Finite Group Databasebeta

← Group #6259

Character table — Group #6259

Order 216.

	C₁	C₂	C₃	C₄	C₅	C₆	C₇	C₈	C₉	C₁₀	C₁₁	C₁₂	C₁₃	C₁₄	C₁₅	C₁₆
size	1	2	3	6	6	6	6	6	9	12	12	24	24	27	36	36
order	1	3	2	6	9	18	18	18	2	3	3	9	9	2	6	6
χ₁	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1
χ₂	1	1	1	1	1	1	1	1	1	$\frac{- 1 + i \sqrt{3}}{2}$	$\frac{- 1 - i \sqrt{3}}{2}$	$\frac{- 1 + i \sqrt{3}}{2}$	$\frac{- 1 - i \sqrt{3}}{2}$	1	$\frac{- 1 + i \sqrt{3}}{2}$	$\frac{- 1 - i \sqrt{3}}{2}$
χ₃	1	1	1	1	1	1	1	1	1	$\frac{- 1 - i \sqrt{3}}{2}$	$\frac{- 1 + i \sqrt{3}}{2}$	$\frac{- 1 - i \sqrt{3}}{2}$	$\frac{- 1 + i \sqrt{3}}{2}$	1	$\frac{- 1 - i \sqrt{3}}{2}$	$\frac{- 1 + i \sqrt{3}}{2}$
χ₄	1	1	1	1	1	1	1	1	-1	1	1	1	1	-1	-1	-1
χ₅	1	1	1	1	1	1	1	1	-1	$\frac{- 1 + i \sqrt{3}}{2}$	$\frac{- 1 - i \sqrt{3}}{2}$	$\frac{- 1 + i \sqrt{3}}{2}$	$\frac{- 1 - i \sqrt{3}}{2}$	-1	$\frac{1 - i \sqrt{3}}{2}$	$\frac{1 + i \sqrt{3}}{2}$
χ₆	1	1	1	1	1	1	1	1	-1	$\frac{- 1 - i \sqrt{3}}{2}$	$\frac{- 1 + i \sqrt{3}}{2}$	$\frac{- 1 - i \sqrt{3}}{2}$	$\frac{- 1 + i \sqrt{3}}{2}$	-1	$\frac{1 + i \sqrt{3}}{2}$	$\frac{1 - i \sqrt{3}}{2}$
χ₇	2	2	2	2	-1	-1	-1	-1	0	2	2	-1	-1	0	0	0
χ₈	2	2	2	2	-1	-1	-1	-1	0	$- 1 + i \sqrt{3}$	$- 1 - i \sqrt{3}$	$\frac{1 - i \sqrt{3}}{2}$	$\frac{1 + i \sqrt{3}}{2}$	0	0	0
χ₉	2	2	2	2	-1	-1	-1	-1	0	$- 1 - i \sqrt{3}$	$- 1 + i \sqrt{3}$	$\frac{1 + i \sqrt{3}}{2}$	$\frac{1 - i \sqrt{3}}{2}$	0	0	0
χ₁₀	3	3	-1	-1	3	-1	-1	-1	3	0	0	0	0	-1	0	0
χ₁₁	3	3	-1	-1	3	-1	-1	-1	-3	0	0	0	0	1	0	0
χ₁₂	6	6	-2	-2	-3	1	1	1	0	0	0	0	0	0	0	0
χ₁₃	6	-3	6	-3	0	0	0	0	0	0	0	0	0	0	0	0
χ₁₄	6	-3	-2	1	0	2ζ+2ζ⁸	2ζ²+2ζ⁷	2ζ⁴+2ζ⁵	0	0	0	0	0	0	0	0
χ₁₅	6	-3	-2	1	0	2ζ²+2ζ⁷	2ζ⁴+2ζ⁵	2ζ+2ζ⁸	0	0	0	0	0	0	0	0
χ₁₆	6	-3	-2	1	0	2ζ⁴+2ζ⁵	2ζ+2ζ⁸	2ζ²+2ζ⁷	0	0	0	0	0	0	0	0

Here ζ is a primitive root of unity of order 9 (ζ⁹ = 1); i = ζ².