/*
J4 as 112 x 112 matrices over GF(2).
Group: G = J4.
Field: F = GF(2).
Vector space: V = F^112.
Standard gens: a=x and b=y.
v1 has 173067389 images under G, stabiliser 2^11:M24.
v3 has 8474719242 images under G, stabiliser 2^10:L5(2).
*/

F:=FiniteField(2);

x:=CambridgeMatrix(1,F,112,[
"0111100110001011110001001001111110010101001101100000010010011000011001001101100110011100111001100111110001000110",
"0000111001001111110111010100110101111000111100110110111110011111011100001000100111100011101010000110001000000111",
"1010000111010100001011000110011111011110001100100010011100111110001110111001001110000110001111010011001110000111",
"0001010000110010111111000001111011010111010100100010110000100011011010101101011001001100000100110101010010010011",
"0010100000001101101001101110001100100011010101111010111000101001001011001110101100110100101010001111111101100010",
"0111011010111000100001100010011010100101000010111101000110101110001010000111001000011011110011111001011110100101",
"0100000110111100011010011000011011001011110010101011011001000011011101011111000010110010111000011001000100010010",
"0010100001010110110000010110111100101110111110101100111110100010001101111101101011101101110001101010010011010001",
"1101110000000000110101111000011000011101111001011000101010011010000001111100100010001100111010101000000011011110",
"0111101110001111001101010111111111001011110001110011001000000100000111010010011011011111011000110101011100110000",
"0100011010100010000111011011110001011111000100100110110111010010001110010101001011001001000000100100001100100110",
"1110010011010100101010111101100011001111001110101110001001101111110000010111100000010000001011000100110111000001",
"1010111010001110110111000101011011100111101101000010000111000101111100011011000100001110011111111001111001000111",
"0000111000010010100110001011000001010010001011111110110110011000010011000111001011111101001111111100101010000101",
"0011011010011011001101111110001001111100100100111010100100100111100111100000111001011101010000100110000010011011",
"1001011001011111111100110111010010100111010101110010100111111000110000101010101101000010011010110101011001110011",
"0110011101101011101100100001111111111001001101000111011011111001100100000101110011000000101111001011110111011100",
"0111101111100101001101001001100011111000100111011011011110100000110010101110100111100010110011000010001001001010",
"0011100101011011101110101001100101000010000011111111110101100101010101101011110111000011111001110101001001011000",
"0010101111010011010011010011011000001011010110001001000111110111110011001000110001100011000111001100110001111111",
"1110001001000001000110101010100010000111100101001000000110101101100000011000000110111100100101001010000111011011",
"1110010110010100001000110110110111010010011011011100000000101010101101010010011100010101010001010110110111011011",
"1100111010011001010011000111111011100100011110110100000110111010010110011110111001111010000011001011111000111111",
"0010110001010001001001101000000011000100001110111101010010011011011000100110011010001111110001111100111001110011",
"1001111111101010001110000101101011101100111100111001101001111000110101100011101011011001011110101011011010101100",
"0001111100101110000010011111011001011011111000000101101010011011000100011011011010000101100011101011110001100000",
"0100011000000100000010101010000100101101100000011100111010101000110000111100000000001001110100001001010010111011",
"1000010011101011100011111111001100010110001111110110100011111110110100101111101111110110100111111010110011001001",
"1011100001011011001010010011111011110110101001001001110001101000111110000010011111001110011000111101011000001000",
"0001011010110101011001011010010001101110101101000111111100001001100110001000011011110111100010110001001011000010",
"1010010011101001000100111111010100110111111110000101100111111000101100001111110110101011001001111000110000110000",
"0111011011100011101001000111111100010101100001100001100000000010010110100011000011001010110001111001010110111101",
"0001110101111100010000110011010011110001000111110011110100111100110011001011001010111010100111101100010001100110",
"1100010101111010101111001111110101100011101101001101011101001011001111101000000111011011111110101100011010101111",
