Nilpotency class and order determine degrees of irreducible representations for groups up to prime-fourth order

Statement
Suppose $$p$$ is a prime number and $$0 \le k \le 4$$. Then, for a group of prime power order of order $$p^k$$, the nilpotency class $$c$$ of the group determines the degrees of irreducible representations of the group.

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Similar facts

 * Nilpotency class and order determine conjugacy class size statistics for groups up to prime-fourth order