GAP Manual: 7.17. Centre

Centre( G )

Centre returns the centre of G.

The centre of a group G is defined as the centralizer of G in G.

Note that Centre sets and tests the record component G.centre.

    gap> d8 := Group( (1,2,3,4), (1,2)(3,4) );
    Group( (1,2,3,4), (1,2)(3,4) )
    gap> Centre( d8 );
    Subgroup( Group( (1,2,3,4), (1,2)(3,4) ), [ (1,3)(2,4) ] ) 

The default group function GroupOps.Centre uses Centralizer (see Centralizer) in order to compute the centralizer of G in G.