Finite Group Databasebeta

← Group #1615

Character table — Group #1615

Order 128.

	C₁	C₂	C₃	C₄	C₅	C₆	C₇	C₈	C₉	C₁₀	C₁₁	C₁₂	C₁₃	C₁₄	C₁₅	C₁₆	C₁₇	C₁₈	C₁₉	C₂₀	C₂₁	C₂₂	C₂₃
size	1	1	1	1	2	2	4	4	4	4	8	8	8	8	8	8	8	8	8	8	8	8	8
order	1	2	2	2	2	2	4	4	4	4	2	4	4	4	4	4	4	4	4	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
χ₂	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
χ₄	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	1	-1	-1	1	1	-1	-1
χ₆	1	1	1	1	1	1	-1	-1	1	1	1	-1	1	-1	-1	-1	-1	1	1	-1	-1	1	1
χ₇	1	1	1	1	1	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	1	1	1	-1	-1
χ₉	2	2	2	2	2	2	2	2	-2	-2	0	-2	0	0	0	0	0	0	0	0	0	0	0
χ₁₀	2	2	2	2	2	2	-2	-2	-2	-2	0	2	0	0	0	0	0	0	0	0	0	0	0
χ₁₁	2	2	2	2	-2	-2	0	0	2	-2	0	0	0	2	-2	0	0	0	0	0	0	0	0
χ₁₂	2	2	2	2	-2	-2	0	0	2	-2	0	0	0	-2	2	0	0	0	0	0	0	0	0
χ₁₃	2	2	2	2	-2	-2	0	0	-2	2	2	0	-2	0	0	0	0	0	0	0	0	0	0
χ₁₄	2	2	2	2	-2	-2	0	0	-2	2	-2	0	2	0	0	0	0	0	0	0	0	0	0
χ₁₅	2	2	-2	-2	-2	2	$2 i$	$- 2 i$	0	0	0	0	0	0	0	0	0	0	0	$i \sqrt{2}$	$- i \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$
χ₁₆	2	2	-2	-2	-2	2	$2 i$	$- 2 i$	0	0	0	0	0	0	0	0	0	0	0	$- i \sqrt{2}$	$i \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$
χ₁₇	2	2	-2	-2	-2	2	$- 2 i$	$2 i$	0	0	0	0	0	0	0	0	0	0	0	$i \sqrt{2}$	$- i \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$
χ₁₈	2	2	-2	-2	-2	2	$- 2 i$	$2 i$	0	0	0	0	0	0	0	0	0	0	0	$- i \sqrt{2}$	$i \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$
χ₁₉	4	4	-4	-4	4	-4	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₀	4	-4	4	-4	0	0	0	0	0	0	0	0	0	0	0	$2 i$	$- 2 i$	0	0	0	0	0	0
χ₂₁	4	-4	4	-4	0	0	0	0	0	0	0	0	0	0	0	$- 2 i$	$2 i$	0	0	0	0	0	0
χ₂₂	4	-4	-4	4	0	0	0	0	0	0	0	0	0	0	0	0	0	$2 i$	$- 2 i$	0	0	0	0
χ₂₃	4	-4	-4	4	0	0	0	0	0	0	0	0	0	0	0	0	0	$- 2 i$	$2 i$	0	0	0	0

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