Group #4063 — character table

	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	C₂₆	C₂₇	C₂₈
size	1	1	2	2	2	4	4	2	2	4	4	4	8	8	2	2	4	4	4	8	8	5	5	10	10	10	20	20
order	1	2	4	8	8	4	4	5	10	20	40	40	20	20	5	10	20	40	40	20	20	2	2	4	8	8	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	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	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	-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	-1	-1	1
χ₅	2	2	-2	0	0	0	0	2	2	-2	0	0	0	0	2	2	-2	0	0	0	0	2	2	-2	0	0	0	0
χ₆	2	-2	0	$\sqrt{2}$	$- \sqrt{2}$	0	0	2	-2	0	$\sqrt{2}$	$- \sqrt{2}$	0	0	2	-2	0	$\sqrt{2}$	$- \sqrt{2}$	0	0	2	-2	0	$\sqrt{2}$	$- \sqrt{2}$	0	0
χ₇	2	-2	0	$- \sqrt{2}$	$\sqrt{2}$	0	0	2	-2	0	$- \sqrt{2}$	$\sqrt{2}$	0	0	2	-2	0	$- \sqrt{2}$	$\sqrt{2}$	0	0	2	-2	0	$- \sqrt{2}$	$\sqrt{2}$	0	0
χ₈	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	-1	-1	-1
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	-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	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	1	1	-1
χ₁₂	2	2	-2	0	0	0	0	2	2	-2	0	0	0	0	2	2	-2	0	0	0	0	-2	-2	2	0	0	0	0
χ₁₃	2	-2	0	$\sqrt{2}$	$- \sqrt{2}$	0	0	2	-2	0	$\sqrt{2}$	$- \sqrt{2}$	0	0	2	-2	0	$\sqrt{2}$	$- \sqrt{2}$	0	0	-2	2	0	$- \sqrt{2}$	$\sqrt{2}$	0	0
χ₁₄	2	-2	0	$- \sqrt{2}$	$\sqrt{2}$	0	0	2	-2	0	$- \sqrt{2}$	$\sqrt{2}$	0	0	2	-2	0	$- \sqrt{2}$	$\sqrt{2}$	0	0	-2	2	0	$\sqrt{2}$	$- \sqrt{2}$	0	0
χ₁₅	2	2	2	2	2	2	2	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	0	0	0	0	0	0	0
χ₁₆	2	2	2	2	2	-2	-2	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	0	0	0	0	0	0	0
χ₁₇	2	2	2	-2	-2	2	-2	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	0	0	0	0	0	0	0
χ₁₈	2	2	2	-2	-2	-2	2	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	0	0	0	0	0	0	0
χ₁₉	4	4	-4	0	0	0	0	$- 1 + \sqrt{5}$	$- 1 + \sqrt{5}$	$1 - \sqrt{5}$	0	0	0	0	$- 1 - \sqrt{5}$	$- 1 - \sqrt{5}$	$1 + \sqrt{5}$	0	0	0	0	0	0	0	0	0	0	0
χ₂₀	4	-4	0	$2 \sqrt{2}$	$- 2 \sqrt{2}$	0	0	$- 1 + \sqrt{5}$	$1 - \sqrt{5}$	0	−ζ⁷+ζ¹³−ζ²³+ζ³⁷	ζ⁷−ζ¹³+ζ²³−ζ³⁷	0	0	$- 1 - \sqrt{5}$	$1 + \sqrt{5}$	0	ζ²¹+ζ²⁹−ζ³¹−ζ³⁹	−ζ²¹−ζ²⁹+ζ³¹+ζ³⁹	0	0	0	0	0	0	0	0	0
χ₂₁	4	-4	0	$- 2 \sqrt{2}$	$2 \sqrt{2}$	0	0	$- 1 + \sqrt{5}$	$1 - \sqrt{5}$	0	ζ⁷−ζ¹³+ζ²³−ζ³⁷	−ζ⁷+ζ¹³−ζ²³+ζ³⁷	0	0	$- 1 - \sqrt{5}$	$1 + \sqrt{5}$	0	−ζ²¹−ζ²⁹+ζ³¹+ζ³⁹	ζ²¹+ζ²⁹−ζ³¹−ζ³⁹	0	0	0	0	0	0	0	0	0
χ₂₂	2	2	2	2	2	2	2	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	0	0	0	0	0	0	0
χ₂₃	2	2	2	2	2	-2	-2	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	0	0	0	0	0	0	0
χ₂₄	2	2	2	-2	-2	2	-2	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	0	0	0	0	0	0	0
χ₂₅	2	2	2	-2	-2	-2	2	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	0	0	0	0	0	0	0
χ₂₆	4	4	-4	0	0	0	0	$- 1 - \sqrt{5}$	$- 1 - \sqrt{5}$	$1 + \sqrt{5}$	0	0	0	0	$- 1 + \sqrt{5}$	$- 1 + \sqrt{5}$	$1 - \sqrt{5}$	0	0	0	0	0	0	0	0	0	0	0
χ₂₇	4	-4	0	$2 \sqrt{2}$	$- 2 \sqrt{2}$	0	0	$- 1 - \sqrt{5}$	$1 + \sqrt{5}$	0	ζ²¹+ζ²⁹−ζ³¹−ζ³⁹	−ζ²¹−ζ²⁹+ζ³¹+ζ³⁹	0	0	$- 1 + \sqrt{5}$	$1 - \sqrt{5}$	0	−ζ⁷+ζ¹³−ζ²³+ζ³⁷	ζ⁷−ζ¹³+ζ²³−ζ³⁷	0	0	0	0	0	0	0	0	0
χ₂₈	4	-4	0	$- 2 \sqrt{2}$	$2 \sqrt{2}$	0	0	$- 1 - \sqrt{5}$	$1 + \sqrt{5}$	0	−ζ²¹−ζ²⁹+ζ³¹+ζ³⁹	ζ²¹+ζ²⁹−ζ³¹−ζ³⁹	0	0	$- 1 + \sqrt{5}$	$1 - \sqrt{5}$	0	ζ⁷−ζ¹³+ζ²³−ζ³⁷	−ζ⁷+ζ¹³−ζ²³+ζ³⁷	0	0	0	0	0	0	0	0	0

Character table — Group #4063