Finite Group Databasebeta

← Group #6318

Character table — Group #6318

Order 216.

	C₁	C₂	C₃	C₄	C₅	C₆	C₇	C₈	C₉	C₁₀	C₁₁	C₁₂	C₁₃	C₁₄	C₁₅
size	1	2	8	8	8	9	9	9	18	18	18	27	27	27	27
order	1	3	3	3	3	2	4	4	6	12	12	8	8	8	8
χ₁	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	1	1	-1	-1	-1	-1
χ₃	1	1	1	1	1	1	-1	-1	1	-1	-1	$i$	$i$	$- i$	$- i$
χ₄	1	1	1	1	1	1	-1	-1	1	-1	-1	$- i$	$- i$	$i$	$i$
χ₅	1	1	1	1	1	-1	$i$	$- i$	-1	$i$	$- i$	ζ⁷+ζ²³	−ζ⁷−ζ²³	−ζ⁵−ζ¹³	ζ⁵+ζ¹³
χ₆	1	1	1	1	1	-1	$i$	$- i$	-1	$i$	$- i$	−ζ⁷−ζ²³	ζ⁷+ζ²³	ζ⁵+ζ¹³	−ζ⁵−ζ¹³
χ₇	1	1	1	1	1	-1	$- i$	$i$	-1	$- i$	$i$	−ζ⁵−ζ¹³	ζ⁵+ζ¹³	ζ⁷+ζ²³	−ζ⁷−ζ²³
χ₈	1	1	1	1	1	-1	$- i$	$i$	-1	$- i$	$i$	ζ⁵+ζ¹³	−ζ⁵−ζ¹³	−ζ⁷−ζ²³	ζ⁷+ζ²³
χ₉	2	-1	2	-1	-1	2	2	2	-1	-1	-1	0	0	0	0
χ₁₀	2	-1	2	-1	-1	2	-2	-2	-1	1	1	0	0	0	0
χ₁₁	2	-1	2	-1	-1	-2	$2 i$	$- 2 i$	1	$- i$	$i$	0	0	0	0
χ₁₂	2	-1	2	-1	-1	-2	$- 2 i$	$2 i$	1	$i$	$- i$	0	0	0	0
χ₁₃	8	8	-1	-1	-1	0	0	0	0	0	0	0	0	0	0
χ₁₄	8	-4	-1	$\frac{1 - 3 i \sqrt{3}}{2}$	$\frac{1 + 3 i \sqrt{3}}{2}$	0	0	0	0	0	0	0	0	0	0
χ₁₅	8	-4	-1	$\frac{1 + 3 i \sqrt{3}}{2}$	$\frac{1 - 3 i \sqrt{3}}{2}$	0	0	0	0	0	0	0	0	0	0

Here ζ is a primitive root of unity of order 24 (ζ²⁴ = 1); i = ζ⁶.