[GAP Forum] G = O^+_8(2), H = 3^D_4(2) and K = 2^F_4(2)^\prime
Frank Lübeck
frank.luebeck at math.rwth-aachen.de
Sun May 11 09:05:27 BST 2014
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/
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