[GAP Forum] G = O^+_8(2), H = 3^D_4(2) and K = 2^F_4(2)^\prime

[Frank Lübeck]

On Sat, May 10, 2014 at 07:54:12PM +0430, arashrafi at kashanu.ac.ir wrote:
> Suppose G = O^+_8(2), H = 3^D_4(2) and K = 2^F_4(2)^\prime. I need to
> the element orders and their multiplicity for these groups.
> Unfortunately, I could not obtain this information from GAP. Any
> comments will be highly appreciated.
> 
> Regards, Alireza

Dear Alireza, dear Forum,

This information is contained in the character tables which are available
with GAP:

gap> t := CharacterTable("O8+(2)");
CharacterTable( "O8+(2)" )
gap> # i-th entry is order of elements in i-th class:
gap> OrdersClassRepresentatives(t); 
[ 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 6, 6, 6, 6, 6, 
  6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 8, 8, 9, 9, 9, 10, 10, 10, 12, 12, 12, 12, 
  12, 12, 12, 15, 15, 15 ]
gap> # i-th entry is number of elements in i-th class:
gap> SizesConjugacyClasses(t);
[ 1, 1575, 3780, 3780, 3780, 56700, 2240, 2240, 2240, 89600, 268800, 37800, 
  340200, 907200, 907200, 907200, 2721600, 580608, 580608, 580608, 100800, 
  100800, 100800, 604800, 604800, 604800, 806400, 806400, 806400, 806400, 
  2419200, 2419200, 2419200, 7257600, 24883200, 5443200, 5443200, 6451200, 
  6451200, 6451200, 8709120, 8709120, 8709120, 1209600, 1209600, 1209600, 
  4838400, 7257600, 7257600, 7257600, 11612160, 11612160, 11612160 ]

So, for example, there are 3*11612160 elements of order 15 in O8+(2).

The other two cases you get with
  t := CharacterTable("3D4(2)");
  t := CharacterTable("2F4(2)'");

Best regards,
   Frank

-- 
///  Dr. Frank Lübeck, Lehrstuhl D für Mathematik, Templergraben 64,
\\\                    52062 Aachen, Germany
///  E-mail: Frank.Luebeck at Math.RWTH-Aachen.De
\\\  WWW:    http://www.math.rwth-aachen.de/~Frank.Luebeck/