Group #13014141 — 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	C₄₂	C₄₃	C₄₄	C₄₅	C₄₆	C₄₇	C₄₈	C₄₉	C₅₀	C₅₁	C₅₂	C₅₃	C₅₄	C₅₅	C₅₆	C₅₇	C₅₈	C₅₉	C₆₀	C₆₁	C₆₂
size	1	1	1	1	2	2	4	4	4	4	4	4	4	4	4	4	4	4	4	4	8	8	8	8	8	8	8	8	8	8	8	8	16	16	16	16	16	16	16	16	16	16	20	20	20	20	20	20	20	20	40	40	40	40	80	80	80	80	80	80	80	80
order	1	2	4	4	2	4	2	4	4	4	4	4	5	10	10	10	20	20	20	20	10	10	20	20	20	20	20	20	20	20	20	20	4	4	20	20	20	20	20	20	20	20	4	4	4	4	4	4	4	4	8	8	8	8	16	16	16	16	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	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	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	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	1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	$i$	$i$	$i$	$i$	$- i$	$- i$	$- i$	$- i$
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	1	1	1	1	1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	$- i$	$- i$	$- i$	$- i$	$i$	$i$	$i$	$i$
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	-1	-1	-1	-1	-1	1	1	1	1	1	1	1	1	-1	-1	-1	-1	$i$	$i$	$- i$	$- i$	$i$	$i$	$- i$	$- i$
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	-1	-1	-1	-1	-1	1	1	1	1	1	1	1	1	-1	-1	-1	-1	$- i$	$- i$	$i$	$i$	$- i$	$- i$	$i$	$i$
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	-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	-1	-1	-1	-1	-1	-1	-1	-1	-1	1	1	1	1	-1	-1	1	1	1	1	-1	-1
χ₉	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	-1	$i$	$i$	$i$	$i$	$- i$	$- i$	$- i$	$- i$	$i$	$i$	$- i$	$- i$	−ζ¹³−ζ²¹−ζ²⁹−ζ³⁷	ζ¹³+ζ²¹+ζ²⁹+ζ³⁷	−ζ¹³−ζ²¹−ζ²⁹−ζ³⁷	ζ¹³+ζ²¹+ζ²⁹+ζ³⁷	−ζ⁷−ζ²³−ζ³¹−ζ³⁹	ζ⁷+ζ²³+ζ³¹+ζ³⁹	−ζ⁷−ζ²³−ζ³¹−ζ³⁹	ζ⁷+ζ²³+ζ³¹+ζ³⁹
χ₁₀	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	-1	$i$	$i$	$i$	$i$	$- i$	$- i$	$- i$	$- i$	$i$	$i$	$- i$	$- i$	ζ¹³+ζ²¹+ζ²⁹+ζ³⁷	−ζ¹³−ζ²¹−ζ²⁹−ζ³⁷	ζ¹³+ζ²¹+ζ²⁹+ζ³⁷	−ζ¹³−ζ²¹−ζ²⁹−ζ³⁷	ζ⁷+ζ²³+ζ³¹+ζ³⁹	−ζ⁷−ζ²³−ζ³¹−ζ³⁹	ζ⁷+ζ²³+ζ³¹+ζ³⁹	−ζ⁷−ζ²³−ζ³¹−ζ³⁹
