Group #13020123 — 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
size	1	1	1	1	2	2	4	4	4	4	4	4	8	8	8	8	8	8	10	10	10	10	10	10	16	16	16	16	16	16	16	16	16	16	16	20	32	32	40	40	40	40	40	40	40	40	40	40	40	40	40	40	80	80	80	80
order	1	2	2	2	4	4	4	4	5	10	10	10	4	4	20	20	20	20	2	2	4	4	4	4	2	8	20	20	20	20	20	40	40	40	40	4	10	10	2	4	4	4	4	4	8	8	8	8	8	8	8	8	2	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	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
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	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	-1	-1	-1	1	1	1	1	1	1	1	1	-1	-1	-1	-1
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	$i$	$i$	$- i$	$- i$	$i$	$- i$	$i$	$i$	$i$	$- i$	$- i$	$- i$	-1	-1	$i$	$- i$
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	$- i$	$- i$	$i$	$i$	$- i$	$i$	$- i$	$- i$	$- i$	$i$	$i$	$i$	-1	-1	$- i$	$i$
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	$i$	$i$	$- i$	$- i$	$- i$	$i$	$- i$	$- i$	$- i$	$i$	$i$	$i$	1	1	$i$	$- i$
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	$- i$	$- i$	$i$	$i$	$i$	$- i$	$i$	$i$	$i$	$- i$	$- i$	$- i$	1	1	$- i$	$i$
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	1	1	-1	-1	1	1	-1	1	1	-1	1	-1	-1	-1
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	-1	-1	1	1	-1	-1	1	-1	-1	1	1	-1	1	1
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	1	1	1	1	-1	-1	1	-1	-1	1	-1	1	-1	-1
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	-1	-1	-1	-1	1	1	-1	1	1	-1	-1	1	1	1
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	$i$	$i$	$- i$	$- i$	$- i$	$i$	$i$	$i$	$- i$	$- i$	$- i$	$i$	-1	1	$- i$	$i$
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	$- i$	$- i$	$i$	$i$	$i$	$- i$	$- i$	$- i$	$i$	$i$	$i$	$- i$	-1	1	$i$	$- i$
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	$i$	$i$	$- i$	$- i$	$i$	$- i$	$- i$	$- i$	$i$	$i$	$i$	$- i$	1	-1	$- i$	$i$
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	$- i$	$- i$	$i$	$i$	$- i$	$i$	$i$	$i$	$- i$	$- i$	$- i$	$i$	1	-1	$i$	$- i$
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	0	0	-2	2	2	-2	-2	0	0	0	0	-2	0	0	2	-2	0	0	0	0	0	0	0	0	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	0	0	-2	2	2	-2	-2	0	0	0	0	2	0	0	-2	2	0	0	0	0	0	0	0	0	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	0	0	-2	-2	-2	2	2	0	0	0	0	-2	0	0	-2	2	0	0	0	0	0	0	0	0	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	0	0	-2	-2	-2	2	2	0	0	0	0	2	0	0	2	-2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₁	2	2	2	2	-2	-2	2	-2	2	2	2	2	0	0	-2	-2	-2	-2	2	2	-2	2	-2	2	0	0	2	0	0	0	0	0	0	0	0	-2	0	0	0	0	0	0	0	0	0	0	2	-2	0	2	-2	0	0	0	0	0
