Finite Group Databasebeta

← Group #73287

Character table — Group #73287

Order 384.

	C₁	C₂	C₃	C₄	C₅	C₆	C₇	C₈	C₉	C₁₀	C₁₁	C₁₂	C₁₃	C₁₄	C₁₅	C₁₆
size	1	1	3	3	12	12	12	12	12	12	24	24	64	64	64	64
order	1	2	2	2	2	2	2	2	4	4	4	4	3	3	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	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	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	3	3	3	3	3	3	-1	-1	-1	-1	-1	-1	0	0	0	0
χ₅	3	3	3	3	-1	-1	3	3	-1	-1	-1	-1	0	0	0	0
χ₆	3	3	3	3	-1	-1	-1	-1	3	3	-1	-1	0	0	0	0
χ₇	3	3	3	3	-1	-1	-1	-1	-1	-1	3	-1	0	0	0	0
χ₈	3	3	3	3	-1	-1	-1	-1	-1	-1	-1	3	0	0	0	0
χ₉	4	-4	4	-4	0	0	0	0	0	0	0	0	1	1	-1	-1
χ₁₀	4	-4	4	-4	0	0	0	0	0	0	0	0	$\frac{- 1 + i \sqrt{3}}{2}$	$\frac{- 1 - i \sqrt{3}}{2}$	$\frac{1 - i \sqrt{3}}{2}$	$\frac{1 + i \sqrt{3}}{2}$
χ₁₁	4	-4	4	-4	0	0	0	0	0	0	0	0	$\frac{- 1 - i \sqrt{3}}{2}$	$\frac{- 1 + i \sqrt{3}}{2}$	$\frac{1 + i \sqrt{3}}{2}$	$\frac{1 - i \sqrt{3}}{2}$
χ₁₂	6	-6	-2	2	2	-2	2	-2	2	-2	0	0	0	0	0	0
χ₁₃	6	-6	-2	2	2	-2	-2	2	-2	2	0	0	0	0	0	0
χ₁₄	6	-6	-2	2	-2	2	2	-2	-2	2	0	0	0	0	0	0
χ₁₅	6	-6	-2	2	-2	2	-2	2	2	-2	0	0	0	0	0	0
χ₁₆	12	12	-4	-4	0	0	0	0	0	0	0	0	0	0	0	0

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