KöMaL 2019 C1569

In a class of 24, there are an odd number of students whose first name is Sophia. When the class is listed in alphabetical order (of family names) and students are numbered in this order, the number of the first Sophia on the list is equal to the number of Sophias in the class, and the number of the third Sophia on the list is three times the number of Sophias in the class. Given that each Sophia on the list is immediately preceded or followed by another Sophia, determine the numbers assigned to all the Sophias on the list.