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
- 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)
How to use the table?
The main table