For groups H, G with Hleq G, the induced character (1_G)^H is called the permutation character of the operation of G on the right cosets of H. If only the character table of G is known, one can try to get informations about possible subgroups of G by inspection of those characters pi which might be permutation characters, using that such a character must have at least the following properties:
Any character with these properties will be called a permutation character candidate from now on.
GAP provides some algorithms to compute permutation character
candidates, see PermChars. Some information about the subgroup can
computed from a permutation character using
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