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Use the orthonormal condition on irreducible characters to set up a system of equations to solve for the character of the remaining irreducible representation.

 Use the orthonormal condition on irreducible characters to set up a system of equations to solve for thecharacter table of S. conjugacy classes e (12) (123) (12)(34) 1 1 1 1 1 1 1 3 1 0 Xtriv Xsign XV -1 (1234) 1

Use the orthonormal condition on irreducible characters to set up a system of equations to solve for the character of the remaining irreducible representation. What is the dimension of this remaining representation? character table of S. conjugacy classes e (12) (123) (12)(34) 1 1 1 1 1 1 1 3 1 0 Xtriv Xsign XV -1 (1234) 1 -1 -1

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