Finite Group Databasebeta

← Group #85551

Character table — Group #85551

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	1	1	6	6	12	12	24	24	24	24	24	24	24	24	24	32	32	32	32
order	1	2	2	2	2	2	4	4	2	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	2	2	2	2	2	2	2	2	0	0	2	0	0	0	0	0	0	-1	-1	-1	-1
χ₄	2	2	-2	-2	-2	2	0	0	0	0	0	0	0	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	-1	1	1	-1
χ₅	2	2	-2	-2	-2	2	0	0	0	0	0	0	0	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	-1	1	1	-1
χ₆	3	3	3	3	3	3	-1	-1	1	1	-1	1	1	-1	-1	-1	-1	0	0	0	0
χ₇	3	3	3	3	3	3	-1	-1	-1	-1	-1	-1	-1	1	1	1	1	0	0	0	0
χ₈	3	3	3	3	-1	-1	3	-1	1	1	-1	-1	-1	1	-1	1	-1	0	0	0	0
χ₉	3	3	3	3	-1	-1	3	-1	-1	-1	-1	1	1	-1	1	-1	1	0	0	0	0
χ₁₀	3	3	3	3	-1	-1	-1	3	1	1	-1	-1	-1	-1	1	-1	1	0	0	0	0
χ₁₁	3	3	3	3	-1	-1	-1	3	-1	-1	-1	1	1	1	-1	1	-1	0	0	0	0
χ₁₂	4	4	-4	-4	-4	4	0	0	0	0	0	0	0	0	0	0	0	1	-1	-1	1
χ₁₃	4	-4	4	-4	0	0	0	0	2	-2	0	0	0	0	0	0	0	1	1	-1	-1
χ₁₄	4	-4	4	-4	0	0	0	0	-2	2	0	0	0	0	0	0	0	1	1	-1	-1
χ₁₅	4	-4	-4	4	0	0	0	0	0	0	0	2	-2	0	0	0	0	1	-1	1	-1
χ₁₆	4	-4	-4	4	0	0	0	0	0	0	0	-2	2	0	0	0	0	1	-1	1	-1
χ₁₇	6	6	6	6	-2	-2	-2	-2	0	0	2	0	0	0	0	0	0	0	0	0	0
χ₁₈	6	6	-6	-6	2	-2	0	0	0	0	0	0	0	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	0	0	0	0
χ₁₉	6	6	-6	-6	2	-2	0	0	0	0	0	0	0	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	0	0	0	0
χ₂₀	8	-8	8	-8	0	0	0	0	0	0	0	0	0	0	0	0	0	-1	-1	1	1
χ₂₁	8	-8	-8	8	0	0	0	0	0	0	0	0	0	0	0	0	0	-1	1	-1	1

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