The normis a positive integer, because it is the sum of the squares of the multiplicities of the irreducible constituents. The character restriction norm bound and make it at most three. It is therefore , , or .
All three values occur:
- In with , the trivial character remains irreducible on , giving norm .
- For the same pair, the two-dimensional standard representation of the symmetric group restricts to the sum of the trivial and nontrivial linear characters of , giving norm .
- In with its normal Klein four-group , the three-dimensional irreducible representation of the alternating group on four letters restricts to the sum of the three nontrivial linear characters of , giving norm .
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