Finite Group Databasebeta

← Group #13608

Character table — Group #13608

Order 256.

	C₁	C₂	C₃	C₄	C₅	C₆	C₇	C₈	C₉	C₁₀	C₁₁	C₁₂	C₁₃	C₁₄	C₁₅	C₁₆	C₁₇	C₁₈	C₁₉	C₂₀	C₂₁	C₂₂	C₂₃	C₂₄	C₂₅
size	1	1	2	4	4	4	8	8	8	8	8	8	8	8	16	16	16	16	16	16	16	16	16	16	16
order	1	2	2	2	4	4	2	4	4	4	4	4	8	8	4	4	4	4	4	4	8	8	8	8	8
χ₁	1	1	1	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	-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	-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	1	1	1
χ₅	1	1	1	1	1	1	-1	-1	-1	1	1	-1	1	1	-1	-1	$i$	$i$	$- i$	$- i$	1	$i$	$i$	$- i$	$- i$
χ₆	1	1	1	1	1	1	-1	-1	-1	1	1	-1	1	1	-1	-1	$- i$	$- i$	$i$	$i$	1	$- i$	$- i$	$i$	$i$
χ₇	1	1	1	1	1	1	-1	-1	-1	1	1	-1	-1	-1	1	1	$i$	$i$	$- i$	$- i$	-1	$- i$	$- i$	$i$	$i$
χ₈	1	1	1	1	1	1	-1	-1	-1	1	1	-1	-1	-1	1	1	$- i$	$- i$	$i$	$i$	-1	$i$	$i$	$- i$	$- i$
χ₉	1	1	1	-1	-1	1	1	-1	-1	1	-1	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	-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	1	-1	1	-1	1	-1	1	-1	1	-1	1
χ₁₂	1	1	1	-1	-1	1	1	-1	-1	1	-1	1	-1	-1	1	-1	-1	1	-1	1	1	1	-1	1	-1
χ₁₃	1	1	1	-1	-1	1	-1	1	1	1	-1	-1	1	1	1	-1	$i$	$- i$	$- i$	$i$	-1	$i$	$- i$	$- i$	$i$
χ₁₄	1	1	1	-1	-1	1	-1	1	1	1	-1	-1	1	1	1	-1	$- i$	$i$	$i$	$- i$	-1	$- i$	$i$	$i$	$- i$
χ₁₅	1	1	1	-1	-1	1	-1	1	1	1	-1	-1	-1	-1	-1	1	$i$	$- i$	$- i$	$i$	1	$- i$	$i$	$i$	$- i$
χ₁₆	1	1	1	-1	-1	1	-1	1	1	1	-1	-1	-1	-1	-1	1	$- i$	$i$	$i$	$- i$	1	$i$	$- i$	$- i$	$i$
χ₁₇	2	2	2	2	2	2	2	2	-2	-2	-2	-2	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₁₈	2	2	2	2	2	2	-2	-2	2	-2	-2	2	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₁₉	2	2	2	-2	-2	2	2	-2	2	-2	2	-2	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₀	2	2	2	-2	-2	2	-2	2	-2	-2	2	2	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₁	4	4	4	4	-4	-4	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₂	4	4	4	-4	4	-4	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₃	8	8	-8	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₄	8	-8	0	0	0	0	0	0	0	0	0	0	$2 \sqrt{2}$	$- 2 \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0
χ₂₅	8	-8	0	0	0	0	0	0	0	0	0	0	$- 2 \sqrt{2}$	$2 \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0

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