χ₂₂	2	2	2	2	-2	-2	2	-2	2	2	2	2	0	0	-2	-2	-2	-2	2	2	-2	2	-2	2	0	0	2	0	0	0	0	0	0	0	0	-2	0	0	0	0	0	0	0	0	0	0	-2	2	0	-2	2	0	0	0	0	0
χ₂₃	2	2	2	2	-2	-2	2	-2	2	2	2	2	0	0	-2	-2	-2	-2	-2	-2	2	-2	2	-2	0	0	2	0	0	0	0	0	0	0	0	2	0	0	0	0	0	0	0	0	0	0	$2 i$	$- 2 i$	0	$- 2 i$	$2 i$	0	0	0	0	0
χ₂₄	2	2	2	2	-2	-2	2	-2	2	2	2	2	0	0	-2	-2	-2	-2	-2	-2	2	-2	2	-2	0	0	2	0	0	0	0	0	0	0	0	2	0	0	0	0	0	0	0	0	0	0	$- 2 i$	$2 i$	0	$2 i$	$- 2 i$	0	0	0	0	0
χ₂₅	2	2	2	2	-2	-2	-2	2	2	2	2	2	0	0	2	2	-2	-2	2	2	-2	-2	-2	-2	0	0	-2	0	0	0	0	0	0	0	0	2	0	0	0	0	0	0	0	0	$2 i$	$- 2 i$	0	0	$- 2 i$	0	0	$2 i$	0	0	0	0
χ₂₆	2	2	2	2	-2	-2	-2	2	2	2	2	2	0	0	2	2	-2	-2	2	2	-2	-2	-2	-2	0	0	-2	0	0	0	0	0	0	0	0	2	0	0	0	0	0	0	0	0	$- 2 i$	$2 i$	0	0	$2 i$	0	0	$- 2 i$	0	0	0	0
χ₂₇	2	2	2	2	-2	-2	-2	2	2	2	2	2	0	0	2	2	-2	-2	-2	-2	2	2	2	2	0	0	-2	0	0	0	0	0	0	0	0	-2	0	0	0	0	0	0	0	0	2	2	0	0	-2	0	0	-2	0	0	0	0
χ₂₈	2	2	2	2	-2	-2	-2	2	2	2	2	2	0	0	2	2	-2	-2	-2	-2	2	2	2	2	0	0	-2	0	0	0	0	0	0	0	0	-2	0	0	0	0	0	0	0	0	-2	-2	0	0	2	0	0	2	0	0	0	0
χ₂₉	4	4	4	4	4	4	4	4	-1	-1	-1	-1	4	4	-1	-1	-1	-1	0	0	0	0	0	0	4	4	-1	-1	-1	-1	-1	-1	-1	-1	-1	0	-1	-1	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	4	4	-1	-1	-1	-1	4	4	-1	-1	-1	-1	0	0	0	0	0	0	-4	-4	-1	-1	-1	-1	-1	1	1	1	1	0	1	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₁	4	4	4	4	4	4	4	4	-1	-1	-1	-1	-4	-4	-1	-1	-1	-1	0	0	0	0	0	0	4	-4	-1	1	1	1	1	1	1	1	1	0	-1	-1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₂	4	4	4	4	4	4	4	4	-1	-1	-1	-1	-4	-4	-1	-1	-1	-1	0	0	0	0	0	0	-4	4	-1	1	1	1	1	-1	-1	-1	-1	0	1	1	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	-1	-1	-1	-1	4	-4	1	1	-1	-1	0	0	0	0	0	0	0	0	1	-1	-1	1	1	$\sqrt{5}$	$\sqrt{5}$	$- \sqrt{5}$	$- \sqrt{5}$	0	$\sqrt{5}$	$- \sqrt{5}$	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	-1	-1	-1	-1	4	-4	1	1	-1	-1	0	0	0	0	0	0	0	0	1	-1	-1	1	1	$- \sqrt{5}$	$- \sqrt{5}$	$\sqrt{5}$	$\sqrt{5}$	0	$- \sqrt{5}$	$\sqrt{5}$	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	-1	-1	-1	-1	-4	4	1	1	-1	-1	0	0	0	0	0	0	0	0	1	1	1	-1	-1	$\sqrt{5}$	$\sqrt{5}$	$- \sqrt{5}$	$- \sqrt{5}$	0	$- \sqrt{5}$	$\sqrt{5}$	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	-1	-1	-1	-1	-4	4	1	1	-1	-1	0	0	0	0	0	0	0	0	1	1	1	-1	-1	$- \sqrt{5}$	$- \sqrt{5}$	$\sqrt{5}$	$\sqrt{5}$	0	$\sqrt{5}$	$- \sqrt{5}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₇	4	4	-4	-4	0	0	0	0	4	-4	4	-4	0	0	0	0	0	0	0	0	0	4	0	-4	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	0	0	0	0
χ₃₈	4	4	-4	-4	0	0	0	0	4	-4	4	-4	0	0	0	0	0	0	0	0	0	4	0	-4	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	0	0	0	0
