Finite Group Databasebeta

Character table — Group #133

Order 32.

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

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