WOLFRAM

Wolfram Language Fast Introduction for Math Students
Get Started »

Group Theory

SymmetricGroup, AlternatingGroup, DihedralGroup and many other named groups are built-in symbols.

Get a list of group elements:

In[1]:=
Click for copyable input
⨯ 
GroupElements[SymmetricGroup[2]]
Out[1]=

Determine the generators of a group:

In[2]:=
Click for copyable input
⨯ 
GroupGenerators[SymmetricGroup[3]]
Out[2]=

Create a permutation group from two generators:

In[1]:=
Click for copyable input
⨯ 
PermutationGroup[{Cycles[{{3, 1, 2}}], Cycles[{{2, 5, 6}}]}]

Compute its order:

In[2]:=
Click for copyable input
⨯ 
GroupOrder[%]
Out[2]=

Show the multiplication table for a group:

In[1]:=
Click for copyable input
⨯ 
TableForm[GroupMultiplicationTable[DihedralGroup[2]], 
 TableHeadings -> Automatic]
Out[1]=

Visualize it with a Cayley graph:

In[2]:=
Click for copyable input
⨯ 
CayleyGraph[DihedralGroup[2]]
Out[2]=

QUICK REFERENCE: Group Theory »