χ₃₉	4	4	-4	-4	0	0	0	0	4	-4	4	-4	0	0	0	0	0	0	0	0	0	-4	0	4	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	0	0	0	0
χ₄₀	4	4	-4	-4	0	0	0	0	4	-4	4	-4	0	0	0	0	0	0	0	0	0	-4	0	4	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	0	0	0	0
χ₄₁	4	-4	4	-4	4	-4	0	0	4	-4	-4	4	0	0	0	0	4	-4	4	-4	4	0	-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
χ₄₂	4	-4	4	-4	4	-4	0	0	4	-4	-4	4	0	0	0	0	4	-4	-4	4	-4	0	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
χ₄₃	4	-4	4	-4	-4	4	0	0	4	-4	-4	4	0	0	0	0	-4	4	4	-4	-4	0	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
χ₄₄	4	-4	4	-4	-4	4	0	0	4	-4	-4	4	0	0	0	0	-4	4	-4	4	4	0	-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
χ₄₅	8	8	8	8	-8	-8	8	-8	-2	-2	-2	-2	0	0	2	2	2	2	0	0	0	0	0	0	0	0	-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
χ₄₆	8	8	8	8	-8	-8	-8	8	-2	-2	-2	-2	0	0	-2	-2	2	2	0	0	0	0	0	0	0	0	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
χ₄₇	8	-8	8	-8	8	-8	0	0	-2	2	2	-2	0	0	0	0	-2	2	0	0	0	0	0	0	0	0	0	0	0	$2 i \sqrt{5}$	$- 2 i \sqrt{5}$	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
χ₄₈	8	-8	8	-8	8	-8	0	0	-2	2	2	-2	0	0	0	0	-2	2	0	0	0	0	0	0	0	0	0	0	0	$- 2 i \sqrt{5}$	$2 i \sqrt{5}$	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
χ₄₉	8	-8	8	-8	-8	8	0	0	-2	2	2	-2	0	0	0	0	2	-2	0	0	0	0	0	0	0	0	0	$2 \sqrt{5}$	$- 2 \sqrt{5}$	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
χ₅₀	8	-8	8	-8	-8	8	0	0	-2	2	2	-2	0	0	0	0	2	-2	0	0	0	0	0	0	0	0	0	$- 2 \sqrt{5}$	$2 \sqrt{5}$	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
χ₅₁	8	-8	-8	8	0	0	0	0	8	8	-8	-8	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	0	0	0	0	0	0
χ₅₂	8	-8	-8	8	0	0	0	0	-2	-2	2	2	0	0	$2 \sqrt{5}$	$- 2 \sqrt{5}$	0	0	0	0	0	0	0	0	0	0	0	0	0	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	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	0	0	0	0	-2	-2	2	2	0	0	$2 \sqrt{5}$	$- 2 \sqrt{5}$	0	0	0	0	0	0	0	0	0	0	0	0	0	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	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	0	0	0	0	-2	-2	2	2	0	0	$- 2 \sqrt{5}$	$2 \sqrt{5}$	0	0	0	0	0	0	0	0	0	0	0	0	0	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	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	8	0	0	0	0	-2	-2	2	2	0	0	$- 2 \sqrt{5}$	$2 \sqrt{5}$	0	0	0	0	0	0	0	0	0	0	0	0	0	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	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₅₆	16	16	-16	-16	0	0	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	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0

Character table — Group #13020123