Kernel:
Finite Groups, Abelian Groups
Sage has some support for computing with permutation groups, finite classical groups (such as ), finite matrix groups (with your own generators), and abelian groups (even infinite ones). Much of this is implemented using the interface to GAP.
For example, to create a permutation group, give a list of generators, as in the following example.
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You can also obtain the character table (in LaTeX format) in Sage:
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Sage also includes classical and matrix groups over finite fields:
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You can also compute using abelian groups (infinite and finite):
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