The table contains the following data for each of the 45 nonabelian groups G of order at most 30:

• the order |G| and, where appropriate, name of G.
• a 3-presentation <x|r|s> for G. It is given using the convention that
  • the first generator in x is denoted by x, the second generator is denoted by y, the third generator (if exists) is denoted by z;
  • the first relator in r is denoted by a, the second relator is denoted by b, the third by c and so on.
• the rank dim of the free abelian group underling the module of identities =₂K(x, r).
• a set v of elements in _r ZG that generates a ZG-submodule ' isomorphic to the ZG-module .
• the integral homology group H_n(G)=H_n(G,Z) for n=1,2,3.

How to use the table?

The main table