Finite Group Databasebeta

← Group #73030

Character table — Group #73030

Order 384.

	C₁	C₂	C₃	C₄	C₅	C₆	C₇	C₈	C₉	C₁₀	C₁₁	C₁₂	C₁₃	C₁₄	C₁₅	C₁₆	C₁₇	C₁₈	C₁₉	C₂₀
size	1	1	4	4	6	12	12	12	12	12	12	24	24	24	32	32	32	32	48	48
order	1	2	4	4	2	2	2	2	4	4	4	4	4	4	3	6	12	12	4	8
χ₁	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
χ₃	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
χ₅	2	2	2	2	2	0	0	2	0	0	2	0	2	0	-1	-1	-1	-1	0	0
χ₆	2	2	-2	-2	2	0	0	2	0	0	2	0	-2	0	-1	-1	1	1	0	0
χ₇	3	3	3	3	3	1	1	-1	1	1	-1	1	-1	1	0	0	0	0	-1	-1
χ₈	3	3	3	3	3	-1	-1	-1	-1	-1	-1	-1	-1	-1	0	0	0	0	1	1
χ₉	3	3	-3	-3	3	1	1	-1	-1	-1	-1	-1	1	1	0	0	0	0	-1	1
χ₁₀	3	3	-3	-3	3	-1	-1	-1	1	1	-1	1	1	-1	0	0	0	0	1	-1
χ₁₁	4	-4	$2 i$	$- 2 i$	0	2	-2	0	$2 i$	$- 2 i$	0	0	0	0	1	-1	$i$	$- i$	0	0
χ₁₂	4	-4	$2 i$	$- 2 i$	0	-2	2	0	$- 2 i$	$2 i$	0	0	0	0	1	-1	$i$	$- i$	0	0
χ₁₃	4	-4	$- 2 i$	$2 i$	0	2	-2	0	$- 2 i$	$2 i$	0	0	0	0	1	-1	$- i$	$i$	0	0
χ₁₄	4	-4	$- 2 i$	$2 i$	0	-2	2	0	$2 i$	$- 2 i$	0	0	0	0	1	-1	$- i$	$i$	0	0
χ₁₅	6	6	0	0	-2	0	0	-2	2	2	2	-2	0	0	0	0	0	0	0	0
χ₁₆	6	6	0	0	-2	0	0	-2	-2	-2	2	2	0	0	0	0	0	0	0	0
χ₁₇	6	6	0	0	-2	2	2	2	0	0	-2	0	0	-2	0	0	0	0	0	0
χ₁₈	6	6	0	0	-2	-2	-2	2	0	0	-2	0	0	2	0	0	0	0	0	0
χ₁₉	8	-8	$4 i$	$- 4 i$	0	0	0	0	0	0	0	0	0	0	-1	1	$- i$	$i$	0	0
χ₂₀	8	-8	$- 4 i$	$4 i$	0	0	0	0	0	0	0	0	0	0	-1	1	$i$	$- i$	0	0

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