Finite Group Databasebeta

← Group #64209

Character table — Group #64209

Order 288.

	C₁	C₂	C₃	C₄	C₅	C₆	C₇	C₈	C₉	C₁₀	C₁₁	C₁₂	C₁₃	C₁₄	C₁₅	C₁₆	C₁₇	C₁₈	C₁₉	C₂₀	C₂₁	C₂₂	C₂₃	C₂₄
size	1	1	2	2	3	3	6	6	6	8	8	12	12	12	12	12	12	16	16	18	24	24	36	36
order	1	2	3	6	2	2	2	6	6	3	6	2	4	6	6	12	12	3	6	2	6	6	4	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	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
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
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
χ₅	2	2	2	2	2	2	2	2	2	-1	-1	0	0	0	0	0	0	-1	-1	2	-1	-1	0	0
χ₆	2	2	2	2	2	2	-2	2	2	-1	-1	0	0	0	0	0	0	-1	-1	-2	1	1	0	0
χ₇	2	2	-1	-1	2	2	0	-1	-1	2	2	2	2	-1	-1	-1	-1	-1	-1	0	0	0	0	0
χ₈	2	2	-1	-1	2	2	0	-1	-1	2	2	-2	-2	1	1	1	1	-1	-1	0	0	0	0	0
χ₉	2	-2	2	-2	2	-2	0	-2	2	2	-2	0	0	0	0	0	0	2	-2	0	0	0	0	0
χ₁₀	2	-2	2	-2	2	-2	0	-2	2	-1	1	0	0	0	0	0	0	-1	1	0	$i \sqrt{3}$	$- i \sqrt{3}$	0	0
χ₁₁	2	-2	2	-2	2	-2	0	-2	2	-1	1	0	0	0	0	0	0	-1	1	0	$- i \sqrt{3}$	$i \sqrt{3}$	0	0
χ₁₂	2	-2	-1	1	2	-2	0	1	-1	2	-2	0	0	$i \sqrt{3}$	$- i \sqrt{3}$	$i \sqrt{3}$	$- i \sqrt{3}$	-1	1	0	0	0	0	0
χ₁₃	2	-2	-1	1	2	-2	0	1	-1	2	-2	0	0	$- i \sqrt{3}$	$i \sqrt{3}$	$- i \sqrt{3}$	$i \sqrt{3}$	-1	1	0	0	0	0	0
χ₁₄	3	3	3	3	-1	-1	3	-1	-1	0	0	1	-1	1	1	-1	-1	0	0	-1	0	0	1	-1
χ₁₅	3	3	3	3	-1	-1	3	-1	-1	0	0	-1	1	-1	-1	1	1	0	0	-1	0	0	-1	1
χ₁₆	3	3	3	3	-1	-1	-3	-1	-1	0	0	1	-1	1	1	-1	-1	0	0	1	0	0	-1	1
χ₁₇	3	3	3	3	-1	-1	-3	-1	-1	0	0	-1	1	-1	-1	1	1	0	0	1	0	0	1	-1
χ₁₈	4	4	-2	-2	4	4	0	-2	-2	-2	-2	0	0	0	0	0	0	1	1	0	0	0	0	0
χ₁₉	4	-4	-2	2	4	-4	0	2	-2	-2	2	0	0	0	0	0	0	1	-1	0	0	0	0	0
χ₂₀	6	6	-3	-3	-2	-2	0	1	1	0	0	2	-2	-1	-1	1	1	0	0	0	0	0	0	0
χ₂₁	6	6	-3	-3	-2	-2	0	1	1	0	0	-2	2	1	1	-1	-1	0	0	0	0	0	0	0
χ₂₂	6	-6	6	-6	-2	2	0	2	-2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₃	6	-6	-3	3	-2	2	0	-1	1	0	0	0	0	$i \sqrt{3}$	$- i \sqrt{3}$	$- i \sqrt{3}$	$i \sqrt{3}$	0	0	0	0	0	0	0
χ₂₄	6	-6	-3	3	-2	2	0	-1	1	0	0	0	0	$- i \sqrt{3}$	$i \sqrt{3}$	$i \sqrt{3}$	$- i \sqrt{3}$	0	0	0	0	0	0	0

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