Finite Group Databasebeta

← Group #85556

Character table — Group #85556

Order 384.

	C₁	C₂	C₃	C₄	C₅	C₆	C₇	C₈	C₉	C₁₀	C₁₁	C₁₂	C₁₃	C₁₄	C₁₅	C₁₆	C₁₇	C₁₈	C₁₉
size	1	1	1	1	12	12	12	24	24	24	24	24	24	24	32	32	32	32	48
order	1	2	2	2	4	4	4	2	8	8	8	8	8	8	3	6	6	6	4
χ₁	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
χ₃	2	2	2	2	2	2	2	2	0	0	0	0	0	0	-1	-1	-1	-1	0
χ₄	3	3	3	3	3	-1	-1	-1	1	1	-1	-1	-1	-1	0	0	0	0	1
χ₅	3	3	3	3	3	-1	-1	-1	-1	-1	1	1	1	1	0	0	0	0	-1
χ₆	3	3	3	3	-1	3	-1	-1	1	1	1	1	-1	-1	0	0	0	0	-1
χ₇	3	3	3	3	-1	3	-1	-1	-1	-1	-1	-1	1	1	0	0	0	0	1
χ₈	3	3	3	3	-1	-1	3	-1	1	1	-1	-1	1	1	0	0	0	0	-1
χ₉	3	3	3	3	-1	-1	3	-1	-1	-1	1	1	-1	-1	0	0	0	0	1
χ₁₀	4	4	-4	-4	0	0	0	0	$2 i$	$- 2 i$	0	0	0	0	1	1	-1	-1	0
χ₁₁	4	4	-4	-4	0	0	0	0	$- 2 i$	$2 i$	0	0	0	0	1	1	-1	-1	0
χ₁₂	4	-4	4	-4	0	0	0	0	0	0	0	0	$2 i$	$- 2 i$	1	-1	1	-1	0
χ₁₃	4	-4	4	-4	0	0	0	0	0	0	0	0	$- 2 i$	$2 i$	1	-1	1	-1	0
χ₁₄	4	-4	-4	4	0	0	0	0	0	0	2	-2	0	0	1	-1	-1	1	0
χ₁₅	4	-4	-4	4	0	0	0	0	0	0	-2	2	0	0	1	-1	-1	1	0
χ₁₆	6	6	6	6	-2	-2	-2	2	0	0	0	0	0	0	0	0	0	0	0
χ₁₇	8	8	-8	-8	0	0	0	0	0	0	0	0	0	0	-1	-1	1	1	0
χ₁₈	8	-8	8	-8	0	0	0	0	0	0	0	0	0	0	-1	1	-1	1	0
χ₁₉	8	-8	-8	8	0	0	0	0	0	0	0	0	0	0	-1	1	1	-1	0

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