"0111011011101100111100101101100010110100100001010001010011101010110110010010101111111100001101010000010010111011",
"0000001111101110001100101110111011010001110010111110000111110110100111011010011111110100101110011011001000101101",
"0010101000010000010011100001111111001111010010000010101111011100010100001010101000000111101111011101010011100101",
"1100000111001111101100110001010010010110011111000001000101011100011000001110100100100101000001101111011011011011",
"1001101101100111100011011100101100111111101111101100100001110111010110011000010101100101010101100010110110001000",
"1110001011000000001100110000101000010111011111001010111011101101010100010111100100000100001110110111000110010000",
"0000100110001111010100101011000011010111100011011100000001010000110111010100110000010101100001101001011100101111",
"1110000001000100000011110111001101010011100101101101000111011111110011011110101011101111100111101100100111000111",
"0001010100111001101110001011011110110010111110010010011101011101000011111011100001110111010000000100001000110001",
"0101100100100001010010100000001101101111011000100000011100001001011001001011100100111001101111011010110100011111",
"0000100000111110100011000010111010011010000100101010110001100111011001001101110101100100101101111110000011000011",
"1011011100001111101100100011111111001100010010011010111111101100001111000011000110000001111111011000101000111011",
"0010101110001001100010111010011011000001000111001000011010010100010011100110110110110101111010100101001101110001",
"0000100110011000000011101111011111010111100000010111011100000100001100111110011101000101100010001001101100001010",
"1111111111100000100111001000000111010110111110001011111111010000110000101011100111110000110100100001000011111110",
"1111010001110011101110010000000011011010111100111000101101010001100000111001000110110001110100011001011010110010",
"0010010001011110000010000000100010111101110000111011100101010101110110110111001011100000001100011000010101010000",
"1000100101011101011001111010111110011011001101011001100001110000010101110001100111010011010100110100100101101010",
"1101101100100101110101000011111000000000011111000101011110001010001111001110010001010010101000101110110101100011",
"0111111001100001000110001001111100101001111101010111000001000011101111001101010011110111010001100000110000010011",
"1100010010101100110100111100011110100001010111010101101001100100101101100000011111000101111111011111010010000011",
"0010000000010010001000110111111100101100001001100011011101111100111101111101111001100011001001100100001001111101",
"1100011111010001010110111011001100111010011101000001111101101111100101100111101101001010011001000010000101000100",
"1110010100000110000001111010100010001100010010000001010011001101001000000111101010100111111011000001011101011110",
"0011111111111001001011100000011001010110000001110100010111001100000001010110010011100100010111100110010111110011",
"1101100100110101111100001101001100110110110101000110111001101111001110010101111111111010101011110110110111011010",
"1000000100001100010110101010010100100011100000001110110001111111010011000001001111010111011100101010011111000010",
"1100111111101101011100000111110111000010001111000010011011101011101100000010001100001011110010100100000101010000",
"1001001001000011101010100010010000110111100110101100101011001000100110001110101100100011001001100110010010000011",
"1000001000000000010111010011100101001000110011100000001101110001010001001100010100111101011111101111010000010110",
"0110000000101000010010001101111100100001000000101101000011111101001000010001010110101100100100011100000100101110",
"0111111111001101011111101100100000001011000001011000100011101011001010101000000101000111111000011011000111010100",
"1010101101010011010101001000100111101100100001110000010110101001000011100111110011110011100110101110011010000011",
"0010101110111111000001100110101100111011110100100010001100001010111001000101010001101011010101101111111111100101",
"1010110011001000000111111100001000010000101101100111001001110001001111100001100101011111111100100101011111100111",
"1101100000000110010000110100101001100001010000011100101000111011100000111111000010100011111100011010110100001001",
"1111111000000000011000101011010101001111000101000111100011111000101101011010001111111111100010010110111011111110",
