Groups of prime power order
From Groupprops
This is a specific information page. For the definition of the term and related information, see group of prime power order
This article gives information about groups of prime power order, i.e., order where
is a prime number and
is a nonnegative integer. The case
, i.e., groups of order 1, only includes the trivial group, so we exclude this case from the discussion below.
Information
Counts
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Generic formula for number of groups of order ![]() ![]() |
Minimum ![]() |
Number of groups of order ![]() |
Number of groups of order ![]() |
Number of groups of order ![]() |
Number of groups of order ![]() |
Number of groups of order ![]() |
---|---|---|---|---|---|---|---|
1 | 1 | 2 | 1 | 1 | 1 | 1 | 1 |
2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
3 | 5 | 2 | 5 | 5 | 5 | 5 | 5 |
4 | 15 | 3 | 14 | 15 | 15 | 15 | 15 |
5 | ![]() |
5 | 51 | 67 | 77 | 83 | 87 |
6 | ![]() |
5 | 267 | 504 | 684 | 860 | 1192 |
7 | ![]() ![]() ![]() ![]() |
7 | 2328 | 9310 | 34297 | 113147 | 750735 |
8 | unknown | 56092 | 1396077 | unknown | unknown | unknown | |
9 | unknown | 10494213 | unknown | unknown | unknown | unknown | |
10 | unknown | 49487365422 | unknown | unknown | unknown | unknown |