Group #13014566 — 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	2	4	4	4	4	4	4	4	8	8	8	8	8	8	8	8	8	8	8	8	8	8	8	8	32	32	32	32	32	40	40	40	40	80	80	160	160	160	160
order	1	2	2	4	4	4	5	10	10	10	8	8	20	20	20	20	20	20	40	40	40	40	40	40	40	40	4	20	20	20	20	8	8	8	8	2	4	4	4	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	$i$	$- i$	$i$	$- i$
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	$- i$	$i$	$- i$	$i$
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	-1	-1	-1	1	1	1	1	-1	-1	$i$	$- i$	$- i$	$i$
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	-1	-1	-1	1	1	1	1	-1	-1	$- i$	$i$	$i$	$- i$
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	-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	-1	-1	-1	-1	-1	-1	-1	1	1	-1	-1	1	1
χ₉	2	2	2	2	2	2	2	2	2	2	-2	-2	2	2	2	2	2	2	-2	-2	-2	-2	-2	-2	-2	-2	0	0	0	0	0	0	0	0	0	2	-2	0	0	0	0
χ₁₀	2	2	2	2	2	2	2	2	2	2	-2	-2	2	2	2	2	2	2	-2	-2	-2	-2	-2	-2	-2	-2	0	0	0	0	0	0	0	0	0	-2	2	0	0	0	0
χ₁₁	4	4	4	4	4	4	-1	-1	-1	-1	4	4	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	4	-1	-1	-1	-1	0	0	0	0	0	0	0	0	0	0
χ₁₂	4	4	4	4	4	4	-1	-1	-1	-1	4	4	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-4	1	1	1	1	0	0	0	0	0	0	0	0	0	0
χ₁₃	4	4	4	4	4	4	-1	-1	-1	-1	-4	-4	-1	-1	-1	-1	-1	-1	1	1	1	1	1	1	1	1	0	$\sqrt{5}$	$\sqrt{5}$	$- \sqrt{5}$	$- \sqrt{5}$	0	0	0	0	0	0	0	0	0	0
χ₁₄	4	4	4	4	4	4	-1	-1	-1	-1	-4	-4	-1	-1	-1	-1	-1	-1	1	1	1	1	1	1	1	1	0	$- \sqrt{5}$	$- \sqrt{5}$	$\sqrt{5}$	$\sqrt{5}$	0	0	0	0	0	0	0	0	0	0