"0001000011111010010000001001010100111101000101100001000010001000010011000100000110101011011110111000101100111010",
"1111110010010000010100011001010111000000100111100000000010000101101101011010011011111110110000100010111101010011",
"0010111100000111101111010101100000101110100100000011010001101011010010000101011000001000010110010011001101100011",
"1101011101000011101010010001001011101101101010000011100001001000001110000011010010010001111111011010111000001111",
"1001111001100001000010101110110010011010010011111000001100001000110010001011101000000110100000001011110011011000",
"0111111111000100110111010111000010000010010000001010111001010111001110010100111011000110010100011111111000111000",
"1010001101111001001011101001110011010101101001100011110001111010100011100010010101111011011111001010000111011111",
"1011111111100111000100111100010010011010010011011110100000010000110111110100110010011010011001001111011010110110",
"1000111011110110100110110101110000001100011001111100110001110011110001111100010100011101010101001011111000001000",
"0000010010101101011000101001110011100001100000101010101111010010110100100100101110010111010110111010001010000000",
"1010100100111010101110010001011001111101011101011010100010011010101010001101111010000001000000110110010110011000",
"1111101000100000101110011011000110001101000101101111101111111110001110011110101011001111011110110100110000100010",
"1011100100101110110101101111101000100001011100011100111100010001011001110110001001100111110111000011000010011110",
"1101000100010001100001101010011000111001111011100011101001000000110010101011010100010100111010110010110110001101",
"1001010001011111011101011100011100000010001000001101001100111010011001001111111101000111100000000001101000101001",
"0001111010110010010010101001011011111100110110110110100000001011100101101001000010111100111001111000010100010001",
"1111011011110000001010111000100100110111110110000001100101011110011101111011110000100101111100101011010010010111",
"0111000001000101110100111000011101101110110010001100110000111000000011110001100001000100110011000100001000110100",
"0101100111100010010100001111110010010000010000001100100000001110111101110110010100100010001001000100011011010111",
"0010100011000011001010111001111111010010011100010100000001101011010111100010010000001000110101010010001111001011",
"0001100011011100101111010011100011100001111111010111110010011010001001010001110110001001001001101101101110101110",
"0001111011110110100101100011100110100101010001001010001100100110111100000101110011111101000010010000011111001110",
"1111011011001000101100000110101100011111101000010111110110001101010110011100110000111011000111101000100011101100",
"0100101011011011001111001000110101011111010010000000100101101010100110001010001011001100010000010000010111100110",
"0000010110000011100001111010010101100001101100101110111101010011111110010011110001101101011001110101000011111101",
"1101001100101010100001111111110000010010010111001110011100100000001110011000010000010100000111010110010010001011",
"1110011100010110001111110010010001011100000000001100010100101111101110101100111010111111111000110110000000011110",
"0110111011111000011010000110010000010000101111010010101111001101011111110100100011100001110101110100110111010101",
"0001000001110001010101101111011010000100111101000100000100101001101010111111110101001110110001111011101010100101",
"1101011110110110001000001111001011111001111011000101101011010100000111011111011110011010110111100100101110101101",
"0001010000000111110111010110110001000011001110110001101100011111001010101000001100110011000001100001000001100001",
"0001000001111110100100110111101101101011111001100100110001100100000100011010000111011110001111010110001110101101",
"1010110001000100001001101101100010110001111100101010001110001111101000110100101100010000100000101001010011110101",
"1101011110010011001101011101110101010001011001110100011001101000010001011000011000001111111001000101110001001000",
"1000101111101001111001111110000010110010110001100100000101100101000000110101110000010111011100011101111001101100",
"1000101001000010011111110010110101001000101000111001101110110111001101001010001000101001011111010010110011111100",
"1101101110011010110101111101000011000010100011100101000011001010010001000001001000010010010110100000000101100011",
