[GAP Forum] Class structure identification of symmetric groups

[Goetz Pfeiffer]

Dear Raghunathan, dear Forum,

the function 'CharacterTableWreathSymmetric' constructs the character
table of the wreath product of a group G with the symmetric group on n
points from the character table of G and supplies it with lists of
partitions as labels for the classes (and the characters).  The
underlying algorithm is described in

Character Tables of Weyl Groups in GAP.
Bayreuther Math. Schr. 47 (1994), 165-222.
(http://schmidt.nuigalway.ie/~goetz/pub/ctweyl.html)

Goetz Pfeiffer


On Fri, Jan 13, 2006 at 10:18:36AM +0000, raghunathan wrote:
> Respected Dr.Frank Luebeck and GAP Forum,
>           Thank you very much for ur valuable suggestion regarding class structures of symmetric groups which can be correlated to numerical partitions of the degree of the symmetric groups.But, for a wreath product group as simple as S2[S2] whose conjugacy classes' structures as given by GAP is as
> 
> gap> > [ ()^G, (3,4)^G, (1,2)(3,4)^G, (1,3)(2,4)^G, (1,3,2,4)^G ]
> 
> has two classes of permutations each with two cycles of length two (1,2)(3,4) and (1,3)(2,4). Also, the sequential commands, 
> 
> gap>s:=SymmetricGroup(2);;w:=WreathProduct(s,s);;t:=CharacterTable(w);;ClassParameters(t); 
>          did not work.Is there a way to overcome this problem by relating the abstract symbols usually displayed above any character table given by GAP as 1a 2a 2b...etc., which in the case of S4 is as follows to the class structures?
> 
>      2  3  2  3  .  2
>      3  1  .  .  1  .
> 
>        1a 2a 2b 3a 4a
>     2P 1a 1a 1a 3a 2b
>     3P 1a 2a 2b 1a 4a
> 
> X.1     1 -1  1  1 -1
> X.2     3 -1 -1  .  1
> X.3     2  .  2 -1  .
> X.4     3  1 -1  . -1
> X.5     1  1  1  1  1
> 
> Thanks,
> Raghunathan,R.,
> M.Sc.Chemistry,
> Department of Chemistry,
> Indian Institute of Technology Madras,
> Chennai-36,
> India.
> 
> 
> 
> 
> 

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