GroupTheory`
GroupTheory`

GTConjugacyClass

GTConjugacyClass[group,subgroup]

constructs the set of all subgroups conjugated to a subgroup of a group.

Details and Options

  • The conjugacy class of a subgroup in consists of the set of groups conjugated 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

Examples

Basic Examples  (1)

First load the package:

Install group .

Find all subgroups.

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

Conjugacy classes to all subgroups.

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