A cyclic number is a number of "n" digits that when multiplied by 1, 2, 3,...n, results in the same digits but in a different order.
For example, the number 142,857 is a cyclic number since 142,857 x 2 = 285,714, 142,857 x 3 = 428,571, 142,857 x 4 = 571,428, and so on. Given an integer input, determine if it is a cyclic number by outputting a truthy value if it is, and a falsy value if not.
Also, to be clear, the input can contain leading 0's: e.g. 0344827586206896551724137931
This is because, if leading zeros are not permitted on numerals, then 142857 is the only cyclic number in decimal.
Since it is code-golf, shortest answer in bytes wins!