Finite Group Databasebeta

← Group #4186

Character table — Group #4186

Order 162.

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

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