Find a known group to which Sn/An is isomorphic

[Guest kelkul]

Suppose n is an integer and n>=2. Show that An is a normal subgroup of Sn and compute Sn/An. That is, find a known group to which Sn/An is isomorphic.

[matt grime]

What are the orders of An and Sn? Hence what is the order of Sn/An? How many groups are there of that order?

[Guest kelkul]

This is all that is given in the question. I don't know what the orders are or anything else. I need help though..haha

[matt grime]

S_n is the permutation group on n objects. It has n! elements. A_n is the subgroup of even elements. If you don't know what that is then you need to learn it, from your notes and understand why it has n!/2 elements. You also should immediately see that there are two cosets of A_n in S_n and thus that A_n is normal so the quotient group exists and has order.....?