Finite Group Databasebeta

← Group #4005

Character table — Group #4005

Order 160.

	C₁	C₂	C₃	C₄	C₅	C₆	C₇	C₈	C₉	C₁₀	C₁₁	C₁₂	C₁₃	C₁₄	C₁₅	C₁₆	C₁₇	C₁₈	C₁₉
size	1	1	2	4	4	4	4	4	4	4	4	4	10	10	20	20	20	20	20
order	1	2	2	4	5	10	10	10	20	20	20	20	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
χ₂	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	$i$	$i$	$- i$	$- i$
χ₄	1	1	1	1	1	1	1	1	1	1	1	1	-1	-1	-1	$- i$	$- i$	$i$	$i$
χ₅	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
χ₇	1	1	1	-1	1	1	1	1	-1	-1	-1	-1	-1	-1	1	$i$	$- i$	$- i$	$i$
χ₈	1	1	1	-1	1	1	1	1	-1	-1	-1	-1	-1	-1	1	$- i$	$i$	$i$	$- i$
χ₉	2	2	-2	0	2	-2	-2	2	0	0	0	0	2	-2	0	0	0	0	0
χ₁₀	2	2	-2	0	2	-2	-2	2	0	0	0	0	-2	2	0	0	0	0	0
χ₁₁	4	4	4	4	-1	-1	-1	-1	-1	-1	-1	-1	0	0	0	0	0	0	0
χ₁₂	4	4	4	-4	-1	-1	-1	-1	1	1	1	1	0	0	0	0	0	0	0
χ₁₃	4	4	-4	0	-1	1	1	-1	$\sqrt{5}$	$\sqrt{5}$	$- \sqrt{5}$	$- \sqrt{5}$	0	0	0	0	0	0	0
χ₁₄	4	4	-4	0	-1	1	1	-1	$- \sqrt{5}$	$- \sqrt{5}$	$\sqrt{5}$	$\sqrt{5}$	0	0	0	0	0	0	0
χ₁₅	4	-4	0	0	4	0	0	-4	0	0	0	0	0	0	0	0	0	0	0
χ₁₆	4	-4	0	0	-1	$\sqrt{5}$	$- \sqrt{5}$	1	−ζ³+ζ⁷−ζ¹¹+ζ¹⁹	ζ³−ζ⁷+ζ¹¹−ζ¹⁹	ζ³−ζ⁷−ζ¹¹+ζ¹⁹	−ζ³+ζ⁷+ζ¹¹−ζ¹⁹	0	0	0	0	0	0	0
χ₁₇	4	-4	0	0	-1	$\sqrt{5}$	$- \sqrt{5}$	1	ζ³−ζ⁷+ζ¹¹−ζ¹⁹	−ζ³+ζ⁷−ζ¹¹+ζ¹⁹	−ζ³+ζ⁷+ζ¹¹−ζ¹⁹	ζ³−ζ⁷−ζ¹¹+ζ¹⁹	0	0	0	0	0	0	0
χ₁₈	4	-4	0	0	-1	$- \sqrt{5}$	$\sqrt{5}$	1	ζ³−ζ⁷−ζ¹¹+ζ¹⁹	−ζ³+ζ⁷+ζ¹¹−ζ¹⁹	ζ³−ζ⁷+ζ¹¹−ζ¹⁹	−ζ³+ζ⁷−ζ¹¹+ζ¹⁹	0	0	0	0	0	0	0
χ₁₉	4	-4	0	0	-1	$- \sqrt{5}$	$\sqrt{5}$	1	−ζ³+ζ⁷+ζ¹¹−ζ¹⁹	ζ³−ζ⁷−ζ¹¹+ζ¹⁹	−ζ³+ζ⁷−ζ¹¹+ζ¹⁹	ζ³−ζ⁷+ζ¹¹−ζ¹⁹	0	0	0	0	0	0	0

Here ζ is a primitive root of unity of order 20 (ζ²⁰ = 1); i = ζ⁵.