"0000000000000001000000110101010011111110011101111010001101011010111010011011001111000010100101011011011111110111",
"0001110010111010010111101000001010010001110011101011010110100110000000110011100000110101110010110110110001011011",
"0100001101010110011100000101011100000011000111001100110111110111100111101101011000110101000010000000100000011110",
"1111111001100101100101101001010110010110000100011010000010011000100111010011001110000100111010011110001010101001"]);


y:=CambridgeMatrix(1,F,112,[
"1001010010110011001101101000100110000001000010001001100111001101001100001100001011011100011010110010011101111110",
"1110001111101101010111100011101100011110001101010011100010110100011100000000100010100101111010111111100111000101",
"0000011000110010000101001010101001010100111101001000110000000101011101110101100011000011010111111100101010100011",
"1111100000000110011101000101101100000001010111110001111010101111110010100011011110101100111001000011110011101000",
"1100000101001110011110000101000110101100000100111111001100100110100000011100011001111000100100110110100110100001",
"0010110001111000101001011100101010011011111110011011010100000101011101010010011001010110110000010111001000001111",
"1111100001100011111011110011000001111001001101000100100101000000110101001001101100100110101010111111000110011111",
"1100100100000110010111100001001011011111011000110000110101100011000101010111000110100100000111110000011100100011",
"0010010100010000110000010010001010100110111011100101100100001101001010011010011000111110010111101100001111110110",
"1000011110001101001100010011101001010110101111101111001100100000110011111111110110110100101011011110001100110100",
"1110000100001110011000101011001000101000000010010001011010000001111000110101011000011010111101000011101010010001",
"1110110110000111001001010011001011010100101101011101101000110100101111001010010010100111101100111000011110011100",
"1101000011110011000001101001100011000110001110110010001100101101001001000101010000010010011001011011111100100111",
"0110111011011101000111100011101101011010100100101100001111101110110110101110101101100000001110101111111011110110",
"1110010001001111011001000111010010010101011100010111100110110001100110011101001110100001010011000011100110010010",
"1101101011010001010001000010000000111011000110110011111110111111010101000000101111001010010000110010011110000000",
"1010011000110001100100110101101000011100000110010011100100000101111111001101010001011010001000010110000001011100",
"0010100000100010010100001110101101111000001011010010110010101100111100100110010101000100110111010110001001101111",
"1000001100001100010010101010110010111011010101001011110000110111100111101101110000010111101110011101010010101001",
"0110111011111010111000101011000111001010101001000110111101010101000000000111001000000100010101101001101111100001",
"1101011000111100110111001100011000110010000011101001110010110010100100110111110111110100111010101000001100101111",
"1011001001101001001011001100110000111010000010111000100011000010001011110111000101111110110010001000110111010100",
"0010101011110110011110111101111000111111001001001100001111000111010110110010101011101000101100110001110111110000",
"1000001110001100111100100011111010111010101111110011001111100010010111100110111111011110001000111101100001100010",
"0111110111101001111000101100101011100110111111100001111001111000001011001010000101001010101100100100000110001000",
"0011000111011000001111110110100000001011111011111000110001101011101100000011100101100110110101001011010000111010",
"1100111101000011011010001001001011111010011101000101001101010010011010101000110001001000000010100000011100010010",
"1111000010101011001001001101100111010011010010101100110000111110101110001001110010011000110000101100010101100110",
"1101100000011010001111000011001000011001010100110101101111111011101000001011110101111010100011001000101000110001",
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"1010011110011001111011010100110101110011010001100000100011100110010101000001111111101001001111010010101111010101",
"0110000000111000111000011101111100001101000100101011111010111011111101110010101011111110010110100101000111000001",
"0110001100100000101111111111000101010111010010011001011011101110111111110001011000111011101011111110100010111000",
"0101001111000011001000110110011111001001101110110010001000101000010010101101010000101100110111001101111011011011",