χ₁₅	4	4	4	4	-4	-4	4	4	4	4	0	0	-4	-4	-4	-4	4	4	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₁₆	4	4	4	4	-4	-4	-1	-1	-1	-1	0	0	1	1	1	1	-1	-1	$\sqrt{5}$	$\sqrt{5}$	$\sqrt{5}$	$\sqrt{5}$	$- \sqrt{5}$	$- \sqrt{5}$	$- \sqrt{5}$	$- \sqrt{5}$	0	−ζ⁴+ζ¹²−ζ²⁸+ζ³⁶	ζ⁴−ζ¹²+ζ²⁸−ζ³⁶	−ζ⁴−ζ¹²+ζ²⁸+ζ³⁶	ζ⁴+ζ¹²−ζ²⁸−ζ³⁶	0	0	0	0	0	0	0	0	0	0
χ₁₇	4	4	4	4	-4	-4	-1	-1	-1	-1	0	0	1	1	1	1	-1	-1	$\sqrt{5}$	$\sqrt{5}$	$\sqrt{5}$	$\sqrt{5}$	$- \sqrt{5}$	$- \sqrt{5}$	$- \sqrt{5}$	$- \sqrt{5}$	0	ζ⁴−ζ¹²+ζ²⁸−ζ³⁶	−ζ⁴+ζ¹²−ζ²⁸+ζ³⁶	ζ⁴+ζ¹²−ζ²⁸−ζ³⁶	−ζ⁴−ζ¹²+ζ²⁸+ζ³⁶	0	0	0	0	0	0	0	0	0	0
χ₁₈	4	4	4	4	-4	-4	-1	-1	-1	-1	0	0	1	1	1	1	-1	-1	$- \sqrt{5}$	$- \sqrt{5}$	$- \sqrt{5}$	$- \sqrt{5}$	$\sqrt{5}$	$\sqrt{5}$	$\sqrt{5}$	$\sqrt{5}$	0	−ζ⁴−ζ¹²+ζ²⁸+ζ³⁶	ζ⁴+ζ¹²−ζ²⁸−ζ³⁶	ζ⁴−ζ¹²+ζ²⁸−ζ³⁶	−ζ⁴+ζ¹²−ζ²⁸+ζ³⁶	0	0	0	0	0	0	0	0	0	0
χ₁₉	4	4	4	4	-4	-4	-1	-1	-1	-1	0	0	1	1	1	1	-1	-1	$- \sqrt{5}$	$- \sqrt{5}$	$- \sqrt{5}$	$- \sqrt{5}$	$\sqrt{5}$	$\sqrt{5}$	$\sqrt{5}$	$\sqrt{5}$	0	ζ⁴+ζ¹²−ζ²⁸−ζ³⁶	−ζ⁴−ζ¹²+ζ²⁸+ζ³⁶	−ζ⁴+ζ¹²−ζ²⁸+ζ³⁶	ζ⁴−ζ¹²+ζ²⁸−ζ³⁶	0	0	0	0	0	0	0	0	0	0
χ₂₀	4	4	4	-4	0	0	4	4	4	4	0	0	0	0	0	0	-4	-4	0	0	0	0	0	0	0	0	0	0	0	0	0	2	2	-2	-2	0	0	0	0	0	0
χ₂₁	4	4	4	-4	0	0	4	4	4	4	0	0	0	0	0	0	-4	-4	0	0	0	0	0	0	0	0	0	0	0	0	0	-2	-2	2	2	0	0	0	0	0	0
χ₂₂	4	4	-4	0	0	0	4	-4	-4	4	2	-2	0	0	0	0	0	0	2	2	-2	-2	2	2	-2	-2	0	0	0	0	0	0	0	$2 \sqrt{2}$	$- 2 \sqrt{2}$	0	0	0	0	0	0
χ₂₃	4	4	-4	0	0	0	4	-4	-4	4	2	-2	0	0	0	0	0	0	2	2	-2	-2	2	2	-2	-2	0	0	0	0	0	0	0	$- 2 \sqrt{2}$	$2 \sqrt{2}$	0	0	0	0	0	0
χ₂₄	4	4	-4	0	0	0	4	-4	-4	4	-2	2	0	0	0	0	0	0	-2	-2	2	2	-2	-2	2	2	0	0	0	0	0	$2 \sqrt{2}$	$- 2 \sqrt{2}$	0	0	0	0	0	0	0	0
χ₂₅	4	4	-4	0	0	0	4	-4	-4	4	-2	2	0	0	0	0	0	0	-2	-2	2	2	-2	-2	2	2	0	0	0	0	0	$- 2 \sqrt{2}$	$2 \sqrt{2}$	0	0	0	0	0	0	0	0
χ₂₆	8	8	8	-8	0	0	-2	-2	-2	-2	0	0	$2 \sqrt{5}$	$2 \sqrt{5}$	$- 2 \sqrt{5}$	$- 2 \sqrt{5}$	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
