OperationCosetsFpGroup( G, H )
OperationCosetsFpGroup
returns the permutation representation of the
finitely presented group G on the cosets of the subgroup H as a
permutation group. Note that this permutation representation is faithful
if and only if H has a trivial core in G.
gap> F2 := FreeGroup( "a", "b" ); Group( a, b ) gap> A5 := F2 / [ F2.1^2, F2.2^3, (F2.1*F2.2)^5 ]; Group( a, b ) gap> OperationCosetsFpGroup( A5, > Subgroup( A5, [ A5.1, A5.2*A5.1*A5.2*A5.1*A5.2^-1 ] ) ); Group( (2,3)(4,5), (1,2,4) ) gap> Size( last ); 60
OperationCosetsFpGroup
simply calls CosetTableFpGroup
, applies
PermList
to each row of the table, and returns the group generated by
those permutations (see CosetTableFpGroup, PermList).
GAP 3.4.4