χ₁₁	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	-1	$- i$	$- i$	$- i$	$- i$	$i$	$i$	$i$	$i$	$- i$	$- i$	$i$	$i$	−ζ⁷−ζ²³−ζ³¹−ζ³⁹	ζ⁷+ζ²³+ζ³¹+ζ³⁹	−ζ⁷−ζ²³−ζ³¹−ζ³⁹	ζ⁷+ζ²³+ζ³¹+ζ³⁹	−ζ¹³−ζ²¹−ζ²⁹−ζ³⁷	ζ¹³+ζ²¹+ζ²⁹+ζ³⁷	−ζ¹³−ζ²¹−ζ²⁹−ζ³⁷	ζ¹³+ζ²¹+ζ²⁹+ζ³⁷
χ₁₂	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	-1	$- i$	$- i$	$- i$	$- i$	$i$	$i$	$i$	$i$	$- i$	$- i$	$i$	$i$	ζ⁷+ζ²³+ζ³¹+ζ³⁹	−ζ⁷−ζ²³−ζ³¹−ζ³⁹	ζ⁷+ζ²³+ζ³¹+ζ³⁹	−ζ⁷−ζ²³−ζ³¹−ζ³⁹	ζ¹³+ζ²¹+ζ²⁹+ζ³⁷	−ζ¹³−ζ²¹−ζ²⁹−ζ³⁷	ζ¹³+ζ²¹+ζ²⁹+ζ³⁷	−ζ¹³−ζ²¹−ζ²⁹−ζ³⁷
χ₁₃	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	1	$i$	$i$	$i$	$i$	$- i$	$- i$	$- i$	$- i$	$- i$	$- i$	$i$	$i$	−ζ⁷−ζ²³−ζ³¹−ζ³⁹	ζ⁷+ζ²³+ζ³¹+ζ³⁹	ζ⁷+ζ²³+ζ³¹+ζ³⁹	−ζ⁷−ζ²³−ζ³¹−ζ³⁹	ζ¹³+ζ²¹+ζ²⁹+ζ³⁷	−ζ¹³−ζ²¹−ζ²⁹−ζ³⁷	−ζ¹³−ζ²¹−ζ²⁹−ζ³⁷	ζ¹³+ζ²¹+ζ²⁹+ζ³⁷
χ₁₄	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	1	$i$	$i$	$i$	$i$	$- i$	$- i$	$- i$	$- i$	$- i$	$- i$	$i$	$i$	ζ⁷+ζ²³+ζ³¹+ζ³⁹	−ζ⁷−ζ²³−ζ³¹−ζ³⁹	−ζ⁷−ζ²³−ζ³¹−ζ³⁹	ζ⁷+ζ²³+ζ³¹+ζ³⁹	−ζ¹³−ζ²¹−ζ²⁹−ζ³⁷	ζ¹³+ζ²¹+ζ²⁹+ζ³⁷	ζ¹³+ζ²¹+ζ²⁹+ζ³⁷	−ζ¹³−ζ²¹−ζ²⁹−ζ³⁷
χ₁₅	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	1	$- i$	$- i$	$- i$	$- i$	$i$	$i$	$i$	$i$	$i$	$i$	$- i$	$- i$	−ζ¹³−ζ²¹−ζ²⁹−ζ³⁷	ζ¹³+ζ²¹+ζ²⁹+ζ³⁷	ζ¹³+ζ²¹+ζ²⁹+ζ³⁷	−ζ¹³−ζ²¹−ζ²⁹−ζ³⁷	ζ⁷+ζ²³+ζ³¹+ζ³⁹	−ζ⁷−ζ²³−ζ³¹−ζ³⁹	−ζ⁷−ζ²³−ζ³¹−ζ³⁹	ζ⁷+ζ²³+ζ³¹+ζ³⁹
χ₁₆	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	1	$- i$	$- i$	$- i$	$- i$	$i$	$i$	$i$	$i$	$i$	$i$	$- i$	$- i$	ζ¹³+ζ²¹+ζ²⁹+ζ³⁷	−ζ¹³−ζ²¹−ζ²⁹−ζ³⁷	−ζ¹³−ζ²¹−ζ²⁹−ζ³⁷	ζ¹³+ζ²¹+ζ²⁹+ζ³⁷	−ζ⁷−ζ²³−ζ³¹−ζ³⁹	ζ⁷+ζ²³+ζ³¹+ζ³⁹	ζ⁷+ζ²³+ζ³¹+ζ³⁹	−ζ⁷−ζ²³−ζ³¹−ζ³⁹
χ₁₇	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	-2	-2	-2	-2	-2	-2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	2	-2	2	-2	0	0	0	0	0	0	0	0
χ₁₈	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	-2	-2	-2	-2	-2	-2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	-2	2	-2	2	0	0	0	0	0	0	0	0
χ₁₉	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	-2	-2	2	2	2	2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	$2 i$	$- 2 i$	$- 2 i$	$2 i$	0	0	0	0	0	0	0	0
χ₂₀	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	-2	-2	2	2	2	2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	$- 2 i$	$2 i$	$2 i$	$- 2 i$	0	0	0	0	0	0	0	0
