On Sun, May 31, 2015 at 04:48:59PM +0800, 杨高 wrote: Do you work with GAP3? Is it really necessary for you?

> > Is this the correct and most concise way to construct PGL(2,3) with GAP? In GAP4 you can just do gap> ProjectiveGeneralLinearGroup(2,3); Group([ (3,4), (1,2,4) ]) > > > > W:=GeneralLinearGroup(2,3);; > > H:=Subgroup(W,[[[Z(3),0*Z(3)],[0*Z(3),Z(3)]]]);; > > B:=W/H;; > > > Morevoer, I want to construct the character table of this group. But there is > ian error. > > > >Display(CharTable(B)); > Error, sorry, I don't know how to construct the table of <grp> > in > CharTable( B ) called from > main loop well, GAP4 has no difficulty here: gap> H:=Subgroup(W,[[[Z(3),0*Z(3)],[0*Z(3),Z(3)]]]);; gap> B:=W/H;; gap> Display(CharacterTable(B)); CT2 2 3 2 . 3 2 3 1 . 1 . . 1a 2a 3a 2b 4a 2P 1a 1a 3a 1a 2b 3P 1a 2a 1a 2b 4a X.1 1 1 1 1 1 X.2 1 -1 1 1 -1 X.3 2 . -1 2 . X.4 3 -1 . -1 1 X.5 3 1 . -1 -1 gap> > So there are question I would like to ask. For constructing character tables, > what kind of groups can GAP deal with? Can GAP construct the character table > of PGL(n,m)? If the answer is yes, then how can I do this with it? You can contruct the character table of a given group, but it gets slower as the size etc grows. How far do you need to go with n and m? There are some infinite families of groups for which GAP can construct character tables directly, see http://www.gap-system.org/Manuals/pkg/ctbllib/doc/chap4.html#X81E3F9A384365282 E.g. for n=2 one can have tables of the PSL groups. HTH, Dmitrii > > > Thanks to everyone. > _______________________________________________ > Forum mailing list > Forum@mail.gap-system.org > http://mail.gap-system.org/mailman/listinfo/forum _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum