Finite Group Databasebeta

← Group #6197

Character table — Group #6197

Order 216.

	C₁	C₂	C₃	C₄	C₅	C₆	C₇	C₈	C₉	C₁₀	C₁₁	C₁₂	C₁₃	C₁₄	C₁₅	C₁₆	C₁₇	C₁₈	C₁₉	C₂₀	C₂₁	C₂₂
size	1	1	2	2	6	6	6	6	9	9	9	9	9	9	12	12	18	18	18	18	18	18
order	1	2	3	6	3	3	6	6	2	2	4	4	4	4	3	6	6	6	12	12	12	12
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	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
χ₅	1	-1	1	-1	1	1	-1	-1	1	-1	$i$	$- i$	$i$	$- i$	1	-1	1	-1	$i$	$- i$	$i$	$- i$
χ₆	1	-1	1	-1	1	1	-1	-1	1	-1	$- i$	$i$	$- i$	$i$	1	-1	1	-1	$- i$	$i$	$- i$	$i$
χ₇	1	-1	1	-1	1	1	-1	-1	-1	1	$i$	$- i$	$- i$	$i$	1	-1	-1	1	$i$	$- i$	$- i$	$i$
χ₈	1	-1	1	-1	1	1	-1	-1	-1	1	$- i$	$i$	$i$	$- i$	1	-1	-1	1	$- i$	$i$	$i$	$- i$
χ₉	2	2	2	2	2	-1	-1	2	2	2	0	0	0	0	-1	-1	-1	-1	0	0	0	0
χ₁₀	2	2	2	2	2	-1	-1	2	-2	-2	0	0	0	0	-1	-1	1	1	0	0	0	0
χ₁₁	2	2	2	2	-1	2	2	-1	0	0	0	0	2	2	-1	-1	0	0	0	0	-1	-1
χ₁₂	2	2	2	2	-1	2	2	-1	0	0	0	0	-2	-2	-1	-1	0	0	0	0	1	1
χ₁₃	2	-2	2	-2	2	-1	1	-2	2	-2	0	0	0	0	-1	1	-1	1	0	0	0	0
χ₁₄	2	-2	2	-2	2	-1	1	-2	-2	2	0	0	0	0	-1	1	1	-1	0	0	0	0
χ₁₅	2	-2	2	-2	-1	2	-2	1	0	0	0	0	$2 i$	$- 2 i$	-1	1	0	0	0	0	$- i$	$i$
χ₁₆	2	-2	2	-2	-1	2	-2	1	0	0	0	0	$- 2 i$	$2 i$	-1	1	0	0	0	0	$i$	$- i$
χ₁₇	4	4	4	4	-2	-2	-2	-2	0	0	0	0	0	0	1	1	0	0	0	0	0	0
χ₁₈	4	-4	4	-4	-2	-2	2	2	0	0	0	0	0	0	1	-1	0	0	0	0	0	0
χ₁₉	6	6	-3	-3	0	0	0	0	0	0	2	2	0	0	0	0	0	0	-1	-1	0	0
χ₂₀	6	6	-3	-3	0	0	0	0	0	0	-2	-2	0	0	0	0	0	0	1	1	0	0
χ₂₁	6	-6	-3	3	0	0	0	0	0	0	$2 i$	$- 2 i$	0	0	0	0	0	0	$- i$	$i$	0	0
χ₂₂	6	-6	-3	3	0	0	0	0	0	0	$- 2 i$	$2 i$	0	0	0	0	0	0	$i$	$- i$	0	0

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