Finite Group Databasebeta

Character table — Group #859

Order 96.

	C₁	C₂	C₃	C₄	C₅	C₆	C₇	C₈	C₉	C₁₀	C₁₁	C₁₂	C₁₃	C₁₄	C₁₅	C₁₆
size	1	1	1	1	6	6	6	6	6	6	8	8	8	8	12	12
order	1	2	2	2	4	4	8	8	8	8	3	6	6	6	4	4
χ₁	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
χ₃	1	-1	1	-1	1	-1	$i$	$i$	$- i$	$- i$	1	1	-1	-1	$i$	$- i$
χ₄	1	-1	1	-1	1	-1	$- i$	$- i$	$i$	$i$	1	1	-1	-1	$- i$	$i$
χ₅	2	2	2	2	2	2	0	0	0	0	-1	-1	-1	-1	0	0
χ₆	2	2	-2	-2	0	0	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	-1	1	1	-1	0	0
χ₇	2	2	-2	-2	0	0	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	-1	1	1	-1	0	0
χ₈	2	-2	2	-2	2	-2	0	0	0	0	-1	-1	1	1	0	0
χ₉	2	-2	-2	2	0	0	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	-1	1	-1	1	0	0
χ₁₀	2	-2	-2	2	0	0	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	-1	1	-1	1	0	0
χ₁₁	3	3	3	3	-1	-1	1	1	1	1	0	0	0	0	-1	-1
χ₁₂	3	3	3	3	-1	-1	-1	-1	-1	-1	0	0	0	0	1	1
χ₁₃	3	-3	3	-3	-1	1	$i$	$i$	$- i$	$- i$	0	0	0	0	$- i$	$i$
χ₁₄	3	-3	3	-3	-1	1	$- i$	$- i$	$i$	$i$	0	0	0	0	$i$	$- i$
χ₁₅	4	4	-4	-4	0	0	0	0	0	0	1	-1	-1	1	0	0
χ₁₆	4	-4	-4	4	0	0	0	0	0	0	1	-1	1	-1	0	0

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