Finite Group Databasebeta

← Group #11711404

Character table — Group #11711404

Order 768.

	C₁	C₂	C₃	C₄	C₅	C₆	C₇	C₈	C₉	C₁₀	C₁₁	C₁₂	C₁₃	C₁₄	C₁₅	C₁₆	C₁₇	C₁₈	C₁₉	C₂₀	C₂₁	C₂₂	C₂₃
size	1	1	3	3	8	12	12	16	24	32	32	48	48	48	48	48	48	48	48	48	64	64	64
order	1	2	2	2	4	2	2	2	4	3	6	4	4	4	4	4	8	8	8	8	6	6	12
χ₁	1	1	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	1	1
χ₃	1	1	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	-1	1
χ₅	2	2	2	2	2	2	2	2	2	-1	-1	0	2	0	0	0	0	0	0	0	-1	-1	-1
χ₆	2	2	2	2	2	2	2	-2	2	-1	-1	0	-2	0	0	0	0	0	0	0	1	1	-1
χ₇	2	2	2	2	-2	2	2	0	-2	2	2	0	0	0	0	0	0	0	0	0	0	0	-2
χ₈	2	2	2	2	-2	2	2	0	-2	-1	-1	0	0	0	0	0	0	0	0	0	$- i \sqrt{3}$	$i \sqrt{3}$	1
χ₉	2	2	2	2	-2	2	2	0	-2	-1	-1	0	0	0	0	0	0	0	0	0	$i \sqrt{3}$	$- i \sqrt{3}$	1
χ₁₀	2	-2	2	-2	0	2	-2	0	0	2	-2	0	0	0	0	0	$- i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	0	0	0
χ₁₁	2	-2	2	-2	0	2	-2	0	0	2	-2	0	0	0	0	0	$i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	0	0	0
χ₁₂	3	3	3	3	3	-1	-1	3	-1	0	0	1	-1	1	-1	-1	1	1	-1	-1	0	0	0
χ₁₃	3	3	3	3	3	-1	-1	3	-1	0	0	-1	-1	-1	1	1	-1	-1	1	1	0	0	0
χ₁₄	3	3	3	3	3	-1	-1	-3	-1	0	0	1	1	1	-1	-1	-1	-1	1	1	0	0	0
χ₁₅	3	3	3	3	3	-1	-1	-3	-1	0	0	-1	1	-1	1	1	1	1	-1	-1	0	0	0
χ₁₆	4	-4	4	-4	0	4	-4	0	0	-2	2	0	0	0	0	0	0	0	0	0	0	0	0
χ₁₇	6	6	6	6	-6	-2	-2	0	2	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₁₈	6	-6	6	-6	0	-2	2	0	0	0	0	0	0	0	0	0	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	0	0	0
χ₁₉	6	-6	6	-6	0	-2	2	0	0	0	0	0	0	0	0	0	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	0	0	0
χ₂₀	12	12	-4	-4	0	0	0	0	0	0	0	2	0	-2	0	0	0	0	0	0	0	0	0
χ₂₁	12	12	-4	-4	0	0	0	0	0	0	0	-2	0	2	0	0	0	0	0	0	0	0	0
χ₂₂	12	-12	-4	4	0	0	0	0	0	0	0	0	0	0	$2 i$	$- 2 i$	0	0	0	0	0	0	0
χ₂₃	12	-12	-4	4	0	0	0	0	0	0	0	0	0	0	$- 2 i$	$2 i$	0	0	0	0	0	0	0

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