Finite Group Databasebeta

← Group #73006

Character table — Group #73006

Order 384.

	C₁	C₂	C₃	C₄	C₅	C₆	C₇	C₈	C₉	C₁₀	C₁₁	C₁₂	C₁₃	C₁₄	C₁₅	C₁₆	C₁₇	C₁₈	C₁₉	C₂₀	C₂₁
size	1	1	3	3	8	12	12	12	12	24	24	24	24	24	24	24	24	32	32	32	32
order	1	2	2	2	2	4	4	4	4	2	4	4	4	8	8	8	8	3	6	6	6
χ₁	1	1	1	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	1	1	1
χ₃	1	1	1	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	1	-1	-1
χ₅	2	2	2	2	2	2	2	2	2	0	0	0	0	0	0	0	0	-1	-1	-1	-1
χ₆	2	2	2	2	-2	-2	-2	2	2	0	0	0	0	0	0	0	0	-1	-1	1	1
χ₇	3	3	3	3	3	-1	-1	-1	-1	1	1	1	1	-1	-1	-1	-1	0	0	0	0
χ₈	3	3	3	3	3	-1	-1	-1	-1	-1	-1	-1	-1	1	1	1	1	0	0	0	0
χ₉	3	3	3	3	-3	1	1	-1	-1	1	-1	1	-1	-1	-1	1	1	0	0	0	0
χ₁₀	3	3	3	3	-3	1	1	-1	-1	-1	1	-1	1	1	1	-1	-1	0	0	0	0
χ₁₁	4	-4	4	-4	0	0	0	0	0	0	0	0	0	0	0	0	0	1	-1	$- i \sqrt{3}$	$i \sqrt{3}$
χ₁₂	4	-4	4	-4	0	0	0	0	0	0	0	0	0	0	0	0	0	1	-1	$i \sqrt{3}$	$- i \sqrt{3}$
χ₁₃	4	-4	4	-4	0	0	0	0	0	0	0	0	0	0	0	0	0	-2	2	0	0
χ₁₄	6	6	-2	-2	0	0	0	2	-2	0	2	0	-2	0	0	0	0	0	0	0	0
χ₁₅	6	6	-2	-2	0	0	0	2	-2	0	-2	0	2	0	0	0	0	0	0	0	0
χ₁₆	6	6	-2	-2	0	0	0	-2	2	2	0	-2	0	0	0	0	0	0	0	0	0
χ₁₇	6	6	-2	-2	0	0	0	-2	2	-2	0	2	0	0	0	0	0	0	0	0	0
χ₁₈	6	-6	-2	2	0	$2 i$	$- 2 i$	0	0	0	0	0	0	$\sqrt{2}$	$- \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	0	0	0	0
χ₁₉	6	-6	-2	2	0	$2 i$	$- 2 i$	0	0	0	0	0	0	$- \sqrt{2}$	$\sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	0	0	0	0
χ₂₀	6	-6	-2	2	0	$- 2 i$	$2 i$	0	0	0	0	0	0	$\sqrt{2}$	$- \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	0	0	0	0
χ₂₁	6	-6	-2	2	0	$- 2 i$	$2 i$	0	0	0	0	0	0	$- \sqrt{2}$	$\sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	0	0	0	0

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