I assume you mean the dihedral group of order 16, so define it: gap> D16 := DihedralGroup( 16 ); <pc group of size 16 with 4 generators>
and then run the command gap> LatticeSubgroups( D16 ); which should display gap> <subgroup lattice of <pc group of size 16 with 4 generators>, 11 classes, 19 subgroups> This displays information about the lattice of subgroups of D16 using the conjugacy relation for subgroups (http://www.gap-system.org/Manuals/doc/ref/chap39.html#X7FA267497CFC0550). The classes are the equivalence classes, 11 in this case, and there are 19 subgroups in total. You cannot access the subgroups from the lattice directly (it is not a list of subgroups), but through the conjugacy classes. To do this you have to call the ConjugacyClassesOfSubgroups( <lattice> ) function with a given lattice, which gives you a list of the classes, and then flatten that list. So you could do something like: gap> subs := Flat( List( cls, c -> Elements( c ) ) ) ); [ Group([ ]), Group([ f4 ]), Group([ f1 ]), Group([ f1*f3 ]), Group([ f1*f4 ]), Group([ f1*f3*f4 ]), Group([ f1*f2 ]), Group([ f1*f2*f3 ]), Group([ f1*f2*f4 ]), Group([ f1*f2*f3*f4 ]), Group([ f4, f3 ]), Group([ f4, f1 ]), Group([ f1*f3, f4 ]), Group([ f4, f1*f2 ]), Group([ f1*f2*f3, f4 ]), Group([ f4, f3, f1 ]), Group([ f4, f3, f2 ]), Group([ f4, f3, f1*f2 ]), Group([ f4, f3, f1, f2 ]) ] An alternative to finding the number of subgroups is to load the Sonata package (http://www.gap-system.org/Packages/sonata.html) using gap> LoadPackage( “Sonata” ); and then run the command gap> Number( Subgroups( D16 ) ); which should display 19. Sandeep > On 19 Apr 2015, at 11:35, abdulhakeem alayiwola <lovepgro...@gmail.com> wrote: > > how do i get the number of subgroups of D-16? > _______________________________________________ > Forum mailing list > Forum@mail.gap-system.org > http://mail.gap-system.org/mailman/listinfo/forum Sandeep Murthy s.mur...@mykolab.com
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