"0100111110100110011110001100111101010000100000100101100000010001011010100001010011000010100100100001001101000010",
"1100100111000110001000110000100001101101000010010111100010001101011001111100010101001000011111011011111000001011",
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"0110100011001010010100011100110111011111010111111111110101101011110011100001110111100011100100110001101101000100",
"0011010111011011100011110101010100000100000001000000101001100110111100001101000110101001110110011000011011110100",
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"1001011011110001011110111111000110101100100001101000111100110101100000110011111001010010010100010001111110011111",
"0110100010111111100011011111100101010101100111101011101011001011010100101000000110110100011110011001010110000000",
"1110010110111011001100111000100011100010000001100010011100100001000101010011000111101000010101000111000101100000",
"0111010001111110111001011001101101111010101100001101011010111001000011000001010010111111001010101110110000001001",
"0011011010010111111000100000010101111001111010110101110000011000101001101001101111010111001100010010011011101001",
"0111000101010100100001010010010011001101101110110010000101001001011110010001011010001111111111110000011111101100",
"1101011001010101000110101101001000111000001000100011110110111011110101011100101001001111011011011001000010010001",
"0101011101011110010101100110001010010011000100010111101010000000000111101010000010110000001100011000111000001101",
"0011101101011011100100010000110100001010001110010101100111010000101011010100111001110001101111100110101110010000",
"1110100100111110101010111100010101101010111001110100101111000000001010001010010001111101101100101110001111000011",
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"0010001111110011100111111100111111011000101001110010001100001010101111110101101011101110001001000010010100001101",
"1111110101100100000110111000100011001111010101000100001000010111000000010010101111111001110101111101010100000010",
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"1011110001000100111110111011011111000111011011001110001100100111000001011010010001111000110011111010110011111100",
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"1011011111101101110110001000000111111000011101001101000110000001101000001001011000011010000101111011111101001010",
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"0011010011101010100111010110100101101100010001111100010011011100010100110101111110010010011000101010001001010011",
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"0110111101010001110110100110001101001011011001100100111100110100101111010100101100111101001111010000111001111100",
"0011110011011101101000111110001101100010111000001011101011000011110000001001010011111001010010110100100101111100",
"0001010010111110110011100011001001001000111111110101001011111011011111111010000010000110101001010010101111010110",
"0000000111101110110111010110100010100010111110100011101000000011110001111100000010100110011111101110100001111111",
"0101000101100001000110110100100011100010111101110101001100010110000000101111100100001000010110000000111000100010",
"0101011100111011000011010110100001000101111000011001100000000110100010110110110101010101100011110110010000000101",
"1011011101000010010100000001010111111000100001001000000001010001100101100110100000011101010000011001111100001010",
"0111101011001000111101011011000010101110101101110111101110000100110010100100111110111010100100110111011110110011",
"1110011100010110000010011111010101100000000000101110100011101110110101110100111001000110110010000100100110001010",
"1011010010111001010000010000110110100000100011100111010011100101100001100101110111101111101101100000010110100011",
"1010011011011110011111010011111000110111010100111101011000111000101011011010100101110111010011101011010010111011",
"0000101010011001000111010100001010101111110011101100100111101111010001011001101000000111110111111001000100100000",
"1110110001101001001100110011110101000011010011011010001010101100010011111000100100111000110101111000000110000011",
"1011000000001000000001100001111010100001000001011111110011101110010110001110101000001000101001110000011111011001",