χ₂₁	4	4	4	4	4	4	4	4	4	4	4	4	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	4	4	-1	-1	-1	-1	-1	-1	-1	-1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₂	4	4	4	4	4	4	4	4	4	4	4	4	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-4	-4	1	1	1	1	1	1	1	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₃	4	4	4	4	4	4	4	4	-4	-4	-4	-4	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	1	1	1	1	1	1	1	1	0	0	$\sqrt{5}$	$\sqrt{5}$	$- \sqrt{5}$	$- \sqrt{5}$	$\sqrt{5}$	$\sqrt{5}$	$- \sqrt{5}$	$- \sqrt{5}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₄	4	4	4	4	4	4	4	4	-4	-4	-4	-4	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	1	1	1	1	1	1	1	1	0	0	$- \sqrt{5}$	$- \sqrt{5}$	$\sqrt{5}$	$\sqrt{5}$	$- \sqrt{5}$	$- \sqrt{5}$	$\sqrt{5}$	$\sqrt{5}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₅	4	4	4	4	4	4	-4	-4	0	0	0	0	4	4	4	4	4	4	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	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₆	4	4	4	4	4	4	-4	-4	0	0	0	0	-1	-1	-1	-1	-1	-1	-1	-1	1	1	1	1	$\sqrt{5}$	$\sqrt{5}$	$- \sqrt{5}$	$- \sqrt{5}$	$\sqrt{5}$	$\sqrt{5}$	$- \sqrt{5}$	$- \sqrt{5}$	0	0	−ζ⁴+ζ¹²−ζ²⁸+ζ³⁶	ζ⁴−ζ¹²+ζ²⁸−ζ³⁶	−ζ⁴−ζ¹²+ζ²⁸+ζ³⁶	ζ⁴+ζ¹²−ζ²⁸−ζ³⁶	−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	0	0	0	0	0	0	0	0	0	0
χ₂₇	4	4	4	4	4	4	-4	-4	0	0	0	0	-1	-1	-1	-1	-1	-1	-1	-1	1	1	1	1	$\sqrt{5}$	$\sqrt{5}$	$- \sqrt{5}$	$- \sqrt{5}$	$\sqrt{5}$	$\sqrt{5}$	$- \sqrt{5}$	$- \sqrt{5}$	0	0	ζ⁴−ζ¹²+ζ²⁸−ζ³⁶	−ζ⁴+ζ¹²−ζ²⁸+ζ³⁶	ζ⁴+ζ¹²−ζ²⁸−ζ³⁶	−ζ⁴−ζ¹²+ζ²⁸+ζ³⁶	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	0	0	0	0	0	0	0	0	0	0
χ₂₈	4	4	4	4	4	4	-4	-4	0	0	0	0	-1	-1	-1	-1	-1	-1	-1	-1	1	1	1	1	$- \sqrt{5}$	$- \sqrt{5}$	$\sqrt{5}$	$\sqrt{5}$	$- \sqrt{5}$	$- \sqrt{5}$	$\sqrt{5}$	$\sqrt{5}$	0	0	−ζ⁴−ζ¹²+ζ²⁸+ζ³⁶	ζ⁴+ζ¹²−ζ²⁸−ζ³⁶	ζ⁴−ζ¹²+ζ²⁸−ζ³⁶	−ζ⁴+ζ¹²−ζ²⁸+ζ³⁶	−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	0	0	0	0	0	0	0	0	0	0
