[GAP Forum] Is there a way

[PAUL HJELMSTAD]

GAP Forum,
 
I am looking for a way to study groups based on complementation, for example,
D4 X S3 X S2 where S2 is the complementation group of white and black beads
in a two colored necklace (This is after the convention used in Gilbert and Riordan
"Symmetry Types of Periodic Sequences, Ill. Journ. of Math. 1961)
 
I would like to study these groups and construct character tables as well.
 
An easy example is C4 X C3 X S2, here there are 44 necklaces with 6 white and 6 black
beads and the others merely collapse (12/0, 11/1, 10/2, 9/3, 8/4 and 7/5) so the 
answer here has order 1+1+6+19+43+66+44=180
 
I am happy to say I finally completely understand the construction of character tables
for the Symmetric Groups, small steps I guess.
 
Thanks
 
Paul