(1) > )r axiom/directProduct
)set output algebra off
)set output mathml on
 first calculate C2 x C3
C2 := FiniteGroup(2,[[1,2],[2,1]],["1","m"])
Type: Type
DP := directProduct([[1,2,3],[2,3,1],[3,1,2]],["1","r","rr"])$C2
Type: Type
toTable()$DP
1 
r 
rr 
m 
mr 
mrr 
r 
rr 
1 
mr 
mrr 
m 
rr 
1 
r 
mrr 
m 
mr 
m 
mr 
mrr 
1 
r 
rr 
mr 
mrr 
m 
r 
rr 
1 
mrr 
m 
mr 
rr 
1 
r 
Type: Table(6)
setGenerators([false,true,false,true,false,false])$DP
Type: Void
PDP := toPermutation()$DP
<(1 2 3)(4 5 6),(1 4)(2 5)(3 6)>
Type: PermutationGroup(Integer)
permutationRepresentation(PDP,6)
[

0 
0 
1 
0 
0 
0 
1 
0 
0 
0 
0 
0 
0 
1 
0 
0 
0 
0 
0 
0 
0 
0 
0 
1 
0 
0 
0 
1 
0 
0 
0 
0 
0 
0 
1 
0 

,

0 
0 
0 
1 
0 
0 
0 
0 
0 
0 
1 
0 
0 
0 
0 
0 
0 
1 
1 
0 
0 
0 
0 
0 
0 
1 
0 
0 
0 
0 
0 
0 
1 
0 
0 
0 


]

Type: List(Matrix(Integer))
 now calculate C3 x C2
C3 := FiniteGroup(3,[[1,2,3],[2,3,1],[3,1,2]],["1","r","rr"])
Type: Type
DP := directProduct([[1,2],[2,1]],["1","m"])$C3
Type: Type
toTable()$DP
1 
m 
r 
rm 
rr 
rrm 
m 
1 
rm 
r 
rrm 
rr 
r 
rm 
rr 
rrm 
1 
m 
rm 
r 
rrm 
rr 
m 
1 
rr 
rrm 
1 
m 
r 
rm 
rrm 
rr 
m 
1 
rm 
r 
Type: Table(6)
setGenerators([false,true,true,false,false,false])$DP
Type: Void
PDP := toPermutation()$DP
<(1 2)(3 4)(5 6),(1 3 5)(2 4 6)>
Type: PermutationGroup(Integer)
permutationRepresentation(PDP,6)
[

0 
1 
0 
0 
0 
0 
1 
0 
0 
0 
0 
0 
0 
0 
0 
1 
0 
0 
0 
0 
1 
0 
0 
0 
0 
0 
0 
0 
0 
1 
0 
0 
0 
0 
1 
0 

,

0 
0 
0 
0 
1 
0 
0 
0 
0 
0 
0 
1 
1 
0 
0 
0 
0 
0 
0 
1 
0 
0 
0 
0 
0 
0 
1 
0 
0 
0 
0 
0 
0 
1 
0 
0 


]

Type: List(Matrix(Integer))
(13) >
