GROUP THEORY SYMBOL

GTConjugacyClass

GTConjugacyClass[group,subgroup]
constructs the set of all subgroups conjugated to a subgroup of a group.

DetailsDetails

  • The conjugacy class of a subgroup in consists of the set of groups conjugate to .
  • If the order of subgroup is larger than the order of group, both groups will be interchanged.
  • The following option can be given:
  • GOFastGOFastValueControls the input validation

ExamplesExamplesopen allclose all

Basic Examples  (1)Basic Examples  (1)

First load the package:

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Install group .

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Find all subgroups.

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Subgroups are , four subgroups isomorphic to , and two subgroups .

Conjugacy classes to all subgroups.

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All subgroups contain two groups in the conjugacy class. All other conjugacy classes contain the subgroup itself.

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