Group #4065 — 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	2	2	2	2	4	4	4	4	4	4	4	4	5	5	8	8	8	8	10	10	10	20	20
order	1	2	4	5	5	8	8	10	10	4	4	20	20	40	40	40	40	4	4	20	20	20	20	2	8	8	2	2
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	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
χ₆	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
χ₇	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
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	2	2	2	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	2	2	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	2	2	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	0	0	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	0	0	0	0	0
χ₁₀	2	2	2	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	2	2	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	-2	-2	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	0	0	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	0	0	0	0	0
χ₁₁	2	2	2	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	-2	-2	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	2	-2	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	0	0	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	0	0	0	0	0
χ₁₂	2	2	2	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	-2	-2	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	-2	2	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	0	0	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	0	0	0	0	0
χ₁₃	2	2	2	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	2	2	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	2	2	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	0	0	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	0	0	0	0	0
χ₁₄	2	2	2	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	2	2	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	-2	-2	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	0	0	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	0	0	0	0	0
χ₁₅	2	2	2	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	-2	-2	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	2	-2	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	0	0	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	0	0	0	0	0
χ₁₆	2	2	2	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	-2	-2	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	-2	2	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	0	0	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	0	0	0	0	0
χ₁₇	2	2	-2	2	2	0	0	2	2	0	0	-2	-2	0	0	0	0	2	2	0	0	0	0	-2	0	0	0	0
χ₁₈	2	2	-2	2	2	0	0	2	2	0	0	-2	-2	0	0	0	0	-2	-2	0	0	0	0	2	0	0	0	0
χ₁₉	2	-2	0	2	2	$\sqrt{2}$	$- \sqrt{2}$	-2	-2	0	0	0	0	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$2 i$	$- 2 i$	0	0	0	0	0	$i \sqrt{2}$	$- i \sqrt{2}$	0	0
χ₂₀	2	-2	0	2	2	$\sqrt{2}$	$- \sqrt{2}$	-2	-2	0	0	0	0	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- 2 i$	$2 i$	0	0	0	0	0	$- i \sqrt{2}$	$i \sqrt{2}$	0	0
χ₂₁	2	-2	0	2	2	$- \sqrt{2}$	$\sqrt{2}$	-2	-2	0	0	0	0	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$2 i$	$- 2 i$	0	0	0	0	0	$- i \sqrt{2}$	$i \sqrt{2}$	0	0
χ₂₂	2	-2	0	2	2	$- \sqrt{2}$	$\sqrt{2}$	-2	-2	0	0	0	0	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$- 2 i$	$2 i$	0	0	0	0	0	$i \sqrt{2}$	$- i \sqrt{2}$	0	0
χ₂₃	4	4	-4	$- 1 + \sqrt{5}$	$- 1 - \sqrt{5}$	0	0	$- 1 + \sqrt{5}$	$- 1 - \sqrt{5}$	0	0	$1 - \sqrt{5}$	$1 + \sqrt{5}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₄	4	4	-4	$- 1 - \sqrt{5}$	$- 1 + \sqrt{5}$	0	0	$- 1 - \sqrt{5}$	$- 1 + \sqrt{5}$	0	0	$1 + \sqrt{5}$	$1 - \sqrt{5}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₅	4	-4	0	$- 1 + \sqrt{5}$	$- 1 - \sqrt{5}$	$2 \sqrt{2}$	$- 2 \sqrt{2}$	$1 - \sqrt{5}$	$1 + \sqrt{5}$	0	0	0	0	−ζ⁷+ζ¹³−ζ²³+ζ³⁷	ζ⁷−ζ¹³+ζ²³−ζ³⁷	ζ²¹+ζ²⁹−ζ³¹−ζ³⁹	−ζ²¹−ζ²⁹+ζ³¹+ζ³⁹	0	0	0	0	0	0	0	0	0	0	0
χ₂₆	4	-4	0	$- 1 + \sqrt{5}$	$- 1 - \sqrt{5}$	$- 2 \sqrt{2}$	$2 \sqrt{2}$	$1 - \sqrt{5}$	$1 + \sqrt{5}$	0	0	0	0	ζ⁷−ζ¹³+ζ²³−ζ³⁷	−ζ⁷+ζ¹³−ζ²³+ζ³⁷	−ζ²¹−ζ²⁹+ζ³¹+ζ³⁹	ζ²¹+ζ²⁹−ζ³¹−ζ³⁹	0	0	0	0	0	0	0	0	0	0	0
χ₂₇	4	-4	0	$- 1 - \sqrt{5}$	$- 1 + \sqrt{5}$	$2 \sqrt{2}$	$- 2 \sqrt{2}$	$1 + \sqrt{5}$	$1 - \sqrt{5}$	0	0	0	0	ζ²¹+ζ²⁹−ζ³¹−ζ³⁹	−ζ²¹−ζ²⁹+ζ³¹+ζ³⁹	−ζ⁷+ζ¹³−ζ²³+ζ³⁷	ζ⁷−ζ¹³+ζ²³−ζ³⁷	0	0	0	0	0	0	0	0	0	0	0
χ₂₈	4	-4	0	$- 1 - \sqrt{5}$	$- 1 + \sqrt{5}$	$- 2 \sqrt{2}$	$2 \sqrt{2}$	$1 + \sqrt{5}$	$1 - \sqrt{5}$	0	0	0	0	−ζ²¹−ζ²⁹+ζ³¹+ζ³⁹	ζ²¹+ζ²⁹−ζ³¹−ζ³⁹	ζ⁷−ζ¹³+ζ²³−ζ³⁷	−ζ⁷+ζ¹³−ζ²³+ζ³⁷	0	0	0	0	0	0	0	0	0	0	0

Character table — Group #4065