Is the key of this encryption(transposition cipher) correct? I think it should've been 524736, what do you think?

2 points:
The cipher is supposed to be 7 characters long, yours is only 6.
If you add '1' to your cipher, i.e. 5247136, you will get a permutation which is the inverse of 5263174, i.e. if one sequence is used for encryption then another can be used for decryption.
 
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