χ₂₉	4	4	4	4	4	4	-4	-4	0	0	0	0	-1	-1	-1	-1	-1	-1	-1	-1	1	1	1	1	$- \sqrt{5}$	$- \sqrt{5}$	$\sqrt{5}$	$\sqrt{5}$	$- \sqrt{5}$	$- \sqrt{5}$	$\sqrt{5}$	$\sqrt{5}$	0	0	ζ⁴+ζ¹²−ζ²⁸−ζ³⁶	−ζ⁴−ζ¹²+ζ²⁸+ζ³⁶	−ζ⁴+ζ¹²−ζ²⁸+ζ³⁶	ζ⁴−ζ¹²+ζ²⁸−ζ³⁶	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	0	0	0	0	0	0	0	0	0	0
χ₃₀	4	4	4	4	-4	-4	0	0	0	0	0	0	4	4	-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	$2 i$	$2 i$	$- 2 i$	$- 2 i$	$2 i$	$2 i$	$- 2 i$	$- 2 i$	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₁	4	4	4	4	-4	-4	0	0	0	0	0	0	4	4	-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	$- 2 i$	$- 2 i$	$2 i$	$2 i$	$- 2 i$	$- 2 i$	$2 i$	$2 i$	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₂	4	4	-4	-4	4	-4	4	-4	0	0	0	0	4	4	4	4	-4	-4	-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	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₃	4	4	-4	-4	4	-4	4	-4	0	0	0	0	-1	-1	-1	-1	1	1	1	1	-1	-1	1	1	$\sqrt{5}$	$\sqrt{5}$	$- \sqrt{5}$	$- \sqrt{5}$	$- \sqrt{5}$	$- \sqrt{5}$	$\sqrt{5}$	$\sqrt{5}$	0	0	−ζ⁴+ζ¹²−ζ²⁸+ζ³⁶	ζ⁴−ζ¹²+ζ²⁸−ζ³⁶	−ζ⁴−ζ¹²+ζ²⁸+ζ³⁶	ζ⁴+ζ¹²−ζ²⁸−ζ³⁶	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	0	0	0	0	0	0	0	0	0	0
χ₃₄	4	4	-4	-4	4	-4	4	-4	0	0	0	0	-1	-1	-1	-1	1	1	1	1	-1	-1	1	1	$\sqrt{5}$	$\sqrt{5}$	$- \sqrt{5}$	$- \sqrt{5}$	$- \sqrt{5}$	$- \sqrt{5}$	$\sqrt{5}$	$\sqrt{5}$	0	0	ζ⁴−ζ¹²+ζ²⁸−ζ³⁶	−ζ⁴+ζ¹²−ζ²⁸+ζ³⁶	ζ⁴+ζ¹²−ζ²⁸−ζ³⁶	−ζ⁴−ζ¹²+ζ²⁸+ζ³⁶	−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	0	0	0	0	0	0	0	0	0	0
χ₃₅	4	4	-4	-4	4	-4	4	-4	0	0	0	0	-1	-1	-1	-1	1	1	1	1	-1	-1	1	1	$- \sqrt{5}$	$- \sqrt{5}$	$\sqrt{5}$	$\sqrt{5}$	$\sqrt{5}$	$\sqrt{5}$	$- \sqrt{5}$	$- \sqrt{5}$	0	0	−ζ⁴−ζ¹²+ζ²⁸+ζ³⁶	ζ⁴+ζ¹²−ζ²⁸−ζ³⁶	ζ⁴−ζ¹²+ζ²⁸−ζ³⁶	−ζ⁴+ζ¹²−ζ²⁸+ζ³⁶	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	0	0	0	0	0	0	0	0	0	0
χ₃₆	4	4	-4	-4	4	-4	4	-4	0	0	0	0	-1	-1	-1	-1	1	1	1	1	-1	-1	1	1	$- \sqrt{5}$	$- \sqrt{5}$	$\sqrt{5}$	$\sqrt{5}$	$\sqrt{5}$	$\sqrt{5}$	$- \sqrt{5}$	$- \sqrt{5}$	0	0	ζ⁴+ζ¹²−ζ²⁸−ζ³⁶	−ζ⁴−ζ¹²+ζ²⁸+ζ³⁶	−ζ⁴+ζ¹²−ζ²⁸+ζ³⁶	ζ⁴−ζ¹²+ζ²⁸−ζ³⁶	−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	0	0	0	0	0	0	0	0	0	0
