[GAP Forum] [newbie] Direct product decomposition

Joe Bohanon jbohanon2 at gmail.com
Tue Feb 17 19:25:02 GMT 2009

You can try DirectFactorsOfGroup(G);

You can also try StructureDescription(G), but keep in mind that that 
sometimes works very slowly, and it doesn't give you the actual subgroups.

For example:

gap> G:=DirectProduct(SmallGroup(8,4),DihedralGroup(8));
<pc group of size 64 with 6 generators>
gap> DirectFactorsOfGroup(G);
#I  Step 3, 4 invariant subgroups
#I  Step 4, 15 invariant subgroups
#I  Step 5, 66 invariant subgroups
#I  Step 6, 77 invariant subgroups
#I  Step 7, 90 invariant subgroups
#I  Step 3, 4 invariant subgroups
#I  Step 4, 5 invariant subgroups
#I  Step 3, 4 invariant subgroups
#I  Step 4, 5 invariant subgroups
[ Group([ f1, f2, f3 ]), Group([ f3*f4, f5, f6 ]) ]
gap> StructureDescription(G);
"Q8 x D8"

By the way, is it possible for some future version of GAP to have the 
functions QuaternionGroup, SemidihedralGroup and ModularGroup?


T 145 wrote:
> With apologies if this is a FAQ ... how do I get GAP to decompose (factorise) a group into the essentially-unique direct product of indecomposable groups?
> Thanks,
> Ed.
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