"0101001011011000101101101000011010100011000010100001100110110111110100101100101011100101100100010010100001110010",
"0101101110100010000110101100110000101110010100000100000011111001101000100010001100110011000101001100111010000110",
"1010000100011010011010101010110010111000000101110001000100011100100001000101011111011001000101011111010100100000",
"1001110110110010011001001101100001111111001010000110110110011101110010111001000100101101010110010110100001001110",
"1011101010011110110100000100110000111001101100011101110111100010010001000101111110111100000010001100110000000011",
"0101111001111011000101101110101010111111010100110100110010101010101111101001110111101000111011010101101110101111",
"1111000001001011001100010100111011100101000110011010010101001100011010100111010001001000111001010111101001111111",
"0101111101010110011110010011011011000010110100010110101110001001001001011010111110000110110101101100111000001000",
"1100010010000010100100111100100011111001100101101110110100111101000110110011011111111011010110010010000110010001",
"0001110010110000000111001011111011011111001111111111010100001001101110001001010001110010001101000100000110101000",
"1001111011000111101111110010000101011110111011000101010010111001100111101010011000001100000101011100010101011110",
"0100100111111010001111011011000111001001001001000110000100011011001001111111010011100100011000110100011000111000",
"0100111000111011101000011010011100100010101110001100010010111000010001111110000110001011101101000110101110111001",
"1000000011100010001010101001001100101111111101111000101111000101000101111101011111110101010111110011110101101001",
"1011110111000100111101001111110001000100111001110101111100000001111001000001001101001000101101100011001001011111",
"1101100100011001001010000110111000011110010100011011100011111101111100011110011001100100111101110111101111100101",
"0111001111011111110000101101101011100000011011110000101000010111110000110011001110111011111010111011101010100100",
"1101011001101001001011100111000100100000100010011011100011000110010011110001110010110010011110000010101101101110",
"1000001111010010100100000000110110010011000111111101010100001100100010001011000011100101101010101000001110001011",
"0000110010010100101011101100111100110001001101001100100011110001011111001001111110010110000110001000011011100111",
"0101000001011110101001000111111100100101101001111000011100100110100101001010100110000100101000010111100101100100",
"0111010110101010010010101111101100000111110000100110011110001110001010000111111000010011011000001001010110010000",
"0010110110010001010010011110011000111011010110100111101100010011001001011001001000111011110010110100100011001011",
"0000010110010110101110110001000010111100000001000100000010100001111110000011010100000000111010110000111100110101",
"0110110000100010100101000111110100000110001010010010010011010100010001001011000010111000000100001010100110010101",
"1001001100101100111000000100010111011000111010000000000001110110000101010111011010110100011000010100100110100000",
"0000011011101010001111010100100000101111010000011100001111100110010010110011100011001011101111111000011010110011",
"0110010100011001000010000001001001010001110011100110010110000011101001100101100001111010101010011110110101110110",
"0101011110011110111111000011000011100110011101010100100011111000010111011010101000000010010111011010000000110010"]);

G<x,y>:=MatrixGroup<112,F|x,y>;
a:=x;b:=y;

M1<x1,y1>:=sub<G|x^y,((x*y*x*y*x*y^2)^8)^(x*y^-1)>;
M2<x2,y2>:=sub<G|((x*y*x*y^2)^5)^((x*y)^9),((x*y*x*y*x*y^2)^8)^((x*y^-1)^21)>;
M3<x3,y3>:=sub<G|x^((x*y^-1)^4),y^((x*y)^8)>;
H3<xx3,yy3>:=sub<G|x^y,((x*y*x*y*x*y^2)^8)^((x*y^-1)^2)>;

/*
M1 = 2^11:M24, M2 = 2^{1+12}.3M22.2, M3 = 2^10:L5(2), H3 = L5(2).
v1 is fixed by M1, v3 is fixed by H3.
*/

V:=VectorSpace(F,112);

v1:=V!\[1,0,1,1,1,1,1,0,1,1,1,1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0,0,0,1,1,1,1,1,
0,0,0,1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,1,1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,0,
1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0,1,0,0,0,1,0];

v3:=V!\[1,0,0,0,0,0,1,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0,0,1,0,1,0,0,0,1,
0,0,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,1,1,
0,1,0,0,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0,0,0,0,1,1,1,1,0,1,1,1,1,0,1,1,0,1,0,1];