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# 8.1 Groups and actions

- `OnSubgroups(` subgroup`,` aut`) F`

  For a group G and an automorphism aut of G, `OnSubgroups(`subgroup`,`aut`)` is the image of subgroup under aut

      gap> G:=Group((1,2,3),(2,3));
      Group([ (1,2,3), (2,3) ])
      gap> alpha:=InnerAutomorphism(G,(1,2,3));
      ^(1,2,3)
      gap> OnSubgroups(Subgroup(G,[(2,3)]),alpha);
      Group([ (1,3) ])

- `RepsCClassesGivenOrder(` group`,` order`) O`

  `RepsCClassesGivenOrder(` group`,` order`)` returns all elements of order order up to conjugacy. Note that the representatives are not always the smallest elements of each conjugacy class.

      gap> RepsCClassesGivenOrder(SymmetricGroup(5),2);
      [ (4,5), (2,3)(4,5) ]

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