For an integer n 2 2, let s, be the permutation group on n letters and, a, the alternating group. let c* be the group of non-zero complex number under multiplic

For an integer n 2 2, let s, be the permutation group on n letters and, A, the alternating group. Let C* be the group of non-zero complex number under multiplication. Which of the following are correct statements? For every integern:2, there is a nontrivial homomorphism : S,-C* For every integer n 2 2, there is a unique nontrivial homomorphism : S, - C* For every integer n e3, there is a nontrivial homomorphism ¢: A C For every integern:5, there is no nontrivial homomorphism : A, - C