Group #13103345 — 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
size	1	1	2	8	8	8	8	8	8	8	8	8	8	10	10	16	20	20	20	25	25	40	40	40	40	40	40	40	40	40	50	80	80	100	100	100	100	100	100	200
order	1	2	4	5	5	5	10	10	10	20	20	20	20	4	4	20	2	8	8	2	2	4	10	10	20	20	40	40	40	40	4	20	20	4	4	4	4	8	8	4
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
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
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
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
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
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
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
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
χ₉	2	2	2	2	2	2	2	2	2	2	2	2	2	0	0	2	0	0	0	-2	-2	0	0	0	0	0	0	0	0	0	-2	0	0	$2 i$	$- 2 i$	0	0	0	0	0
χ₁₀	2	2	2	2	2	2	2	2	2	2	2	2	2	0	0	2	0	0	0	-2	-2	0	0	0	0	0	0	0	0	0	-2	0	0	$- 2 i$	$2 i$	0	0	0	0	0
χ₁₁	2	2	-2	2	2	2	2	2	2	-2	-2	-2	-2	0	0	-2	0	0	0	-2	-2	0	0	0	0	0	0	0	0	0	2	0	0	0	0	$2 i$	$- 2 i$	0	0	0
χ₁₂	2	2	-2	2	2	2	2	2	2	-2	-2	-2	-2	0	0	-2	0	0	0	-2	-2	0	0	0	0	0	0	0	0	0	2	0	0	0	0	$- 2 i$	$2 i$	0	0	0
χ₁₃	2	2	-2	2	2	2	2	2	2	-2	-2	-2	-2	2	2	-2	-2	0	0	2	2	0	-2	-2	2	2	0	0	0	0	-2	0	0	0	0	0	0	0	0	0
χ₁₄	2	2	-2	2	2	2	2	2	2	-2	-2	-2	-2	-2	-2	-2	2	0	0	2	2	0	2	2	-2	-2	0	0	0	0	-2	0	0	0	0	0	0	0	0	0
χ₁₅	2	-2	0	2	2	2	-2	-2	-2	0	0	0	0	$2 i$	$- 2 i$	0	0	$i \sqrt{2}$	$- i \sqrt{2}$	-2	2	0	0	0	$2 i$	$- 2 i$	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	0	0	0	0	0	0	0	$\sqrt{2}$	$- \sqrt{2}$	0
χ₁₆	2	-2	0	2	2	2	-2	-2	-2	0	0	0	0	$2 i$	$- 2 i$	0	0	$- i \sqrt{2}$	$i \sqrt{2}$	-2	2	0	0	0	$2 i$	$- 2 i$	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	0	0	0	0	0	0	0	$- \sqrt{2}$	$\sqrt{2}$	0
χ₁₇	2	-2	0	2	2	2	-2	-2	-2	0	0	0	0	$- 2 i$	$2 i$	0	0	$i \sqrt{2}$	$- i \sqrt{2}$	-2	2	0	0	0	$- 2 i$	$2 i$	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	0	0	0	0	0	0	0	$- \sqrt{2}$	$\sqrt{2}$	0
χ₁₈	2	-2	0	2	2	2	-2	-2	-2	0	0	0	0	$- 2 i$	$2 i$	0	0	$- i \sqrt{2}$	$i \sqrt{2}$	-2	2	0	0	0	$- 2 i$	$2 i$	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	0	0	0	0	0	0	0	$\sqrt{2}$	$- \sqrt{2}$	0
χ₁₉	4	-4	0	4	4	4	-4	-4	-4	0	0	0	0	0	0	0	0	0	0	4	-4	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₀	8	8	8	3	-2	-2	3	-2	-2	-2	-2	3	3	0	0	-2	0	4	4	0	0	0	0	0	0	0	-1	-1	-1	-1	0	0	0	0	0	0	0	0	0	0
χ₂₁	8	8	8	3	-2	-2	3	-2	-2	-2	-2	3	3	0	0	-2	0	-4	-4	0	0	0	0	0	0	0	1	1	1	1	0	0	0	0	0	0	0	0	0	0
χ₂₂	8	8	8	-2	3	-2	-2	-2	3	-2	-2	-2	-2	0	0	3	0	0	0	0	0	4	0	0	0	0	0	0	0	0	0	-1	-1	0	0	0	0	0	0	0
χ₂₃	8	8	8	-2	3	-2	-2	-2	3	-2	-2	-2	-2	0	0	3	0	0	0	0	0	-4	0	0	0	0	0	0	0	0	0	1	1	0	0	0	0	0	0	0
