Nilpotency class and order determine degrees of irreducible representations for groups up to prime-fourth order
From Groupprops
This article gives a fact that is true for small groups of prime power order.More specifically, it is true for all groups of orderwhere
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 is a prime number and
. Then, for a group of prime power order of order
, the nilpotency class
of the group determines the degrees of irreducible representations of the group.
Here is the complete list:
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number of irreducible representations of degree 1 | number of irreducible representations of degree ![]() |
---|---|---|---|
0 | 0 | 1 | 0 |
1 | 1 | ![]() |
0 |
2 | 1 | ![]() |
0 |
3 | 1 | ![]() |
0 |
3 | 2 | ![]() |
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4 | 1 | ![]() |
0 |
4 | 2 | ![]() |
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4 | 3 | ![]() |
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