Groups of order 81

This article gives basic information comparing and contrasting groups of order $$81$$. See also more detailed information on specific subtopics through the links:

Summary information
Here, rows are arithmetic functions taking values between 0 and 4, and the columns give the possible values of these functions. The entry in each cell is the number of isomorphism classes of groups for which the row arithmetic function takes this column value. Note that all the row sums must equal 15, which is the total number of groups of order 81.

Functions taking values between 0 and 4
These measure ranks of subgroups, lengths of series, or the prime-base logarithms of orders of certain subgroups.