<html><head><title>[grpconst] 3 Construction of All Groups</title></head>
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<h1>3 Construction of All Groups</h1><p>
<p>
The following function can be used to determine up to isomorphism
all groups of a given order. This method implements a combination
of the more specific functions described below.
<p>
Note that the chosen combination might not be the best possible for
every application. Thus, if this function takes too long to construct
the desired groups, then it might still be possible to determine these
groups using the functions outlined in the following chapters. Moreover,
the functions described in the following chapters provide more facilities
and this might help to determine groups with certain properties more
efficiently.
<p>
<a name = ""></a>
<li><code>ConstructAllGroups( </code><var>order</var><code> ) F</code>
<p>
Usually the output of this function is a list of groups. The soluble
groups in the list are given as pc groups and the others as permutation
groups. However, in some cases the output might contain lists of groups
as well. The groups is such a list could not be proved to be pairwise
non-isomorphic by the algorithm, although this is likely to be the case,
see Section <a href="CHAP004.htm#SECT004">Verifying non-isomorphism</a> for further details.
<p>
<pre>
gap> ConstructAllGroups( 60 );
[ <pc group of size 60 with 4 generators>,
<pc group of size 60 with 4 generators>,
<pc group of size 60 with 4 generators>,
<pc group of size 60 with 4 generators>,
<pc group of size 60 with 4 generators>,
<pc group of size 60 with 4 generators>,
<pc group of size 60 with 4 generators>,
<pc group of size 60 with 4 generators>,
<pc group of size 60 with 4 generators>,
<pc group of size 60 with 4 generators>,
<pc group of size 60 with 4 generators>,
<pc group of size 60 with 4 generators>,
A5 ]
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