Finite Group Databasebeta

← Group #1405

Character table — Group #1405

Order 128.

	C₁	C₂	C₃	C₄	C₅	C₆	C₇	C₈	C₉	C₁₀	C₁₁	C₁₂	C₁₃	C₁₄	C₁₅	C₁₆	C₁₇
size	1	1	2	4	4	4	8	8	8	8	8	8	8	8	16	16	16
order	1	2	2	4	4	4	2	4	4	4	8	8	8	8	8	8	8
χ₁	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
χ₃	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
χ₅	1	1	1	-1	1	-1	1	1	1	-1	$i$	$i$	$- i$	$- i$	-1	$i$	$- i$
χ₆	1	1	1	-1	1	-1	1	1	1	-1	$- i$	$- i$	$i$	$i$	-1	$- i$	$i$
χ₇	1	1	1	-1	1	-1	-1	1	-1	-1	$i$	$i$	$- i$	$- i$	1	$- i$	$i$
χ₈	1	1	1	-1	1	-1	-1	1	-1	-1	$- i$	$- i$	$i$	$i$	1	$i$	$- i$
χ₉	2	2	2	2	2	2	0	-2	0	-2	0	0	0	0	0	0	0
χ₁₀	2	2	2	-2	2	-2	0	-2	0	2	0	0	0	0	0	0	0
χ₁₁	4	4	4	0	-4	0	0	0	0	0	0	0	0	0	0	0	0
χ₁₂	4	4	-4	0	0	0	2	0	-2	0	0	0	0	0	0	0	0
χ₁₃	4	4	-4	0	0	0	-2	0	2	0	0	0	0	0	0	0	0
χ₁₄	4	-4	0	2	0	-2	0	0	0	0	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	0	0	0
χ₁₅	4	-4	0	2	0	-2	0	0	0	0	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	0	0	0
χ₁₆	4	-4	0	-2	0	2	0	0	0	0	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	0	0	0
χ₁₇	4	-4	0	-2	0	2	0	0	0	0	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	0	0	0

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