χ₂₇	8	8	8	-8	0	0	-2	-2	-2	-2	0	0	$- 2 \sqrt{5}$	$- 2 \sqrt{5}$	$2 \sqrt{5}$	$2 \sqrt{5}$	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
χ₂₈	8	8	-8	0	0	0	-2	2	2	-2	4	-4	0	0	0	0	$2 \sqrt{5}$	$- 2 \sqrt{5}$	$- 1 + \sqrt{5}$	$- 1 + \sqrt{5}$	$1 - \sqrt{5}$	$1 - \sqrt{5}$	$- 1 - \sqrt{5}$	$- 1 - \sqrt{5}$	$1 + \sqrt{5}$	$1 + \sqrt{5}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₉	8	8	-8	0	0	0	-2	2	2	-2	4	-4	0	0	0	0	$- 2 \sqrt{5}$	$2 \sqrt{5}$	$- 1 - \sqrt{5}$	$- 1 - \sqrt{5}$	$1 + \sqrt{5}$	$1 + \sqrt{5}$	$- 1 + \sqrt{5}$	$- 1 + \sqrt{5}$	$1 - \sqrt{5}$	$1 - \sqrt{5}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₀	8	8	-8	0	0	0	-2	2	2	-2	-4	4	0	0	0	0	$2 \sqrt{5}$	$- 2 \sqrt{5}$	$1 - \sqrt{5}$	$1 - \sqrt{5}$	$- 1 + \sqrt{5}$	$- 1 + \sqrt{5}$	$1 + \sqrt{5}$	$1 + \sqrt{5}$	$- 1 - \sqrt{5}$	$- 1 - \sqrt{5}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₁	8	8	-8	0	0	0	-2	2	2	-2	-4	4	0	0	0	0	$- 2 \sqrt{5}$	$2 \sqrt{5}$	$1 + \sqrt{5}$	$1 + \sqrt{5}$	$- 1 - \sqrt{5}$	$- 1 - \sqrt{5}$	$1 - \sqrt{5}$	$1 - \sqrt{5}$	$- 1 + \sqrt{5}$	$- 1 + \sqrt{5}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₂	8	-8	0	0	4	-4	8	0	0	-8	0	0	4	-4	4	-4	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
χ₃₃	8	-8	0	0	4	-4	-2	$2 \sqrt{5}$	$- 2 \sqrt{5}$	2	0	0	$- 1 + \sqrt{5}$	$1 - \sqrt{5}$	$- 1 - \sqrt{5}$	$1 + \sqrt{5}$	0	0	−ζ⁷−ζ¹³−ζ²¹+ζ²³+ζ²⁹+ζ³¹+ζ³⁷−ζ³⁹	ζ⁷+ζ¹³+ζ²¹−ζ²³−ζ²⁹−ζ³¹−ζ³⁷+ζ³⁹	ζ⁷+ζ¹³−ζ²¹−ζ²³+ζ²⁹+ζ³¹−ζ³⁷−ζ³⁹	−ζ⁷−ζ¹³+ζ²¹+ζ²³−ζ²⁹−ζ³¹+ζ³⁷+ζ³⁹	ζ⁷+ζ¹³−ζ²¹−ζ²³+ζ²⁹+ζ³¹−ζ³⁷−ζ³⁹	−ζ⁷−ζ¹³+ζ²¹+ζ²³−ζ²⁹−ζ³¹+ζ³⁷+ζ³⁹	−ζ⁷−ζ¹³−ζ²¹+ζ²³+ζ²⁹+ζ³¹+ζ³⁷−ζ³⁹	