Group #13088276 — character table

	C₁	C₂	C₃	C₄	C₅	C₆	C₇	C₈	C₉	C₁₀	C₁₁	C₁₂	C₁₃	C₁₄	C₁₅	C₁₆	C₁₇	C₁₈	C₁₉	C₂₀
size	1	1	72	72	72	72	72	72	72	72	72	80	80	90	90	90	90	90	90	90
order	1	2	2	5	5	10	10	10	10	10	10	3	6	4	8	8	16	16	16	16
χ₁	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
χ₃	8	8	2	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	-1	-1	0	0	0	0	0	0	0
χ₄	8	8	2	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	-1	-1	0	0	0	0	0	0	0
χ₅	8	8	-2	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	-1	-1	0	0	0	0	0	0	0
χ₆	8	8	-2	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	-1	-1	0	0	0	0	0	0	0
χ₇	8	-8	0	-2	-2	2	2	0	0	0	0	-1	1	0	0	0	0	0	0	0
χ₈	8	-8	0	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	ζ²⁴−ζ⁵⁶	−ζ²⁴+ζ⁵⁶	−ζ⁸+ζ⁷²	ζ⁸−ζ⁷²	-1	1	0	0	0	0	0	0	0
χ₉	8	-8	0	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	−ζ²⁴+ζ⁵⁶	ζ²⁴−ζ⁵⁶	ζ⁸−ζ⁷²	−ζ⁸+ζ⁷²	-1	1	0	0	0	0	0	0	0
χ₁₀	8	-8	0	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	−ζ⁸+ζ⁷²	ζ⁸−ζ⁷²	−ζ²⁴+ζ⁵⁶	ζ²⁴−ζ⁵⁶	-1	1	0	0	0	0	0	0	0
χ₁₁	8	-8	0	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	ζ⁸−ζ⁷²	−ζ⁸+ζ⁷²	ζ²⁴−ζ⁵⁶	−ζ²⁴+ζ⁵⁶	-1	1	0	0	0	0	0	0	0
χ₁₂	9	9	1	-1	-1	-1	-1	1	1	1	1	0	0	1	1	1	-1	-1	-1	-1
χ₁₃	9	9	-1	-1	-1	-1	-1	-1	-1	-1	-1	0	0	1	1	1	1	1	1	1
χ₁₄	10	10	0	0	0	0	0	0	0	0	0	1	1	2	-2	-2	0	0	0	0
χ₁₅	10	10	0	0	0	0	0	0	0	0	0	1	1	-2	0	0	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$
χ₁₆	10	10	0	0	0	0	0	0	0	0	0	1	1	-2	0	0	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$
χ₁₇	10	-10	0	0	0	0	0	0	0	0	0	1	-1	0	$\sqrt{2}$	$- \sqrt{2}$	−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
χ₁₈	10	-10	0	0	0	0	0	0	0	0	0	1	-1	0	$\sqrt{2}$	$- \sqrt{2}$	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
χ₁₉	10	-10	0	0	0	0	0	0	0	0	0	1	-1	0	$- \sqrt{2}$	$\sqrt{2}$	−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
χ₂₀	10	-10	0	0	0	0	0	0	0	0	0	1	-1	0	$- \sqrt{2}$	$\sqrt{2}$	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

Character table — Group #13088276