Finite Group Databasebeta

← Group #6319

Character table — Group #6319

Order 216.

	C₁	C₂	C₃	C₄	C₅	C₆	C₇	C₈	C₉	C₁₀	C₁₁	C₁₂	C₁₃	C₁₄	C₁₅	C₁₆	C₁₇	C₁₈
size	1	4	4	9	9	9	2	8	8	18	18	18	3	12	12	27	27	27
order	1	3	3	2	4	4	3	3	3	6	12	12	2	6	6	2	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	4	1	-2	0	0	0	4	1	-2	0	0	0	4	1	-2	0	0	0
χ₆	4	-2	1	0	0	0	4	-2	1	0	0	0	4	-2	1	0	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	4	1	-2	0	0	0	4	1	-2	0	0	0	-4	-1	2	0	0	0
χ₁₂	4	-2	1	0	0	0	4	-2	1	0	0	0	-4	2	-1	0	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	8	2	-4	0	0	0	-4	-1	2	0	0	0	0	0	0	0	0	0
χ₁₈	8	-4	2	0	0	0	-4	2	-1	0	0	0	0	0	0	0	0	0

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