χ₂₄	8	8	8	-2	-2	3	-2	3	-2	3	3	-2	-2	4	4	-2	4	0	0	0	0	0	-1	-1	-1	-1	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₅	8	8	8	-2	-2	3	-2	3	-2	3	3	-2	-2	-4	-4	-2	-4	0	0	0	0	0	1	1	1	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₆	8	8	-8	3	-2	-2	3	-2	-2	2	2	-3	-3	0	0	2	0	0	0	0	0	0	0	0	0	0	$i \sqrt{5}$	$- i \sqrt{5}$	$i \sqrt{5}$	$- i \sqrt{5}$	0	0	0	0	0	0	0	0	0	0
χ₂₇	8	8	-8	3	-2	-2	3	-2	-2	2	2	-3	-3	0	0	2	0	0	0	0	0	0	0	0	0	0	$- i \sqrt{5}$	$i \sqrt{5}$	$- i \sqrt{5}$	$i \sqrt{5}$	0	0	0	0	0	0	0	0	0	0
χ₂₈	8	8	-8	-2	3	-2	-2	-2	3	2	2	2	2	0	0	-3	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	$\sqrt{5}$	$- \sqrt{5}$	0	0	0	0	0	0	0
χ₂₉	8	8	-8	-2	3	-2	-2	-2	3	2	2	2	2	0	0	-3	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	$- \sqrt{5}$	$\sqrt{5}$	0	0	0	0	0	0	0
χ₃₀	8	8	-8	-2	-2	3	-2	3	-2	-3	-3	2	2	4	4	2	-4	0	0	0	0	0	1	1	-1	-1	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₁	8	8	-8	-2	-2	3	-2	3	-2	-3	-3	2	2	-4	-4	2	4	0	0	0	0	0	-1	-1	1	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₂	8	-8	0	3	-2	-2	-3	2	2	$2 i \sqrt{5}$	$- 2 i \sqrt{5}$	$i \sqrt{5}$	$- i \sqrt{5}$	0	0	0	0	$2 i \sqrt{2}$	$- 2 i \sqrt{2}$	0	0	0	0	0	0	0	ζ⁷+ζ²¹+ζ²³+ζ²⁹	ζ¹³+ζ³¹+ζ³⁷+ζ³⁹	−ζ⁷−ζ²¹−ζ²³−ζ²⁹	−ζ¹³−ζ³¹−ζ³⁷−ζ³⁹	0	0	0	0	0	0	0	0	0	0
χ₃₃	8	-8	0	3	-2	-2	-3	2	2	$2 i \sqrt{5}$	$- 2 i \sqrt{5}$	$i \sqrt{5}$	$- i \sqrt{5}$	0	0	0	0	$- 2 i \sqrt{2}$	$2 i \sqrt{2}$	0	0	0	0	0	0	0	−ζ⁷−ζ²¹−ζ²³−ζ²⁹	−ζ¹³−ζ³¹−ζ³⁷−ζ³⁹	ζ⁷+ζ²¹+ζ²³+ζ²⁹	ζ¹³+ζ³¹+ζ³⁷+ζ³⁹	0	0	0	0	0	0	0	0	0	0
χ₃₄	8	-8	0	3	-2	-2	-3	2	2	$- 2 i \sqrt{5}$	$2 i \sqrt{5}$	$- i \sqrt{5}$	$i \sqrt{5}$	0	0	0	0	$2 i \sqrt{2}$	$- 2 i \sqrt{2}$	0	0	0	0	0	0	0	ζ¹³+ζ³¹+ζ³⁷+ζ³⁹	ζ⁷+ζ²¹+ζ²³+ζ²⁹	−ζ¹³−ζ³¹−ζ³⁷−ζ³⁹	−ζ⁷−ζ²¹−ζ²³−ζ²⁹	0	0	0	0	0	0	0	0	0	0
χ₃₅	8	-8	0	3	-2	-2	-3	2	2	$- 2 i \sqrt{5}$	$2 i \sqrt{5}$	$- i \sqrt{5}$	$i \sqrt{5}$	0	0	0	0	$- 2 i \sqrt{2}$	$2 i \sqrt{2}$	0	0	0	0	0	0	0	−ζ¹³−ζ³¹−ζ³⁷−ζ³⁹	−ζ⁷−ζ²¹−ζ²³−ζ²⁹	ζ¹³+ζ³¹+ζ³⁷+ζ³⁹	ζ⁷+ζ²¹+ζ²³+ζ²⁹	0	0	0	0	0	0	0	0	0	0
χ₃₆	8	-8	0	-2	-2	3	2	-3	2	$i \sqrt{5}$	$- i \sqrt{5}$	$- 2 i \sqrt{5}$	$2 i \sqrt{5}$	$4 i$	$- 4 i$	0	0	0	0	0	0	0	$\sqrt{5}$	$- \sqrt{5}$	$- i$	$i$	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₇	8	-8	0	-2	-2	3	2	-3	2	$i \sqrt{5}$	$- i \sqrt{5}$	$- 2 i \sqrt{5}$	$2 i \sqrt{5}$	$- 4 i$	$4 i$	0	0	0	0	0	0	0	$- \sqrt{5}$	$\sqrt{5}$	$i$	$- i$	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₈	8	-8	0	-2	-2	3	2	-3	2	$- i \sqrt{5}$	$i \sqrt{5}$	$2 i \sqrt{5}$	$- 2 i \sqrt{5}$	$4 i$	$- 4 i$	0	0	0	0	0	0	0	$- \sqrt{5}$	$\sqrt{5}$	$- i$	$i$	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₉	8	-8	0	-2	-2	3	2	-3	2	$- i \sqrt{5}$	$i \sqrt{5}$	$2 i \sqrt{5}$	$- 2 i \sqrt{5}$	$- 4 i$	$4 i$	0	0	0	0	0	0	0	$\sqrt{5}$	$- \sqrt{5}$	$i$	$- i$	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₀	16	-16	0	-4	6	-4	4	4	-6	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 #13103345