Group #3960 — 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
size	1	1	2	2	2	2	2	2	2	4	4	4	4	4	4	8	8	8	8	8	10	10	10	10	40
order	1	2	4	5	5	8	8	10	10	20	20	40	40	40	40	4	20	20	20	20	16	16	16	16	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
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
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
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
χ₅	2	2	2	2	2	-2	-2	2	2	2	2	-2	-2	-2	-2	0	0	0	0	0	0	0	0	0	0
χ₆	2	2	2	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	2	2	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	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
χ₇	2	2	2	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	2	2	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	-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
χ₈	2	2	2	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	-2	-2	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	0	ζ²⁴−ζ⁵⁶	−ζ²⁴+ζ⁵⁶	−ζ⁸+ζ⁷²	ζ⁸−ζ⁷²	0	0	0	0	0
χ₉	2	2	2	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	-2	-2	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	0	−ζ²⁴+ζ⁵⁶	ζ²⁴−ζ⁵⁶	ζ⁸−ζ⁷²	−ζ⁸+ζ⁷²	0	0	0	0	0
χ₁₀	2	2	2	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	2	2	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	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
χ₁₁	2	2	2	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	2	2	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	-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
χ₁₂	2	2	2	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	-2	-2	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	0	−ζ⁸+ζ⁷²	ζ⁸−ζ⁷²	−ζ²⁴+ζ⁵⁶	ζ²⁴−ζ⁵⁶	0	0	0	0	0
χ₁₃	2	2	2	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	-2	-2	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	0	ζ⁸−ζ⁷²	−ζ⁸+ζ⁷²	ζ²⁴−ζ⁵⁶	−ζ²⁴+ζ⁵⁶	0	0	0	0	0
χ₁₄	2	2	-2	2	2	0	0	2	2	-2	-2	0	0	0	0	0	0	0	0	0	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	0
χ₁₅	2	2	-2	2	2	0	0	2	2	-2	-2	0	0	0	0	0	0	0	0	0	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	0