χ₃₇	4	4	-4	-4	4	-4	-4	4	4	4	-4	-4	-1	-1	-1	-1	1	1	1	1	1	1	-1	-1	-1	-1	-1	-1	1	1	1	1	4	-4	-1	-1	-1	-1	1	1	1	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₈	4	4	-4	-4	4	-4	-4	4	4	4	-4	-4	-1	-1	-1	-1	1	1	1	1	1	1	-1	-1	-1	-1	-1	-1	1	1	1	1	-4	4	1	1	1	1	-1	-1	-1	-1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₉	4	4	-4	-4	4	-4	-4	4	-4	-4	4	4	-1	-1	-1	-1	1	1	1	1	1	1	-1	-1	1	1	1	1	-1	-1	-1	-1	0	0	$\sqrt{5}$	$\sqrt{5}$	$- \sqrt{5}$	$- \sqrt{5}$	$- \sqrt{5}$	$- \sqrt{5}$	$\sqrt{5}$	$\sqrt{5}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₀	4	4	-4	-4	4	-4	-4	4	-4	-4	4	4	-1	-1	-1	-1	1	1	1	1	1	1	-1	-1	1	1	1	1	-1	-1	-1	-1	0	0	$- \sqrt{5}$	$- \sqrt{5}$	$\sqrt{5}$	$\sqrt{5}$	$\sqrt{5}$	$\sqrt{5}$	$- \sqrt{5}$	$- \sqrt{5}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₁	4	4	-4	-4	-4	4	0	0	0	0	0	0	4	4	-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	2	2	-2	-2	-2	-2	2	2	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₂	4	4	-4	-4	-4	4	0	0	0	0	0	0	4	4	-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	-2	-2	2	2	2	2	-2	-2	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₃	4	-4	$4 i$	$- 4 i$	0	0	0	0	$2 i$	$- 2 i$	2	-2	4	-4	0	0	$4 i$	$- 4 i$	0	0	0	0	0	0	$2 i$	$- 2 i$	$2 i$	$- 2 i$	2	-2	2	-2	0	0	0	0	0	0	0	0	0	0	2	-2	$2 i$	$- 2 i$	$2 i$	$- 2 i$	2	-2	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₄	4	-4	$4 i$	$- 4 i$	0	0	0	0	$2 i$	$- 2 i$	2	-2	4	-4	0	0	$4 i$	$- 4 i$	0	0	0	0	0	0	$2 i$	$- 2 i$	$2 i$	$- 2 i$	2	-2	2	-2	0	0	0	0	0	0	0	0	0	0	-2	2	$- 2 i$	$2 i$	$- 2 i$	$2 i$	-2	2	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₅	4	-4	$4 i$	$- 4 i$	0	0	0	0	$- 2 i$	$2 i$	-2	2	4	-4	0	0	$4 i$	$- 4 i$	0	0	0	0	0	0	$- 2 i$	$2 i$	$- 2 i$	$2 i$	-2	2	-2	2	0	0	0	0	0	0	0	0	0	0	$2 i$	$- 2 i$	2	-2	-2	2	$- 2 i$	$2 i$	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₆	4	-4	$4 i$	$- 4 i$	0	0	0	0	$- 2 i$	$2 i$	-2	2	4	-4	0	0	$4 i$	$- 4 i$	0	0	0	0	0	0	$- 2 i$	$2 i$	$- 2 i$	$2 i$	-2	2	-2	2	0	0	0	0	0	0	0	0	0	0	$- 2 i$	$2 i$	-2	2	2	-2	$2 i$	$- 2 i$	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₇	