Finite Group Databasebeta

← Group #6321

Character table — Group #6321

Order 216.

	C₁	C₂	C₃	C₄	C₅	C₆	C₇	C₈	C₉	C₁₀	C₁₁	C₁₂	C₁₃	C₁₄	C₁₅	C₁₆	C₁₇	C₁₈
size	1	2	4	4	4	4	6	6	6	8	9	12	12	12	18	18	36	54
order	1	3	3	3	3	3	2	6	6	3	2	6	6	6	2	6	6	4
χ₁	1	1	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	1	1	1	1	1	-1	1	-1	-1
χ₃	1	1	1	1	1	1	-1	-1	-1	1	1	-1	-1	-1	1	1	1	-1
χ₄	1	1	1	1	1	1	-1	-1	-1	1	1	-1	-1	-1	-1	1	-1	1
χ₅	2	2	2	2	2	2	0	0	0	2	-2	0	0	0	0	-2	0	0
χ₆	2	-1	2	-1	-1	2	0	$i \sqrt{3}$	$- i \sqrt{3}$	-1	-2	0	$i \sqrt{3}$	$- i \sqrt{3}$	0	1	0	0
χ₇	2	-1	2	-1	-1	2	0	$- i \sqrt{3}$	$i \sqrt{3}$	-1	-2	0	$- i \sqrt{3}$	$i \sqrt{3}$	0	1	0	0
χ₈	2	-1	2	-1	-1	2	2	-1	-1	-1	2	2	-1	-1	0	-1	0	0
χ₉	2	-1	2	-1	-1	2	-2	1	1	-1	2	-2	1	1	0	-1	0	0
χ₁₀	4	4	1	1	1	-2	2	2	2	-2	0	-1	-1	-1	0	0	0	0
χ₁₁	4	4	1	1	1	-2	-2	-2	-2	-2	0	1	1	1	0	0	0	0
χ₁₂	4	4	-2	-2	-2	1	0	0	0	1	0	0	0	0	2	0	-1	0
χ₁₃	4	4	-2	-2	-2	1	0	0	0	1	0	0	0	0	-2	0	1	0
χ₁₄	4	-2	1	$\frac{- 1 + 3 i \sqrt{3}}{2}$	$\frac{- 1 - 3 i \sqrt{3}}{2}$	-2	2	$- 1 + i \sqrt{3}$	$- 1 - i \sqrt{3}$	1	0	-1	$\frac{1 - i \sqrt{3}}{2}$	$\frac{1 + i \sqrt{3}}{2}$	0	0	0	0
χ₁₅	4	-2	1	$\frac{- 1 + 3 i \sqrt{3}}{2}$	$\frac{- 1 - 3 i \sqrt{3}}{2}$	-2	-2	$1 - i \sqrt{3}$	$1 + i \sqrt{3}$	1	0	1	$\frac{- 1 + i \sqrt{3}}{2}$	$\frac{- 1 - i \sqrt{3}}{2}$	0	0	0	0
χ₁₆	4	-2	1	$\frac{- 1 - 3 i \sqrt{3}}{2}$	$\frac{- 1 + 3 i \sqrt{3}}{2}$	-2	2	$- 1 - i \sqrt{3}$	$- 1 + i \sqrt{3}$	1	0	-1	$\frac{1 + i \sqrt{3}}{2}$	$\frac{1 - i \sqrt{3}}{2}$	0	0	0	0
χ₁₇	4	-2	1	$\frac{- 1 - 3 i \sqrt{3}}{2}$	$\frac{- 1 + 3 i \sqrt{3}}{2}$	-2	-2	$1 + i \sqrt{3}$	$1 - i \sqrt{3}$	1	0	1	$\frac{- 1 - i \sqrt{3}}{2}$	$\frac{- 1 + i \sqrt{3}}{2}$	0	0	0	0
χ₁₈	8	-4	-4	2	2	2	0	0	0	-1	0	0	0	0	0	0	0	0

Here i is the imaginary unit (i² = −1).