Group #13046152 — 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	C₂₉	C₃₀	C₃₁	C₃₂	C₃₃	C₃₄	C₃₅	C₃₆	C₃₇	C₃₈	C₃₉	C₄₀	C₄₁
size	1	1	1	1	2	2	10	10	10	10	10	10	20	20	20	32	32	32	32	32	32	32	32	32	32	32	32	32	32	32	32	40	40	40	40	80	80	80	80	80	80
order	1	2	2	2	4	4	2	2	4	4	4	4	2	2	4	5	5	10	10	10	10	10	10	20	20	20	20	20	20	20	20	4	4	4	4	2	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	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	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	-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	-1	-1	-1	-1	-1	1	1	-1	1	-1	-1	1	1
χ₅	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	0	0	0	0	0	0	0	0	0	0
χ₆	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	0	0	0	0	0	0	0	0	0	0
χ₇	2	2	2	2	-2	-2	2	2	2	2	2	2	-2	-2	-2	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	0	0	0	0	0	0	0	0	0	0
χ₈	2	2	2	2	-2	-2	2	2	2	2	2	2	-2	-2	-2	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	0	0	0	0	0	0	0	0	0	0
χ₉	2	-2	2	-2	0	0	2	-2	2	2	-2	-2	0	0	0	2	2	-2	-2	-2	-2	2	2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₁₀	2	-2	2	-2	0	0	2	-2	2	2	-2	-2	0	0	0	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	ζ⁶−ζ¹⁴	ζ⁶−ζ¹⁴	−ζ⁶+ζ¹⁴	−ζ⁶+ζ¹⁴	−ζ²+ζ¹⁸	−ζ²+ζ¹⁸	ζ²−ζ¹⁸	ζ²−ζ¹⁸	0	0	0	0	0	0	0	0	0	0
χ₁₁	2	-2	2	-2	0	0	2	-2	2	2	-2	-2	0	0	0	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	−ζ⁶+ζ¹⁴	−ζ⁶+ζ¹⁴	ζ⁶−ζ¹⁴	ζ⁶−ζ¹⁴	ζ²−ζ¹⁸	ζ²−ζ¹⁸	−ζ²+ζ¹⁸	−ζ²+ζ¹⁸	0	0	0	0	0	0	0	0	0	0
χ₁₂	2	-2	2	-2	0	0	2	-2	2	2	-2	-2	0	0	0	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	−ζ²+ζ¹⁸	−ζ²+ζ¹⁸	ζ²−ζ¹⁸	ζ²−ζ¹⁸	−ζ⁶+ζ¹⁴	−ζ⁶+ζ¹⁴	ζ⁶−ζ¹⁴	ζ⁶−ζ¹⁴	0	0	0	0	0	0	0	0	0	0
χ₁₃	2	-2	2	-2	0	0	2	-2	2	2	-2	-2	0	0	0	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	ζ²−ζ¹⁸	ζ²−ζ¹⁸	−ζ²+ζ¹⁸	−ζ²+ζ¹⁸	ζ⁶−ζ¹⁴	ζ⁶−ζ¹⁴	−ζ⁶+ζ¹⁴	−ζ⁶+ζ¹⁴	0	0	0	0	0	0	0	0	0	0
χ₁₄	4	4	-4	-4	$4 i$	$- 4 i$	0	0	0	0	0	0	0	0	0	-1	-1	1	-1	1	-1	1	1	$i$	$- i$	$i$	$- i$	$i$	$- i$	$i$	$- i$	$2 i$	$- 2 i$	2	-2	0	0	0	0	0	0
χ₁₅	4	4	-4	-4	$4 i$	$- 4 i$	0	0	0	0	0	0	0	0	0	-1	-1	1	-1	1	-1	1	1	$i$	$- i$	$i$	$- i$	$i$	$- i$	$i$	$- i$	$- 2 i$	$2 i$	-2	2	0	0	0	0	0	0
χ₁₆	4	4	-4	-4	$- 4 i$	$4 i$	0	0	0	0	0	0	0	0	0	-1	-1	1	-1	1	-1	1	1	$- i$	$i$	$- i$	$i$	$- i$	$i$	$- i$	$i$	$2 i$	$- 2 i$	-2	2	0	0	0	0	0	0
χ₁₇	4	4	-4	-4	$- 4 i$	$4 i$	0	0	0	0	0	0	0	0	0	-1	-1	1	-1	1	-1	1	1	$- i$	$i$	$- i$	$i$	$- i$	$i$	$- i$	$i$	$- 2 i$	$2 i$	2	-2	0	0	0	0	0	0
χ₁₈	5	5	5	5	5	5	1	1	1	-3	1	-3	1	-3	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	1	1	1	-1	-1	1	-1	1	-1
χ₁₉	5	5	5	5	5	5	1	1	1	-3	1	-3	1	-3	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	-1	-1	-1	-1	1	1	-1	1	-1	1
χ₂₀	5	5	5	5	5	5	1	1	-3	1	-3	1	-3	1	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	1	1	1	-1	-1	-1	1	-1	1
χ₂₁	5	5	5	5	5	5	1	1	-3	1	-3	1	-3	1	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	-1	-1	-1	-1	1	1	1	-1	1	-1