4	-4	$- 4 i$	$4 i$	0	0	0	0	$2 i$	$- 2 i$	-2	2	4	-4	0	0	$- 4 i$	$4 i$	0	0	0	0	0	0	$2 i$	$- 2 i$	$2 i$	$- 2 i$	-2	2	-2	2	0	0	0	0	0	0	0	0	0	0	$2 i$	$- 2 i$	-2	2	2	-2	$- 2 i$	$2 i$	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₈	4	-4	$- 4 i$	$4 i$	0	0	0	0	$2 i$	$- 2 i$	-2	2	4	-4	0	0	$- 4 i$	$4 i$	0	0	0	0	0	0	$2 i$	$- 2 i$	$2 i$	$- 2 i$	-2	2	-2	2	0	0	0	0	0	0	0	0	0	0	$- 2 i$	$2 i$	2	-2	-2	2	$2 i$	$- 2 i$	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₉	4	-4	$- 4 i$	$4 i$	0	0	0	0	$- 2 i$	$2 i$	2	-2	4	-4	0	0	$- 4 i$	$4 i$	0	0	0	0	0	0	$- 2 i$	$2 i$	$- 2 i$	$2 i$	2	-2	2	-2	0	0	0	0	0	0	0	0	0	0	2	-2	$- 2 i$	$2 i$	$- 2 i$	$2 i$	2	-2	0	0	0	0	0	0	0	0	0	0	0	0
χ₅₀	4	-4	$- 4 i$	$4 i$	0	0	0	0	$- 2 i$	$2 i$	2	-2	4	-4	0	0	$- 4 i$	$4 i$	0	0	0	0	0	0	$- 2 i$	$2 i$	$- 2 i$	$2 i$	2	-2	2	-2	0	0	0	0	0	0	0	0	0	0	-2	2	$2 i$	$- 2 i$	$2 i$	$- 2 i$	-2	2	0	0	0	0	0	0	0	0	0	0	0	0
χ₅₁	8	8	8	8	-8	-8	0	0	0	0	0	0	-2	-2	2	2	-2	-2	2	2	$2 \sqrt{5}$	$- 2 \sqrt{5}$	$2 \sqrt{5}$	$- 2 \sqrt{5}$	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	0	0	0	0	0	0	0	0	0
χ₅₂	8	8	8	8	-8	-8	0	0	0	0	0	0	-2	-2	2	2	-2	-2	2	2	$- 2 \sqrt{5}$	$2 \sqrt{5}$	$- 2 \sqrt{5}$	$2 \sqrt{5}$	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	0	0	0	0	0	0	0	0	0
χ₅₃	8	8	-8	-8	-8	8	0	0	0	0	0	0	-2	-2	2	2	2	2	-2	-2	$2 \sqrt{5}$	$- 2 \sqrt{5}$	$- 2 \sqrt{5}$	$2 \sqrt{5}$	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	0	0	0	0	0	0	0	0	0
χ₅₄	8	8	-8	-8	-8	8	0	0	0	0	0	0	-2	-2	2	2	2	2	-2	-2	$- 2 \sqrt{5}$	$2 \sqrt{5}$	$2 \sqrt{5}$	$- 2 \sqrt{5}$	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	0	0	0	0	0	0	0	0	0
χ₅₅	8	-8	$8 i$	$- 8 i$	0	0	0	0	$4 i$	$- 4 i$	4	-4	-2	2	$2 \sqrt{5}$	$- 2 \sqrt{5}$	$- 2 i$	$2 i$	$2 i \sqrt{5}$	$- 2 i \sqrt{5}$	0	0	0	0	−2ζ⁶−2ζ¹⁴	2ζ⁶+2ζ¹⁴	−2ζ²²−2ζ³⁸	2ζ²²+2ζ³⁸	$- 1 - \sqrt{5}$	$1 + \sqrt{5}$	$- 1 + \sqrt{5}$	$1 - \sqrt{5}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₅₆	8	-8	$8 i$	$- 8 i$	0	0	0	0	$4 i$	$- 4 i$	4	-4	-2	2	$- 2 \sqrt{5}$	$2 \sqrt{5}$	$- 2 i$	