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===Klein Four-Group===
===Klein Four-Group V<sub>4</sub>===
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| <math>\operatorname{e}</math>
| <math>\operatorname{e}</math>
|}
|}
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===Symmetric Group S<sub>3</sub>===
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<pre>
Permutations or Substitutions in Sym_{A, B, C}
o---------o---------o---------o---------o---------o---------o
| | | | | | |
| e | f | g | h | i | j |
| | | | | | |
o=========o=========o=========o=========o=========o=========o
| | | | | | |
| A B C | A B C | A B C | A B C | A B C | A B C |
| | | | | | |
| | | | | | | | | | | | | | | | | | | | | | | | |
| v v v | v v v | v v v | v v v | v v v | v v v |
| | | | | | |
| A B C | C A B | B C A | A C B | C B A | B A C |
| | | | | | |
o---------o---------o---------o---------o---------o---------o
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Symmetric Group S_3
o-------------------------------------------------o
| |
| ^ |
| e / \ e |
| / \ |
| / e \ |
| f / \ / \ f |
| / \ / \ |
| / f \ f \ |
| g / \ / \ / \ g |
| / \ / \ / \ |
| / g \ g \ g \ |
| h / \ / \ / \ / \ h |
| / \ / \ / \ / \ |
| / h \ e \ e \ h \ |
| i / \ / \ / \ / \ / \ i |
| / \ / \ / \ / \ / \ |
| / i \ i \ f \ j \ i \ |
| j / \ / \ / \ / \ / \ / \ j |
| / \ / \ / \ / \ / \ / \ |
| ( j \ j \ j \ i \ h \ j ) |
| \ / \ / \ / \ / \ / \ / |
| \ / \ / \ / \ / \ / \ / |
| \ h \ h \ e \ j \ i / |
| \ / \ / \ / \ / \ / |
| \ / \ / \ / \ / \ / |
| \ i \ g \ f \ h / |
| \ / \ / \ / \ / |
| \ / \ / \ / \ / |
| \ f \ e \ g / |
| \ / \ / \ / |
| \ / \ / \ / |
| \ g \ f / |
| \ / \ / |
| \ / \ / |
| \ e / |
| \ / |
| \ / |
| v |
| |
o-------------------------------------------------o
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