This sentence is impossible in English. It should be: "The group of youths is big". Youths are people, "youth" is one person or an abstract noun referring to the state of being young.
The youth's group is big? Duolingo seems to have abandoned the apostrophe in this course.
The group of the youth?
A simple "youth group" would suffice in english. The way this course phrases the genitive case in english in a lot of sentences is very unnatural.