ζ⁷+ζ¹³+ζ²¹−ζ²³−ζ²⁹−ζ³¹−ζ³⁷+ζ³⁹	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₄	8	-8	0	0	4	-4	-2	$2 \sqrt{5}$	$- 2 \sqrt{5}$	2	0	0	$- 1 + \sqrt{5}$	$1 - \sqrt{5}$	$- 1 - \sqrt{5}$	$1 + \sqrt{5}$	0	0	ζ⁷+ζ¹³+ζ²¹−ζ²³−ζ²⁹−ζ³¹−ζ³⁷+ζ³⁹	−ζ⁷−ζ¹³−ζ²¹+ζ²³+ζ²⁹+ζ³¹+ζ³⁷−ζ³⁹	−ζ⁷−ζ¹³+ζ²¹+ζ²³−ζ²⁹−ζ³¹+ζ³⁷+ζ³⁹	ζ⁷+ζ¹³−ζ²¹−ζ²³+ζ²⁹+ζ³¹−ζ³⁷−ζ³⁹	−ζ⁷−ζ¹³+ζ²¹+ζ²³−ζ²⁹−ζ³¹+ζ³⁷+ζ³⁹	ζ⁷+ζ¹³−ζ²¹−ζ²³+ζ²⁹+ζ³¹−ζ³⁷−ζ³⁹	ζ⁷+ζ¹³+ζ²¹−ζ²³−ζ²⁹−ζ³¹−ζ³⁷+ζ³⁹	−ζ⁷−ζ¹³−ζ²¹+ζ²³+ζ²⁹+ζ³¹+ζ³⁷−ζ³⁹	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₅	8	-8	0	0	4	-4	-2	$- 2 \sqrt{5}$	$2 \sqrt{5}$	2	0	0	$- 1 - \sqrt{5}$	$1 + \sqrt{5}$	$- 1 + \sqrt{5}$	$1 - \sqrt{5}$	0	0	ζ⁷+ζ¹³−ζ²¹−ζ²³+ζ²⁹+ζ³¹−ζ³⁷−ζ³⁹	−ζ⁷−ζ¹³+ζ²¹+ζ²³−ζ²⁹−ζ³¹+ζ³⁷+ζ³⁹	ζ⁷+ζ¹³+ζ²¹−ζ²³−ζ²⁹−ζ³¹−ζ³⁷+ζ³⁹	−ζ⁷−ζ¹³−ζ²¹+ζ²³+ζ²⁹+ζ³¹+ζ³⁷−ζ³⁹	ζ⁷+ζ¹³+ζ²¹−ζ²³−ζ²⁹−ζ³¹−ζ³⁷+ζ³⁹	−ζ⁷−ζ¹³−ζ²¹+ζ²³+ζ²⁹+ζ³¹+ζ³⁷−ζ³⁹	ζ⁷+ζ¹³−ζ²¹−ζ²³+ζ²⁹+ζ³¹−ζ³⁷−ζ³⁹	−ζ⁷−ζ¹³+ζ²¹+ζ²³−ζ²⁹−ζ³¹+ζ³⁷+ζ³⁹	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₆	8	-8	0	0	4	-4	-2	$- 2 \sqrt{5}$	$2 \sqrt{5}$	2	0	0	$- 1 - \sqrt{5}$	$1 + \sqrt{5}$	$- 1 + \sqrt{5}$	$1 - \sqrt{5}$	0	0	−ζ⁷−ζ¹³+ζ²¹+ζ²³−ζ²⁹−ζ³¹+ζ³⁷+ζ³⁹	ζ⁷+ζ¹³−ζ²¹−ζ²³+ζ²⁹+ζ³¹−ζ³⁷−ζ³⁹	−ζ⁷−ζ¹³−ζ²¹+ζ²³+ζ²⁹+ζ³¹+ζ³⁷−ζ³⁹	ζ⁷+ζ¹³+ζ²¹−ζ²³−ζ²⁹−ζ³¹−ζ³⁷+ζ³⁹	−ζ⁷−ζ¹³−ζ²¹+ζ²³+ζ²⁹+ζ³¹+ζ³⁷−ζ³⁹	ζ⁷+ζ¹³+ζ²¹−ζ²³−ζ²⁹−ζ³¹−ζ³⁷+ζ³⁹	−ζ⁷−ζ¹³+ζ²¹+ζ²³−ζ²⁹−ζ³¹+ζ³⁷+ζ³⁹	ζ⁷+ζ¹³−ζ²¹−ζ²³+ζ²⁹+ζ³¹−ζ³⁷−ζ³⁹	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₇	8	-8	0	0	-4	4	8	0	0	-8	0	0	-4	4	-4	4	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
