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

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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


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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