Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
DanielMcDonald`GroupTheoryPaclet`
GroupDirectProduct  |
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Examples
(1)
Basic Examples
(1)
▪
Compute the direct product of the cyclic and symmetric groups of degree 3:
In[1]:=
 | GroupDirectProduct |
Out[1]=
PermutationGroup[{Cycles[{}],Cycles[{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,14},{15,16},{17,18}}],Cycles[{{1,3},{2,5},{4,6},{7,9},{8,11},{10,12},{13,15},{14,17},{16,18}}],Cycles[{{1,5,4},{2,3,6},{7,11,10},{8,9,12},{13,17,16},{14,15,18}}],Cycles[{{1,4,5},{2,6,3},{7,10,11},{8,12,9},{13,16,17},{14,18,15}}],Cycles[{{1,6},{2,4},{3,5},{7,12},{8,10},{9,11},{13,18},{14,16},{15,17}}],Cycles[{{1,13,7},{2,14,8},{3,15,9},{4,16,10},{5,17,11},{6,18,12}}],Cycles[{{1,14,7,2,13,8},{3,16,9,4,15,10},{5,18,11,6,17,12}}],Cycles[{{1,15,7,3,13,9},{2,17,8,5,14,11},{4,18,10,6,16,12}}],Cycles[{{1,17,10},{2,15,12},{3,18,8},{4,13,11},{5,16,7},{6,14,9}}],Cycles[{{1,16,11},{2,18,9},{3,14,12},{4,17,7},{5,13,10},{6,15,8}}],Cycles[{{1,18,7,6,13,12},{2,16,8,4,14,10},{3,17,9,5,15,11}}],Cycles[{{1,7,13},{2,8,14},{3,9,15},{4,10,16},{5,11,17},{6,12,18}}],Cycles[{{1,8,13,2,7,14},{3,10,15,4,9,16},{5,12,17,6,11,18}}],Cycles[{{1,9,13,3,7,15},{2,11,14,5,8,17},{4,12,16,6,10,18}}],Cycles[{{1,11,16},{2,9,18},{3,12,14},{4,7,17},{5,10,13},{6,8,15}}],Cycles[{{1,10,17},{2,12,15},{3,8,18},{4,11,13},{5,7,16},{6,9,14}}],Cycles[{{1,12,13,6,7,18},{2,10,14,4,8,16},{3,11,15,5,9,17}}]}]
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