# 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 forsmallgroups of prime power order.More specifically, it is true for all groups of order where 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:

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 | ||

4 | 1 | 0 | |

4 | 2 | ||

4 | 3 |