Finite Group Databasebeta

← Group #10596398

Character table — Group #10596398

Order 576.

	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	6	8	8	8	8	18	24	24	32	32	32	32	36	36	36	36	48	72	72
order	1	2	2	2	4	3	3	6	6	4	6	6	3	3	6	6	8	8	8	8	12	2	4
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	2	2	2	2	2	2	-1	-1	2	2	-1	-1	-1	-1	-1	-1	0	0	0	0	2	0	0
χ₄	2	2	2	2	2	-1	2	2	-1	2	2	2	-1	-1	-1	-1	0	0	0	0	-1	0	0
χ₅	2	2	2	2	2	-1	-1	-1	-1	2	-1	-1	2	-1	2	-1	0	0	0	0	-1	0	0
χ₆	2	2	2	2	2	-1	-1	-1	-1	2	-1	-1	-1	2	-1	2	0	0	0	0	-1	0	0
χ₇	2	-2	-2	2	0	2	-1	1	-2	0	1	-1	-1	-1	1	1	$i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	0	0	0
χ₈	2	-2	-2	2	0	2	-1	1	-2	0	1	-1	-1	-1	1	1	$- i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	0	0	0
χ₉	3	3	3	3	-1	3	0	0	3	-1	0	0	0	0	0	0	1	1	1	1	-1	-1	-1
χ₁₀	3	3	3	3	-1	3	0	0	3	-1	0	0	0	0	0	0	-1	-1	-1	-1	-1	1	1
χ₁₁	3	3	-1	-1	3	0	3	3	0	-1	-1	-1	0	0	0	0	1	1	-1	-1	0	1	-1
χ₁₂	3	3	-1	-1	3	0	3	3	0	-1	-1	-1	0	0	0	0	-1	-1	1	1	0	-1	1
χ₁₃	4	-4	-4	4	0	4	1	-1	-4	0	-1	1	1	1	-1	-1	0	0	0	0	0	0	0
χ₁₄	4	-4	-4	4	0	-2	1	-1	2	0	-1	1	1	-2	-1	2	0	0	0	0	0	0	0
χ₁₅	4	-4	-4	4	0	-2	1	-1	2	0	-1	1	-2	1	2	-1	0	0	0	0	0	0	0
χ₁₆	4	-4	-4	4	0	-2	-2	2	2	0	2	-2	1	1	-1	-1	0	0	0	0	0	0	0
χ₁₇	6	6	6	6	-2	-3	0	0	-3	-2	0	0	0	0	0	0	0	0	0	0	1	0	0
χ₁₈	6	6	-2	-2	6	0	-3	-3	0	-2	1	1	0	0	0	0	0	0	0	0	0	0	0
χ₁₉	6	-6	2	-2	0	0	-3	3	0	0	-1	1	0	0	0	0	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	0	0	0
χ₂₀	6	-6	2	-2	0	0	-3	3	0	0	-1	1	0	0	0	0	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	0	0	0
χ₂₁	9	9	-3	-3	-3	0	0	0	0	1	0	0	0	0	0	0	1	1	-1	-1	0	-1	1
χ₂₂	9	9	-3	-3	-3	0	0	0	0	1	0	0	0	0	0	0	-1	-1	1	1	0	1	-1
χ₂₃	12	-12	4	-4	0	0	3	-3	0	0	1	-1	0	0	0	0	0	0	0	0	0	0	0

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