Finite Group Databasebeta

← Group #64903

Character table — Group #64903

Order 320.

	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	2	4	4	4	8	8	8	8	10	10	10	10	16	16	20	20	20	20	40	40	40
order	1	2	4	5	8	10	2	20	40	40	2	4	8	8	10	10	16	16	16	16	4	4	4
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	$i$	$i$	$- i$	$- i$	-1	$i$	$- i$
χ₄	1	1	1	1	1	1	1	1	1	1	-1	-1	-1	-1	1	1	$- i$	$- i$	$i$	$i$	-1	$- i$	$i$
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	$i$	$i$	$- i$	$- i$	1	$- i$	$i$
χ₈	1	1	1	1	1	1	-1	1	1	1	-1	-1	-1	-1	-1	-1	$- i$	$- i$	$i$	$i$	1	$i$	$- i$
χ₉	2	2	2	2	-2	2	0	2	-2	-2	2	2	-2	-2	0	0	0	0	0	0	0	0	0
χ₁₀	2	2	2	2	-2	2	0	2	-2	-2	-2	-2	2	2	0	0	0	0	0	0	0	0	0
χ₁₁	2	2	-2	2	0	2	0	-2	0	0	2	-2	0	0	0	0	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	0	0	0
χ₁₂	2	2	-2	2	0	2	0	-2	0	0	2	-2	0	0	0	0	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	0	0	0
χ₁₃	2	2	-2	2	0	2	0	-2	0	0	-2	2	0	0	0	0	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	0	0	0
χ₁₄	2	2	-2	2	0	2	0	-2	0	0	-2	2	0	0	0	0	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	0	0	0
χ₁₅	4	4	4	-1	4	-1	4	-1	-1	-1	0	0	0	0	-1	-1	0	0	0	0	0	0	0
χ₁₆	4	4	4	-1	4	-1	-4	-1	-1	-1	0	0	0	0	1	1	0	0	0	0	0	0	0
χ₁₇	4	4	4	-1	-4	-1	0	-1	1	1	0	0	0	0	$\sqrt{5}$	$- \sqrt{5}$	0	0	0	0	0	0	0
χ₁₈	4	4	4	-1	-4	-1	0	-1	1	1	0	0	0	0	$- \sqrt{5}$	$\sqrt{5}$	0	0	0	0	0	0	0
χ₁₉	4	-4	0	4	0	-4	0	0	0	0	0	0	$2 i \sqrt{2}$	$- 2 i \sqrt{2}$	0	0	0	0	0	0	0	0	0
χ₂₀	4	-4	0	4	0	-4	0	0	0	0	0	0	$- 2 i \sqrt{2}$	$2 i \sqrt{2}$	0	0	0	0	0	0	0	0	0
χ₂₁	8	8	-8	-2	0	-2	0	2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₂	8	-8	0	-2	0	2	0	0	$\sqrt{10}$	$- \sqrt{10}$	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₃	8	-8	0	-2	0	2	0	0	$- \sqrt{10}$	$\sqrt{10}$	0	0	0	0	0	0	0	0	0	0	0	0	0

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