Which of the following numbers can be orders of a permutation $\sigma$ of $11$ symbols Which of the following numbers can be orders of a permutation $\sigma$ of $11$ symbols, such that $\sigma$ does not fix any symbols?

$1. \;18$

$2.\; 30$

$3.\;15$

$4.\; 28$

could any one just give me hints?
Think about the orders of the permutations (1 2) (3 4 5) and (1 2) (3 4 5 6) and see if you can think of a rule that gives the order of a permutation written in disjoint cycle notation. Now if $\sigma$ fixes no points, what does it tell you about the permutation written in disjoint cycle notation? From this you should be able to tell which orders are possible.
Firstly find all partitions of 11 as follows:
$$\begin{array}{ll}
                                 &amp; \text{ corresponding l.c.m }   \\       
   11                          &amp;11\\
10+1.                        &amp;10 (\text{l.cm of }10,1)\\
9+2.                          &amp; 18 \text{l.cm of }9,2 \\
9+1+1\\
8+3\\
8+2+1\\
8+1+1+1\\
.\\
.7+4\\
.\\
.\\
6+5\\
6+4+1\\
.\\
.\\
5+5+1\\
.....\\
5+ 3+2\\
5+3+1+1+1.    &amp;          15( \text{l.c.m of }  5,3,1,1)\\
.......\\
\text{Similarly up to } 1+1.....+1 \ (11 \text{times})\\
\end{array}    $$
When we calculate l.c.m in all above cases we see 28 l.c.m is not possible 
So possible answers are 18,15,30