Finite Group Databasebeta

Character table — Group #623

Order 72.

	C₁	C₂	C₃	C₄	C₅	C₆	C₇	C₈	C₉	C₁₀	C₁₁	C₁₂	C₁₃	C₁₄	C₁₅	C₁₆	C₁₇	C₁₈
size	1	1	2	2	3	3	2	2	4	4	6	6	3	3	6	6	9	9
order	1	2	3	6	4	4	3	6	3	6	12	12	2	2	6	6	4	4
χ₁	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
χ₃	1	-1	1	-1	$i$	$- i$	1	-1	1	-1	$i$	$- i$	1	-1	1	-1	$i$	$- i$
χ₄	1	-1	1	-1	$- i$	$i$	1	-1	1	-1	$- i$	$i$	1	-1	1	-1	$- i$	$i$
χ₅	2	2	-1	-1	0	0	2	2	-1	-1	0	0	2	2	-1	-1	0	0
χ₆	2	-2	-1	1	0	0	2	-2	-1	1	0	0	2	-2	-1	1	0	0
χ₇	1	1	1	1	1	1	1	1	1	1	1	1	-1	-1	-1	-1	-1	-1
χ₈	1	1	1	1	-1	-1	1	1	1	1	-1	-1	-1	-1	-1	-1	1	1
χ₉	1	-1	1	-1	$i$	$- i$	1	-1	1	-1	$i$	$- i$	-1	1	-1	1	$- i$	$i$
χ₁₀	1	-1	1	-1	$- i$	$i$	1	-1	1	-1	$- i$	$i$	-1	1	-1	1	$i$	$- i$
χ₁₁	2	2	-1	-1	0	0	2	2	-1	-1	0	0	-2	-2	1	1	0	0
χ₁₂	2	-2	-1	1	0	0	2	-2	-1	1	0	0	-2	2	1	-1	0	0
χ₁₃	2	2	2	2	2	2	-1	-1	-1	-1	-1	-1	0	0	0	0	0	0
χ₁₄	2	2	2	2	-2	-2	-1	-1	-1	-1	1	1	0	0	0	0	0	0
χ₁₅	2	-2	2	-2	$2 i$	$- 2 i$	-1	1	-1	1	$- i$	$i$	0	0	0	0	0	0
χ₁₆	2	-2	2	-2	$- 2 i$	$2 i$	-1	1	-1	1	$i$	$- i$	0	0	0	0	0	0
χ₁₇	4	4	-2	-2	0	0	-2	-2	1	1	0	0	0	0	0	0	0	0
χ₁₈	4	-4	-2	2	0	0	-2	2	1	-1	0	0	0	0	0	0	0	0

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