χ₂₂	5	5	5	5	5	5	-3	-3	1	1	1	1	1	1	-3	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	1	1	1	1	1	-1	-1	-1	-1
χ₂₃	5	5	5	5	5	5	-3	-3	1	1	1	1	1	1	-3	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	-1	-1	-1	-1	-1	-1	1	1	1	1
χ₂₄	5	5	5	5	-5	-5	1	1	1	-3	1	-3	-1	3	-1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	1	-1	-1	-1	1	1	-1	-1	1
χ₂₅	5	5	5	5	-5	-5	1	1	1	-3	1	-3	-1	3	-1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	-1	-1	1	1	1	-1	-1	1	1	-1
χ₂₆	5	5	5	5	-5	-5	1	1	-3	1	-3	1	3	-1	-1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	1	-1	-1	-1	1	-1	1	1	-1
χ₂₇	5	5	5	5	-5	-5	1	1	-3	1	-3	1	3	-1	-1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	-1	-1	1	1	1	-1	1	-1	-1	1
χ₂₈	5	5	5	5	-5	-5	-3	-3	1	1	1	1	-1	-1	3	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	1	-1	-1	1	-1	-1	-1	1	1
χ₂₉	5	5	5	5	-5	-5	-3	-3	1	1	1	1	-1	-1	3	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	-1	-1	1	1	-1	1	1	1	-1	-1
χ₃₀	8	8	-8	-8	$8 i$	$- 8 i$	0	0	0	0	0	0	0	0	0	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	−ζ¹¹−ζ¹⁹	ζ¹¹+ζ¹⁹	−ζ¹¹−ζ¹⁹	ζ¹¹+ζ¹⁹	−ζ³−ζ⁷	ζ³+ζ⁷	−ζ³−ζ⁷	ζ³+ζ⁷	0	0	0	0	0	0	0	0	0	0
χ₃₁	8	8	-8	-8	$8 i$	$- 8 i$	0	0	0	0	0	0	0	0	0	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	−ζ³−ζ⁷	ζ³+ζ⁷	−ζ³−ζ⁷	ζ³+ζ⁷	−ζ¹¹−ζ¹⁹	ζ¹¹+ζ¹⁹	−ζ¹¹−ζ¹⁹	ζ¹¹+ζ¹⁹	0	0	0	0	0	0	0	0	0	0
χ₃₂	8	8	-8	-8	$- 8 i$	$8 i$	0	0	0	0	0	0	0	0	0	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	ζ¹¹+ζ¹⁹	−ζ¹¹−ζ¹⁹	ζ¹¹+ζ¹⁹	−ζ¹¹−ζ¹⁹	ζ³+ζ⁷	−ζ³−ζ⁷	ζ³+ζ⁷	−ζ³−ζ⁷	0	0	0	0	0	0	0	0	0	0
χ₃₃	8	8	-8	-8	$- 8 i$	$8 i$	0	0	0	0	0	0	0	0	0	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	ζ³+ζ⁷	−ζ³−ζ⁷	ζ³+ζ⁷	−ζ³−ζ⁷	ζ¹¹+ζ¹⁹	−ζ¹¹−ζ¹⁹	ζ¹¹+ζ¹⁹	−ζ¹¹−ζ¹⁹	0	0	0	0	0	0	0	0	0	0
χ₃₄	8	-8	-8	8	0	0	0	0	0	0	0	0	0	0	0	-2	-2	-2	2	-2	2	2	2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₅	8	-8	-8	8	0	0	0	0	0	0	0	0	0	0	0	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	−ζ¹¹+ζ¹⁹	ζ¹¹−ζ¹⁹	ζ¹¹−ζ¹⁹	−ζ¹¹+ζ¹⁹	−ζ³+ζ⁷	ζ³−ζ⁷	ζ³−ζ⁷	−ζ³+ζ⁷	0	0	0	0	0	0	0	0	0	0
χ₃₆	8	-8	-8	8	0	0	0	0	0	0	0	0	0	0	0	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	ζ¹¹−ζ¹⁹	−ζ¹¹+ζ¹⁹	−ζ¹¹+ζ¹⁹	ζ¹¹−ζ¹⁹	ζ³−ζ⁷	−ζ³+ζ⁷	−ζ³+ζ⁷	ζ³−ζ⁷	0	0	0	0	0	0	0	0	0	0
χ₃₇	8	-8	-8	8	0	0	0	0	0	0	0	0	0	0	0	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	ζ³−ζ⁷	−ζ³+ζ⁷	−ζ³+ζ⁷	ζ³−ζ⁷	−ζ¹¹+ζ¹⁹	ζ¹¹−ζ¹⁹	ζ¹¹−ζ¹⁹	−ζ¹¹+ζ¹⁹	0	0	0	0	0	0	0	0	0	0
χ₃₈	8	-8	-8	8	0	0	0	0	0	0	0	0	0	0	0	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	−ζ³+ζ⁷	ζ³−ζ⁷	ζ³−ζ⁷	−ζ³+ζ⁷	ζ¹¹−ζ¹⁹	−ζ¹¹+ζ¹⁹	−ζ¹¹+ζ¹⁹	ζ¹¹−ζ¹⁹	0	0	0	0	0	0	0	0	0	0
χ₃₉	10	-10	10	-10	0	0	2	-2	2	-6	-2	6	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₀	10	-10	10	-10	0	0	2	-2	-6	2	6	-2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₁	10	-10	10	-10	0	0	-6	6	2	2	-2	-2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0

Character table — Group #13046152