A is a non-empty set and G is a finite group that can be seen as a subgroup of the permutations of A. 1. If the order of G is 20 and x belongs to A, can the orbit of x contain exactly 13 elements? Why? 2. Find and justificate an example of a set A and a group G such that A has more than 12 elements, o(G) = 12, and the stabilizer of every element of A is either the trivial group or all of G..

1. A is a non-empty set and G is a finite group that can be seen as a subgroup of the permutations of
A.
1. If the order of G is 20 and x belongs to A, can the orbit of x contain exactly 13 elements? Why?
2. Find and justificate an example of a set A and a group G such that A has more than 12
elements, o(G) = 12, and the stabilizer of every element of A is either the trivial group or all of G.