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
`<`for G. It is given using the convention that__x__|__r__|__s__>- the first generator in
is denoted by__x__`x`, the second generator is denoted by`y`, the third generator (if exists) is denoted by`z`; - the first relator in
is denoted by__r__`a`, the second relator is denoted by`b`, the third by`c`and so on.

- the first generator in
- the rank dim
_{}of the free abelian group underling the module of identities =_{2}K(,__x__).__r__ - a set
__v__of elements in_{r}**Z**G that generates a**Z**G-submodule`'`isomorphic to the**Z**G-module . - the integral homology group H
_{n}(G)=H_{n}(G,**Z**) for n=1,2,3.