Finite Group Databasebeta

← Group #67430

Character table — Group #67430

Order 384.

	C₁	C₂	C₃	C₄	C₅	C₆	C₇	C₈	C₉	C₁₀	C₁₁	C₁₂	C₁₃	C₁₄
size	1	3	4	6	6	12	24	24	24	24	64	64	64	64
order	1	2	2	4	4	4	8	8	8	8	3	3	6	6
χ₁	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	$\frac{- 1 - i \sqrt{3}}{2}$	$\frac{- 1 + i \sqrt{3}}{2}$	$\frac{- 1 - i \sqrt{3}}{2}$	$\frac{- 1 + i \sqrt{3}}{2}$
χ₃	1	1	1	1	1	1	1	1	1	1	$\frac{- 1 + i \sqrt{3}}{2}$	$\frac{- 1 - i \sqrt{3}}{2}$	$\frac{- 1 + i \sqrt{3}}{2}$	$\frac{- 1 - i \sqrt{3}}{2}$
χ₄	2	2	-2	-2	-2	2	0	0	0	0	-1	-1	1	1
χ₅	2	2	-2	-2	-2	2	0	0	0	0	$\frac{1 + i \sqrt{3}}{2}$	$\frac{1 - i \sqrt{3}}{2}$	$\frac{- 1 - i \sqrt{3}}{2}$	$\frac{- 1 + i \sqrt{3}}{2}$
χ₆	2	2	-2	-2	-2	2	0	0	0	0	$\frac{1 - i \sqrt{3}}{2}$	$\frac{1 + i \sqrt{3}}{2}$	$\frac{- 1 + i \sqrt{3}}{2}$	$\frac{- 1 - i \sqrt{3}}{2}$
χ₇	3	3	3	3	3	3	-1	-1	-1	-1	0	0	0	0
χ₈	3	3	3	-1	-1	-1	1	1	$- 1 + 2 i$	$- 1 - 2 i$	0	0	0	0
χ₉	3	3	3	-1	-1	-1	1	1	$- 1 - 2 i$	$- 1 + 2 i$	0	0	0	0
χ₁₀	3	3	3	-1	-1	-1	$- 1 + 2 i$	$- 1 - 2 i$	1	1	0	0	0	0
χ₁₁	3	3	3	-1	-1	-1	$- 1 - 2 i$	$- 1 + 2 i$	1	1	0	0	0	0
χ₁₂	6	6	-6	2	2	-2	0	0	0	0	0	0	0	0
χ₁₃	12	-4	0	4	-4	0	0	0	0	0	0	0	0	0
χ₁₄	12	-4	0	-4	4	0	0	0	0	0	0	0	0	0

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