χ₃₈	8	-8	0	0	-4	4	-2	$2 \sqrt{5}$	$- 2 \sqrt{5}$	2	0	0	$1 - \sqrt{5}$	$- 1 + \sqrt{5}$	$1 + \sqrt{5}$	$- 1 - \sqrt{5}$	0	0	ζ⁷+ζ¹³−ζ²¹−ζ²³+ζ²⁹+ζ³¹−ζ³⁷−ζ³⁹	−ζ⁷−ζ¹³+ζ²¹+ζ²³−ζ²⁹−ζ³¹+ζ³⁷+ζ³⁹	−ζ⁷−ζ¹³−ζ²¹+ζ²³+ζ²⁹+ζ³¹+ζ³⁷−ζ³⁹	ζ⁷+ζ¹³+ζ²¹−ζ²³−ζ²⁹−ζ³¹−ζ³⁷+ζ³⁹	ζ⁷+ζ¹³+ζ²¹−ζ²³−ζ²⁹−ζ³¹−ζ³⁷+ζ³⁹	−ζ⁷−ζ¹³−ζ²¹+ζ²³+ζ²⁹+ζ³¹+ζ³⁷−ζ³⁹	−ζ⁷−ζ¹³+ζ²¹+ζ²³−ζ²⁹−ζ³¹+ζ³⁷+ζ³⁹	ζ⁷+ζ¹³−ζ²¹−ζ²³+ζ²⁹+ζ³¹−ζ³⁷−ζ³⁹	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₉	8	-8	0	0	-4	4	-2	$2 \sqrt{5}$	$- 2 \sqrt{5}$	2	0	0	$1 - \sqrt{5}$	$- 1 + \sqrt{5}$	$1 + \sqrt{5}$	$- 1 - \sqrt{5}$	0	0	−ζ⁷−ζ¹³+ζ²¹+ζ²³−ζ²⁹−ζ³¹+ζ³⁷+ζ³⁹	ζ⁷+ζ¹³−ζ²¹−ζ²³+ζ²⁹+ζ³¹−ζ³⁷−ζ³⁹	ζ⁷+ζ¹³+ζ²¹−ζ²³−ζ²⁹−ζ³¹−ζ³⁷+ζ³⁹	−ζ⁷−ζ¹³−ζ²¹+ζ²³+ζ²⁹+ζ³¹+ζ³⁷−ζ³⁹	−ζ⁷−ζ¹³−ζ²¹+ζ²³+ζ²⁹+ζ³¹+ζ³⁷−ζ³⁹	ζ⁷+ζ¹³+ζ²¹−ζ²³−ζ²⁹−ζ³¹−ζ³⁷+ζ³⁹	ζ⁷+ζ¹³−ζ²¹−ζ²³+ζ²⁹+ζ³¹−ζ³⁷−ζ³⁹	−ζ⁷−ζ¹³+ζ²¹+ζ²³−ζ²⁹−ζ³¹+ζ³⁷+ζ³⁹	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₀	8	-8	0	0	-4	4	-2	$- 2 \sqrt{5}$	$2 \sqrt{5}$	2	0	0	$1 + \sqrt{5}$	$- 1 - \sqrt{5}$	$1 - \sqrt{5}$	$- 1 + \sqrt{5}$	0	0	−ζ⁷−ζ¹³−ζ²¹+ζ²³+ζ²⁹+ζ³¹+ζ³⁷−ζ³⁹	ζ⁷+ζ¹³+ζ²¹−ζ²³−ζ²⁹−ζ³¹−ζ³⁷+ζ³⁹	−ζ⁷−ζ¹³+ζ²¹+ζ²³−ζ²⁹−ζ³¹+ζ³⁷+ζ³⁹	ζ⁷+ζ¹³−ζ²¹−ζ²³+ζ²⁹+ζ³¹−ζ³⁷−ζ³⁹	ζ⁷+ζ¹³−ζ²¹−ζ²³+ζ²⁹+ζ³¹−ζ³⁷−ζ³⁹	−ζ⁷−ζ¹³+ζ²¹+ζ²³−ζ²⁹−ζ³¹+ζ³⁷+ζ³⁹	ζ⁷+ζ¹³+ζ²¹−ζ²³−ζ²⁹−ζ³¹−ζ³⁷+ζ³⁹	−ζ⁷−ζ¹³−ζ²¹+ζ²³+ζ²⁹+ζ³¹+ζ³⁷−ζ³⁹	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₁	8	-8	0	0	-4	4	-2	$- 2 \sqrt{5}$	$2 \sqrt{5}$	2	0	0	$1 + \sqrt{5}$	$- 1 - \sqrt{5}$	$1 - \sqrt{5}$	$- 1 + \sqrt{5}$	0	0	ζ⁷+ζ¹³+ζ²¹−ζ²³−ζ²⁹−ζ³¹−ζ³⁷+ζ³⁹	−ζ⁷−ζ¹³−ζ²¹+ζ²³+ζ²⁹+ζ³¹+ζ³⁷−ζ³⁹	ζ⁷+ζ¹³−ζ²¹−ζ²³+ζ²⁹+ζ³¹−ζ³⁷−ζ³⁹	−ζ⁷−ζ¹³+ζ²¹+ζ²³−ζ²⁹−ζ³¹+ζ³⁷+ζ³⁹	−ζ⁷−ζ¹³+ζ²¹+ζ²³−ζ²⁹−ζ³¹+ζ³⁷+ζ³⁹	ζ⁷+ζ¹³−ζ²¹−ζ²³+ζ²⁹+ζ³¹−ζ³⁷−ζ³⁹	−ζ⁷−ζ¹³−ζ²¹+ζ²³+ζ²⁹+ζ³¹+ζ³⁷−ζ³⁹	ζ⁷+ζ¹³+ζ²¹−ζ²³−ζ²⁹−ζ³¹−ζ³⁷+ζ³⁹	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0

Character table — Group #13014566