Finite Group Databasebeta

Character table — Group #638

Order 72.

	C₁	C₂	C₃	C₄	C₅	C₆	C₇	C₈	C₉	C₁₀	C₁₁	C₁₂	C₁₃	C₁₄	C₁₅	C₁₆	C₁₇	C₁₈	C₁₉	C₂₀	C₂₁
size	1	1	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	18	18
order	1	2	2	3	3	3	3	6	6	6	6	6	6	6	6	6	6	6	6	2	4
χ₁	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
χ₃	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
χ₅	2	2	2	2	-1	-1	-1	2	-1	-1	-1	2	2	-1	-1	-1	-1	-1	-1	0	0
χ₆	2	2	2	-1	2	-1	-1	-1	2	-1	-1	-1	-1	2	2	-1	-1	-1	-1	0	0
χ₇	2	2	2	-1	-1	2	-1	-1	-1	2	-1	-1	-1	-1	-1	2	2	-1	-1	0	0
χ₈	2	2	2	-1	-1	-1	2	-1	-1	-1	2	-1	-1	-1	-1	-1	-1	2	2	0	0
χ₉	2	2	-2	2	-1	-1	-1	2	-1	-1	-1	-2	-2	1	1	1	1	1	1	0	0
χ₁₀	2	2	-2	-1	2	-1	-1	-1	2	-1	-1	1	1	-2	-2	1	1	1	1	0	0
χ₁₁	2	2	-2	-1	-1	2	-1	-1	-1	2	-1	1	1	1	1	-2	-2	1	1	0	0
χ₁₂	2	2	-2	-1	-1	-1	2	-1	-1	-1	2	1	1	1	1	1	1	-2	-2	0	0
χ₁₃	2	-2	0	2	2	2	2	-2	-2	-2	-2	0	0	0	0	0	0	0	0	0	0
χ₁₄	2	-2	0	2	-1	-1	-1	-2	1	1	1	0	0	$i \sqrt{3}$	$- i \sqrt{3}$	$i \sqrt{3}$	$- i \sqrt{3}$	$i \sqrt{3}$	$- i \sqrt{3}$	0	0
χ₁₅	2	-2	0	2	-1	-1	-1	-2	1	1	1	0	0	$- i \sqrt{3}$	$i \sqrt{3}$	$- i \sqrt{3}$	$i \sqrt{3}$	$- i \sqrt{3}$	$i \sqrt{3}$	0	0
χ₁₆	2	-2	0	-1	2	-1	-1	1	-2	1	1	$i \sqrt{3}$	$- i \sqrt{3}$	0	0	$i \sqrt{3}$	$- i \sqrt{3}$	$- i \sqrt{3}$	$i \sqrt{3}$	0	0
χ₁₇	2	-2	0	-1	2	-1	-1	1	-2	1	1	$- i \sqrt{3}$	$i \sqrt{3}$	0	0	$- i \sqrt{3}$	$i \sqrt{3}$	$i \sqrt{3}$	$- i \sqrt{3}$	0	0
χ₁₈	2	-2	0	-1	-1	2	-1	1	1	-2	1	$i \sqrt{3}$	$- i \sqrt{3}$	$- i \sqrt{3}$	$i \sqrt{3}$	0	0	$i \sqrt{3}$	$- i \sqrt{3}$	0	0
χ₁₉	2	-2	0	-1	-1	2	-1	1	1	-2	1	$- i \sqrt{3}$	$i \sqrt{3}$	$i \sqrt{3}$	$- i \sqrt{3}$	0	0	$- i \sqrt{3}$	$i \sqrt{3}$	0	0
χ₂₀	2	-2	0	-1	-1	-1	2	1	1	1	-2	$i \sqrt{3}$	$- i \sqrt{3}$	$i \sqrt{3}$	$- i \sqrt{3}$	$- i \sqrt{3}$	$i \sqrt{3}$	0	0	0	0
χ₂₁	2	-2	0	-1	-1	-1	2	1	1	1	-2	$- i \sqrt{3}$	$i \sqrt{3}$	$- i \sqrt{3}$	$i \sqrt{3}$	$i \sqrt{3}$	$- i \sqrt{3}$	0	0	0	0

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