Finite Group Databasebeta

← Group #11711673

Character table — Group #11711673

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	C₂₄	C₂₅
size	1	1	2	8	8	12	12	12	12	12	24	24	24	24	32	32	48	48	48	48	48	64	64	64	96
order	1	2	2	2	4	4	4	4	8	8	2	4	4	8	3	6	2	8	8	8	8	6	6	12	8
χ₁	1	1	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	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	-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	-1	1
χ₅	2	2	2	2	2	2	2	2	0	0	0	0	2	0	-1	-1	0	0	0	2	0	-1	-1	-1	0
χ₆	2	2	2	-2	-2	2	2	2	0	0	0	0	2	0	-1	-1	0	0	0	-2	0	-1	1	1	0
χ₇	3	3	3	3	3	-1	-1	3	1	1	1	1	-1	1	0	0	1	-1	-1	-1	1	0	0	0	-1
χ₈	3	3	3	3	3	-1	-1	3	-1	-1	-1	-1	-1	-1	0	0	-1	1	1	-1	-1	0	0	0	1
χ₉	3	3	3	-3	-3	-1	-1	3	1	1	-1	-1	-1	1	0	0	1	-1	-1	1	-1	0	0	0	1
χ₁₀	3	3	3	-3	-3	-1	-1	3	-1	-1	1	1	-1	-1	0	0	-1	1	1	1	1	0	0	0	-1
χ₁₁	4	4	-4	2	-2	0	0	0	2	2	-2	2	0	-2	1	1	0	0	0	0	0	-1	-1	1	0
χ₁₂	4	4	-4	2	-2	0	0	0	-2	-2	2	-2	0	2	1	1	0	0	0	0	0	-1	-1	1	0
χ₁₃	4	4	-4	-2	2	0	0	0	2	2	2	-2	0	-2	1	1	0	0	0	0	0	-1	1	-1	0
χ₁₄	4	4	-4	-2	2	0	0	0	-2	-2	-2	2	0	2	1	1	0	0	0	0	0	-1	1	-1	0
χ₁₅	4	-4	0	0	0	-2	2	0	$2 i \sqrt{2}$	$- 2 i \sqrt{2}$	0	0	0	0	-2	2	0	$i \sqrt{2}$	$- i \sqrt{2}$	0	0	0	0	0	0
χ₁₆	4	-4	0	0	0	-2	2	0	$- 2 i \sqrt{2}$	$2 i \sqrt{2}$	0	0	0	0	-2	2	0	$- i \sqrt{2}$	$i \sqrt{2}$	0	0	0	0	0	0
χ₁₇	6	6	6	0	0	2	2	-2	2	2	0	0	-2	2	0	0	-2	0	0	0	0	0	0	0	0
χ₁₈	6	6	6	0	0	2	2	-2	-2	-2	0	0	-2	-2	0	0	2	0	0	0	0	0	0	0	0
χ₁₉	6	6	6	0	0	-2	-2	-2	0	0	2	2	2	0	0	0	0	0	0	0	-2	0	0	0	0
χ₂₀	6	6	6	0	0	-2	-2	-2	0	0	-2	-2	2	0	0	0	0	0	0	0	2	0	0	0	0
χ₂₁	8	8	-8	4	-4	0	0	0	0	0	0	0	0	0	-1	-1	0	0	0	0	0	1	1	-1	0
χ₂₂	8	8	-8	-4	4	0	0	0	0	0	0	0	0	0	-1	-1	0	0	0	0	0	1	-1	1	0
χ₂₃	8	-8	0	0	0	-4	4	0	0	0	0	0	0	0	2	-2	0	0	0	0	0	0	0	0	0
χ₂₄	12	-12	0	0	0	2	-2	0	$2 i \sqrt{2}$	$- 2 i \sqrt{2}$	0	0	0	0	0	0	0	$- i \sqrt{2}$	$i \sqrt{2}$	0	0	0	0	0	0
χ₂₅	12	-12	0	0	0	2	-2	0	$- 2 i \sqrt{2}$	$2 i \sqrt{2}$	0	0	0	0	0	0	0	$i \sqrt{2}$	$- i \sqrt{2}$	0	0	0	0	0	0

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