@ DavidHarden. I am Sorry. I mean the size of cd(G) is six.

Also, when I was working with simple group G/M, I got some possibility for cd(G), but I am not sure that occurs.

I would like to find a non-solvable finite group G such that it has exactly six irreducible character and {1, 3, 4 , 5} is contained in cd(G), and about the other two degrees a, b in cd(G), I know that 6 divides a, 10 divides b , but 5 does not divides a and 3 does not divide b. Since the smallest positive integers with these condition are 6 and 10, I choose the first set as character degree set.

The first sentence is a special case of the second. In other words, the relation between the degrees are important.