62.75 IsIsomorphicGroup

IsIsomorphicGroup( g1, g2 )

IsIsomorphicGroup determines if the groups g1 and g2 are isomorphic and if so, returns a group homomorphism that is an isomorphism between these two groups and false otherwise.

  gap> g1 := Group( (1,2,3) );
  Group( (1,2,3) )
  gap> g2 := Group( (7,8,9) );
  Group( (7,8,9) )
  gap> g1 = g2;
  false
  gap> IsIsomorphicGroup( g1, g2 );
  GroupHomomorphismByImages( Group( (1,2,3) ), Group( (7,8,9) ), 
  [ (1,2,3) ], [ (7,8,9) ] )

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