In our online calculator, you can easily determine the order of the standard and cyclic permutation. To do this, enter the required numbers in the empty fields separated by commas in any order without repetitions and click the “Calculate” button, after which the system will give a ready answer..
Determine the order of the permutation
The order of permutation for absolutely any group of arbitrarily specified, but non-repeating digits is easy enough if you represent them as two strings.
Consider the following example. Let’s say the following numbers are given:4, 1, 7, 5, 6, 2 and 3. As you can see, they do not repeat themselves and it is easy to calculate that their total number is 7. Let’s write down the given numbers in the first line in order: 1, 2, 3, 4, 5, 6 and 7, and in the second – so, as it is in the example, i.e. randomly.
As a result , we get:
It can be seen that 1 moved to 4 (the first column), in turn 4 – to 5 (the fourth column), then 5 – to 6 (the fifth column), 6 – to 2 (the sixth column) and 2, in fact, to 1 (the second column). The cycle has closed. We have formed the following group of digits: (1 4 5 6 2); in the other group were the remaining ones – (3 7). In the first group, the resulting number of digits = 5, and in the second their number =2. Now we find the smallest common multiple for 5 and 2; this is -10, which will be the answer for the case of the order of the standard permutation.
In the case of calculating the order of a cyclic permutation, you just need to add 5 and 2, and then we get: 5 + 2 = 7, which will be the desired answer.