111110011010110000111111011001011010",
"0000000000000000000000000000000000000001000000000000000000000000",
"1100000101010111101010011000110101001110010100111010101001100000",
"1100001101000011011011100010000000110110110110100110110100010011",
"0000000000000000000000000000000000000000000000010000000000000000"]);

y:=CambridgeMatrix(1,F,64,[
"1000000000000000000000000000000000000000000000000000000000000000",
"0010000000000000000000000000000000000000000000000000000000000000",
"0000100000000000000000000000000000000000000000000000000000000000",
"0000010000000000000000000000000000000000000000000000000000000000",
"0000000100000000000000000000000000000000000000000000000000000000",
"0000000001000000000000000000000000000000000000000000000000000000",
"0000000000100000000000000000000000000000000000000000000000000000",
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"0000000000000100000000000000000000000000000000000000000000000000",
"0000000000000001000000000000000000000000000000000000000000000000",
"0000000000000000010000000000000000000000000000000000000000000000",
"0000000000000000001000000000000000000000000000000000000000000000",
"0000000000000000000010000000000000000000000000000000000000000000",
"0000000000000000000000100000000000000000000000000000000000000000",
"0000000000000000000000010000000000000000000000000000000000000000",
"0000000000000000000000000100000000000000000000000000000000000000",
"1001111011010011011000100000000000000000000000000000000000000000",
"0000000000000000000000000001000000000000000000000000000000000000",
"0000000000000000000000000000010000000000000000000000000000000000",
"0000000000000000000000000000001000000000000000000000000000000000",
"0000000000000000000000000000000010000000000000000000000000000000",
"1101110100011111101001110000000000000000000000000000000000000000",
"0000000000000000000000000000000000100000000000000000000000000000",
"0000000000000000000000000000000000001000000000000000000000000000",
"0000000000000000000000000000000000000100000000000000000000000000",
"0000000000000000000000000000000000000001000000000000000000000000",
"0000000000000000000000000000000000000000100000000000000000000000",
"0000000000000000000000000000000000000000001000000000000000000000",
"0000000000000000000000000000000000000000000100000000000000000000",
"0000000000000000000000000000000000000000000001000000000000000000",
"0000000000000000000000000000000000000000000000010000000000000000",
"0000000000000000000000000000000000000000000000001000000000000000",
"0000000000000000000000000000000000000000000000000010000000000000",
"0000000000000000000000000000000000000000000000000001000000000000",
"0000000000000000000000000000000000000000000000000000010000000000",
"0000000000000000000000000000000000000000000000000000001000000000",
"0000000000000000000000000000000000000000000000000000000010000000",
"0000000000000000000000000000000000000000000000000000000000100000",
"0000000000000000000000000000000000000000000000000000000000010000",
"0000000000000000000000000000000000000000000000000000000000000100",
"0000000000000000000000000000000000000000000000000000000000000010",
"1111100011000011101110100110100010100111111110101001000101010000",
"0100110001101000101111010011100000000001101101101011011001010100",
"0010111000101101100100011011110110000110100110110001100111110000",
"1001000100110000100000000001000100000001010001001000000010000000",
"0100000100000001100110011100100000010000110000100011100001000000",
"0000101001011100010010010100110010101011010010010000100010000000",
"0000100010010111100010000010000111101011010110001000000010001100",
"1000100101011100101010010000101010110111110010101011100011001100",
"0010111000101101010111000110011011000100110101001010001100000011",
"1111101101000000111110000110011000001000000011010001110101000010",
"1100001011101100010100011000101110100000101111000010010000100111",
"0000100100100000111000001101100010011110011100000000111000010000",
"0111101000010001000100001010110100010111000011100001100110000100",
"0000000000000100101100010101110010010000010000001000000000100000",
"0010000100001001110100011010001010111101010000001000100111010000",
"0101100001100010010100001110111011001001100000000010001001010100",
"0011101001011000011000001101000100001110100111011000000001100000",
"0001110011001001011110011011001111101100111111001111100000001000",
"1100110011001101010100011110001110111100010001011101000100011001",
"0001011110010010111011101000011101010100101111111000110001100101",
"1100010111011101100101011000101010010100100111111010111101001011",
"1110100100010010001000011101000001101000000010100110101011010100",
"1011111111000110101010101000011111101000101011100110001011111111"]);

G<x,y>:=MatrixGroup<64,F|x,y>;
V:=VectorSpace(F,64);
v9:=V.1;

/*
G<x,y>:=OrbitImage(G,v9);
c:=x;d:=y;
*/