$2 i$	$- 2 i \sqrt{5}$	$2 i \sqrt{5}$	0	0	0	0	−2ζ²²−2ζ³⁸	2ζ²²+2ζ³⁸	−2ζ⁶−2ζ¹⁴	2ζ⁶+2ζ¹⁴	$- 1 + \sqrt{5}$	$1 - \sqrt{5}$	$- 1 - \sqrt{5}$	$1 + \sqrt{5}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₅₇	8	-8	$8 i$	$- 8 i$	0	0	0	0	$- 4 i$	$4 i$	-4	4	-2	2	$2 \sqrt{5}$	$- 2 \sqrt{5}$	$- 2 i$	$2 i$	$2 i \sqrt{5}$	$- 2 i \sqrt{5}$	0	0	0	0	2ζ⁶+2ζ¹⁴	−2ζ⁶−2ζ¹⁴	2ζ²²+2ζ³⁸	−2ζ²²−2ζ³⁸	$1 + \sqrt{5}$	$- 1 - \sqrt{5}$	$1 - \sqrt{5}$	$- 1 + \sqrt{5}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₅₈	8	-8	$8 i$	$- 8 i$	0	0	0	0	$- 4 i$	$4 i$	-4	4	-2	2	$- 2 \sqrt{5}$	$2 \sqrt{5}$	$- 2 i$	$2 i$	$- 2 i \sqrt{5}$	$2 i \sqrt{5}$	0	0	0	0	2ζ²²+2ζ³⁸	−2ζ²²−2ζ³⁸	2ζ⁶+2ζ¹⁴	−2ζ⁶−2ζ¹⁴	$1 - \sqrt{5}$	$- 1 + \sqrt{5}$	$1 + \sqrt{5}$	$- 1 - \sqrt{5}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₅₉	8	-8	$- 8 i$	$8 i$	0	0	0	0	$4 i$	$- 4 i$	-4	4	-2	2	$2 \sqrt{5}$	$- 2 \sqrt{5}$	$2 i$	$- 2 i$	$- 2 i \sqrt{5}$	$2 i \sqrt{5}$	0	0	0	0	−2ζ⁶−2ζ¹⁴	2ζ⁶+2ζ¹⁴	−2ζ²²−2ζ³⁸	2ζ²²+2ζ³⁸	$1 + \sqrt{5}$	$- 1 - \sqrt{5}$	$1 - \sqrt{5}$	$- 1 + \sqrt{5}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₆₀	8	-8	$- 8 i$	$8 i$	0	0	0	0	$4 i$	$- 4 i$	-4	4	-2	2	$- 2 \sqrt{5}$	$2 \sqrt{5}$	$2 i$	$- 2 i$	$2 i \sqrt{5}$	$- 2 i \sqrt{5}$	0	0	0	0	−2ζ²²−2ζ³⁸	2ζ²²+2ζ³⁸	−2ζ⁶−2ζ¹⁴	2ζ⁶+2ζ¹⁴	$1 - \sqrt{5}$	$- 1 + \sqrt{5}$	$1 + \sqrt{5}$	$- 1 - \sqrt{5}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₆₁	8	-8	$- 8 i$	$8 i$	0	0	0	0	$- 4 i$	$4 i$	4	-4	-2	2	$2 \sqrt{5}$	$- 2 \sqrt{5}$	$2 i$	$- 2 i$	$- 2 i \sqrt{5}$	$2 i \sqrt{5}$	0	0	0	0	2ζ⁶+2ζ¹⁴	−2ζ⁶−2ζ¹⁴	2ζ²²+2ζ³⁸	−2ζ²²−2ζ³⁸	$- 1 - \sqrt{5}$	$1 + \sqrt{5}$	$- 1 + \sqrt{5}$	$1 - \sqrt{5}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₆₂	8	-8	$- 8 i$	$8 i$	0	0	0	0	$- 4 i$	$4 i$	4	-4	-2	2	$- 2 \sqrt{5}$	$2 \sqrt{5}$	$2 i$	$- 2 i$	$2 i \sqrt{5}$	$- 2 i \sqrt{5}$	0	0	0	0	2ζ²²+2ζ³⁸	−2ζ²²−2ζ³⁸	2ζ⁶+2ζ¹⁴	−2ζ⁶−2ζ¹⁴	$- 1 + \sqrt{5}$	$1 - \sqrt{5}$	$- 1 - \sqrt{5}$	$1 + \sqrt{5}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0

Character table — Group #13014141