Finite Group Databasebeta

← Group #11724694

Character table — Group #11724694

Order 864.

	C₁	C₂	C₃	C₄	C₅	C₆	C₇	C₈	C₉	C₁₀	C₁₁	C₁₂	C₁₃	C₁₄	C₁₅	C₁₆	C₁₇	C₁₈	C₁₉	C₂₀	C₂₁	C₂₂
size	1	8	9	24	36	48	54	54	54	72	72	1	8	9	24	36	48	54	54	54	72	72
order	1	3	2	3	2	3	4	8	8	6	6	2	6	2	6	2	6	4	8	8	6	6
χ₁	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
χ₃	2	2	2	-1	0	-1	2	0	0	0	-1	2	2	2	-1	0	-1	2	0	0	0	-1
χ₄	2	2	-2	-1	0	-1	0	$i \sqrt{2}$	$- i \sqrt{2}$	0	1	2	2	-2	-1	0	-1	0	$i \sqrt{2}$	$- i \sqrt{2}$	0	1
χ₅	2	2	-2	-1	0	-1	0	$- i \sqrt{2}$	$i \sqrt{2}$	0	1	2	2	-2	-1	0	-1	0	$- i \sqrt{2}$	$i \sqrt{2}$	0	1
χ₆	3	3	3	0	1	0	-1	-1	-1	1	0	3	3	3	0	1	0	-1	-1	-1	1	0
χ₇	3	3	3	0	-1	0	-1	1	1	-1	0	3	3	3	0	-1	0	-1	1	1	-1	0
χ₈	4	4	-4	1	0	1	0	0	0	0	-1	4	4	-4	1	0	1	0	0	0	0	-1
χ₉	8	-1	0	2	2	-1	0	0	0	-1	0	8	-1	0	2	2	-1	0	0	0	-1	0
χ₁₀	8	-1	0	2	-2	-1	0	0	0	1	0	8	-1	0	2	-2	-1	0	0	0	1	0
χ₁₁	16	-2	0	-2	0	1	0	0	0	0	0	16	-2	0	-2	0	1	0	0	0	0	0
χ₁₂	1	1	1	1	1	1	1	1	1	1	1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1
χ₁₃	1	1	1	1	-1	1	1	-1	-1	-1	1	-1	-1	-1	-1	1	-1	-1	1	1	1	-1
χ₁₄	2	2	2	-1	0	-1	2	0	0	0	-1	-2	-2	-2	1	0	1	-2	0	0	0	1
χ₁₅	2	2	-2	-1	0	-1	0	$i \sqrt{2}$	$- i \sqrt{2}$	0	1	-2	-2	2	1	0	1	0	$- i \sqrt{2}$	$i \sqrt{2}$	0	-1
χ₁₆	2	2	-2	-1	0	-1	0	$- i \sqrt{2}$	$i \sqrt{2}$	0	1	-2	-2	2	1	0	1	0	$i \sqrt{2}$	$- i \sqrt{2}$	0	-1
χ₁₇	3	3	3	0	1	0	-1	-1	-1	1	0	-3	-3	-3	0	-1	0	1	1	1	-1	0
χ₁₈	3	3	3	0	-1	0	-1	1	1	-1	0	-3	-3	-3	0	1	0	1	-1	-1	1	0
χ₁₉	4	4	-4	1	0	1	0	0	0	0	-1	-4	-4	4	-1	0	-1	0	0	0	0	1
χ₂₀	8	-1	0	2	2	-1	0	0	0	-1	0	-8	1	0	-2	-2	1	0	0	0	1	0
χ₂₁	8	-1	0	2	-2	-1	0	0	0	1	0	-8	1	0	-2	2	1	0	0	0	-1	0
χ₂₂	16	-2	0	-2	0	1	0	0	0	0	0	-16	2	0	2	0	-1	0	0	0	0	0

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