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

This article gives a fact that is true for small groups of prime power order.More specifically, it is true for all groups of order $p^k$ where $k$ is at most equal to 4.
See more such facts| See more facts true for prime powers up to the same maximum power 4

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.

Here is the complete list:

$k$	$c$	number of irreducible representations of degree 1	number of irreducible representations of degree $p$
0	0	1	0
1	1	$p$	0
2	1	$p^2$	0
3	1	$p^3$	0
3	2	$p^2$	$p - 1$
4	1	$p^4$	0
4	2	$p^3$	$p^2 - p$
4	3	$p^2$	$p^2 - 1$

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