Summary

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 Hn(G)=Hn(G,Z) for n=1,2,3.

How to use the table?

The main table