Finite Group Databasebeta

Character table — Group #25

Order 13.

	C₁	C₂	C₃	C₄	C₅	C₆	C₇	C₈	C₉	C₁₀	C₁₁	C₁₂	C₁₃
size	1	1	1	1	1	1	1	1	1	1	1	1	1
order	1	13	13	13	13	13	13	13	13	13	13	13	13
χ₁	1	1	1	1	1	1	1	1	1	1	1	1	1
χ₂	1	ζ	ζ²	ζ³	ζ⁴	ζ⁵	ζ⁶	ζ⁷	ζ⁸	ζ⁹	ζ¹⁰	ζ¹¹	ζ¹²
χ₃	1	ζ²	ζ⁴	ζ⁶	ζ⁸	ζ¹⁰	ζ¹²	ζ	ζ³	ζ⁵	ζ⁷	ζ⁹	ζ¹¹
χ₄	1	ζ³	ζ⁶	ζ⁹	ζ¹²	ζ²	ζ⁵	ζ⁸	ζ¹¹	ζ	ζ⁴	ζ⁷	ζ¹⁰
χ₅	1	ζ⁴	ζ⁸	ζ¹²	ζ³	ζ⁷	ζ¹¹	ζ²	ζ⁶	ζ¹⁰	ζ	ζ⁵	ζ⁹
χ₆	1	ζ⁵	ζ¹⁰	ζ²	ζ⁷	ζ¹²	ζ⁴	ζ⁹	ζ	ζ⁶	ζ¹¹	ζ³	ζ⁸
χ₇	1	ζ⁶	ζ¹²	ζ⁵	ζ¹¹	ζ⁴	ζ¹⁰	ζ³	ζ⁹	ζ²	ζ⁸	ζ	ζ⁷
χ₈	1	ζ⁷	ζ	ζ⁸	ζ²	ζ⁹	ζ³	ζ¹⁰	ζ⁴	ζ¹¹	ζ⁵	ζ¹²	ζ⁶
χ₉	1	ζ⁸	ζ³	ζ¹¹	ζ⁶	ζ	ζ⁹	ζ⁴	ζ¹²	ζ⁷	ζ²	ζ¹⁰	ζ⁵
χ₁₀	1	ζ⁹	ζ⁵	ζ	ζ¹⁰	ζ⁶	ζ²	ζ¹¹	ζ⁷	ζ³	ζ¹²	ζ⁸	ζ⁴
χ₁₁	1	ζ¹⁰	ζ⁷	ζ⁴	ζ	ζ¹¹	ζ⁸	ζ⁵	ζ²	ζ¹²	ζ⁹	ζ⁶	ζ³
χ₁₂	1	ζ¹¹	ζ⁹	ζ⁷	ζ⁵	ζ³	ζ	ζ¹²	ζ¹⁰	ζ⁸	ζ⁶	ζ⁴	ζ²
χ₁₃	1	ζ¹²	ζ¹¹	ζ¹⁰	ζ⁹	ζ⁸	ζ⁷	ζ⁶	ζ⁵	ζ⁴	ζ³	ζ²	ζ

Here ζ is a primitive root of unity of order 13 (ζ¹³ = 1).