χ₁₆	2	-2	0	2	2	$\sqrt{2}$	$- \sqrt{2}$	-2	-2	0	0	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	0	0	0	0	0	−ζ⁹−ζ³¹−ζ⁴¹−ζ⁴⁷−ζ⁵⁷−ζ⁶³−ζ⁷³−ζ⁷⁹	ζ⁹+ζ³¹+ζ⁴¹+ζ⁴⁷+ζ⁵⁷+ζ⁶³+ζ⁷³+ζ⁷⁹	−ζ¹¹−ζ¹³−ζ²⁷−ζ²⁹−ζ⁴³−ζ⁵⁹−ζ⁶¹−ζ⁷⁷	ζ¹¹+ζ¹³+ζ²⁷+ζ²⁹+ζ⁴³+ζ⁵⁹+ζ⁶¹+ζ⁷⁷	0
χ₁₇	2	-2	0	2	2	$\sqrt{2}$	$- \sqrt{2}$	-2	-2	0	0	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	0	0	0	0	0	ζ⁹+ζ³¹+ζ⁴¹+ζ⁴⁷+ζ⁵⁷+ζ⁶³+ζ⁷³+ζ⁷⁹	−ζ⁹−ζ³¹−ζ⁴¹−ζ⁴⁷−ζ⁵⁷−ζ⁶³−ζ⁷³−ζ⁷⁹	ζ¹¹+ζ¹³+ζ²⁷+ζ²⁹+ζ⁴³+ζ⁵⁹+ζ⁶¹+ζ⁷⁷	−ζ¹¹−ζ¹³−ζ²⁷−ζ²⁹−ζ⁴³−ζ⁵⁹−ζ⁶¹−ζ⁷⁷	0
χ₁₈	2	-2	0	2	2	$- \sqrt{2}$	$\sqrt{2}$	-2	-2	0	0	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	0	0	0	0	0	−ζ¹¹−ζ¹³−ζ²⁷−ζ²⁹−ζ⁴³−ζ⁵⁹−ζ⁶¹−ζ⁷⁷	ζ¹¹+ζ¹³+ζ²⁷+ζ²⁹+ζ⁴³+ζ⁵⁹+ζ⁶¹+ζ⁷⁷	ζ⁹+ζ³¹+ζ⁴¹+ζ⁴⁷+ζ⁵⁷+ζ⁶³+ζ⁷³+ζ⁷⁹	−ζ⁹−ζ³¹−ζ⁴¹−ζ⁴⁷−ζ⁵⁷−ζ⁶³−ζ⁷³−ζ⁷⁹	0
χ₁₉	2	-2	0	2	2	$- \sqrt{2}$	$\sqrt{2}$	-2	-2	0	0	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	0	0	0	0	0	ζ¹¹+ζ¹³+ζ²⁷+ζ²⁹+ζ⁴³+ζ⁵⁹+ζ⁶¹+ζ⁷⁷	−ζ¹¹−ζ¹³−ζ²⁷−ζ²⁹−ζ⁴³−ζ⁵⁹−ζ⁶¹−ζ⁷⁷	−ζ⁹−ζ³¹−ζ⁴¹−ζ⁴⁷−ζ⁵⁷−ζ⁶³−ζ⁷³−ζ⁷⁹	ζ⁹+ζ³¹+ζ⁴¹+ζ⁴⁷+ζ⁵⁷+ζ⁶³+ζ⁷³+ζ⁷⁹	0
χ₂₀	4	4	-4	$- 1 + \sqrt{5}$	$- 1 - \sqrt{5}$	0	0	$- 1 + \sqrt{5}$	$- 1 - \sqrt{5}$	$1 - \sqrt{5}$	$1 + \sqrt{5}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₁	4	4	-4	$- 1 - \sqrt{5}$	$- 1 + \sqrt{5}$	0	0	$- 1 - \sqrt{5}$	$- 1 + \sqrt{5}$	$1 + \sqrt{5}$	$1 - \sqrt{5}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₂	4	-4	0	$- 1 + \sqrt{5}$	$- 1 - \sqrt{5}$	$2 \sqrt{2}$	$- 2 \sqrt{2}$	$1 - \sqrt{5}$	$1 + \sqrt{5}$	0	0	−ζ¹⁴+ζ²⁶−ζ⁴⁶+ζ⁷⁴	ζ¹⁴−ζ²⁶+ζ⁴⁶−ζ⁷⁴	ζ⁴²+ζ⁵⁸−ζ⁶²−ζ⁷⁸	−ζ⁴²−ζ⁵⁸+ζ⁶²+ζ⁷⁸	0	0	0	0	0	0	0	0	0	0
χ₂₃	4	-4	0	$- 1 + \sqrt{5}$	$- 1 - \sqrt{5}$	$- 2 \sqrt{2}$	$2 \sqrt{2}$	$1 - \sqrt{5}$	$1 + \sqrt{5}$	0	0	ζ¹⁴−ζ²⁶+ζ⁴⁶−ζ⁷⁴	−ζ¹⁴+ζ²⁶−ζ⁴⁶+ζ⁷⁴	−ζ⁴²−ζ⁵⁸+ζ⁶²+ζ⁷⁸	ζ⁴²+ζ⁵⁸−ζ⁶²−ζ⁷⁸	0	0	0	0	0	0	0	0	0	0
χ₂₄	4	-4	0	$- 1 - \sqrt{5}$	$- 1 + \sqrt{5}$	$2 \sqrt{2}$	$- 2 \sqrt{2}$	$1 + \sqrt{5}$	$1 - \sqrt{5}$	0	0	ζ⁴²+ζ⁵⁸−ζ⁶²−ζ⁷⁸	−ζ⁴²−ζ⁵⁸+ζ⁶²+ζ⁷⁸	−ζ¹⁴+ζ²⁶−ζ⁴⁶+ζ⁷⁴	ζ¹⁴−ζ²⁶+ζ⁴⁶−ζ⁷⁴	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	−ζ⁴²−ζ⁵⁸+ζ⁶²+ζ⁷⁸	ζ⁴²+ζ⁵⁸−ζ⁶²−ζ⁷⁸	ζ¹⁴−ζ²⁶+ζ⁴⁶−ζ⁷⁴	−ζ¹⁴+ζ²⁶−ζ⁴⁶+ζ⁷⁴	0	0	0	0	0	0	0	0	0	0

Character table — Group #3960