Dear GAP-Forum,

Pat Callahan wrote in his e-mail

> GAP-forum,
> Is there a simple way to create a list of how many elements of each
order
> there are for a given group? Thanks,
> Pat Callahan

Here is quick solution :-)

# Order distribution of a group (for Pat Callahan)
# Sebastian Egner, 15.11.96, GAP v3.4

#F OrderDistributionGroup( <group> )
#F returns the distribution of the orders of the elements of
#F <group> as a sorted list of pairs [<order>, <frequency>].
#F (The function uses ConjugacyClasses.)
#F

OrderDistributionGroup := function ( G )
local cs, cs1, i;

cs := 
  List(
    ConjugacyClasses(G), 
    C -> [ Order(G, Representative(C)), Size(C) ]
  );

  Sort(cs);
  cs1 := [ cs[1] ];
  for i in [2..Length(cs)] do
    if cs[i][1] = cs1[Length(cs1)][1] then
      cs1[Length(cs1)][2] := cs1[Length(cs1)][2] + cs[i][2];
    else
      Add(cs1, cs[i]);
    fi;
  od;
  return cs1;
end;

- - - 
Sebastian Egner
Institut für Algorithmen und Kognitive Systeme
Universität Karlsruhe
Am Fasanengarten 5
D-76128 Karlsruhe
Tel.    +49 721 608 4304 / +49 721 96400 14
Fax.    +49 721 69 68 93
e-mail  egner@informatik.uni-karlsruhe.de