Group #65722 — 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
size	1	1	2	2	2	4	4	4	4	4	4	4	4	5	5	10	10	10	20	20	20	20	1	1	2	2	2	4	4	4	4	4	4	4	4	5	5	10	10	10	20	20	20	20
order	1	2	4	8	8	5	10	20	20	40	40	40	40	4	4	2	8	8	8	8	8	8	2	2	4	8	8	10	10	20	20	40	40	40	40	4	4	2	8	8	8	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
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
χ₃	1	1	1	1	1	1	1	1	1	1	1	1	1	-1	-1	-1	-1	-1	$i$	$i$	$- i$	$- i$	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	$- i$	$- i$	$i$	$i$	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	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	-1	1	-1	1
χ₇	1	1	1	-1	-1	1	1	1	1	-1	-1	-1	-1	-1	-1	-1	1	1	$i$	$- i$	$- i$	$i$	1	1	1	-1	-1	1	1	1	1	-1	-1	-1	-1	-1	-1	-1	1	1	$i$	$- i$	$- i$	$i$
χ₈	1	1	1	-1	-1	1	1	1	1	-1	-1	-1	-1	-1	-1	-1	1	1	$- i$	$i$	$i$	$- i$	1	1	1	-1	-1	1	1	1	1	-1	-1	-1	-1	-1	-1	-1	1	1	$- i$	$i$	$i$	$- i$
χ₉	2	2	-2	0	0	2	2	-2	-2	0	0	0	0	2	2	-2	0	0	0	0	0	0	2	2	-2	0	0	2	2	-2	-2	0	0	0	0	2	2	-2	0	0	0	0	0	0
χ₁₀	2	2	-2	0	0	2	2	-2	-2	0	0	0	0	-2	-2	2	0	0	0	0	0	0	2	2	-2	0	0	2	2	-2	-2	0	0	0	0	-2	-2	2	0	0	0	0	0	0
χ₁₁	2	-2	0	$i \sqrt{2}$	$- i \sqrt{2}$	2	-2	0	0	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$2 i$	$- 2 i$	0	$\sqrt{2}$	$- \sqrt{2}$	0	0	0	0	2	-2	0	$i \sqrt{2}$	$- i \sqrt{2}$	2	-2	0	0	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$2 i$	$- 2 i$	0	$\sqrt{2}$	$- \sqrt{2}$	0	0	0	0
χ₁₂	2	-2	0	$i \sqrt{2}$	$- i \sqrt{2}$	2	-2	0	0	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$- 2 i$	$2 i$	0	$- \sqrt{2}$	$\sqrt{2}$	0	0	0	0	2	-2	0	$i \sqrt{2}$	$- i \sqrt{2}$	2	-2	0	0	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$- 2 i$	$2 i$	0	$- \sqrt{2}$	$\sqrt{2}$	0	0	0	0
χ₁₃	2	-2	0	$- i \sqrt{2}$	$i \sqrt{2}$	2	-2	0	0	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$2 i$	$- 2 i$	0	$- \sqrt{2}$	$\sqrt{2}$	0	0	0	0	2	-2	0	$- i \sqrt{2}$	$i \sqrt{2}$	2	-2	0	0	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$2 i$	$- 2 i$	0	$- \sqrt{2}$	$\sqrt{2}$	0	0	0	0
χ₁₄	2	-2	0	$- i \sqrt{2}$	$i \sqrt{2}$	2	-2	0	0	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$- 2 i$	$2 i$	0	$\sqrt{2}$	$- \sqrt{2}$	0	0	0	0	2	-2	0	$- i \sqrt{2}$	$i \sqrt{2}$	2	-2	0	0	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$- 2 i$	$2 i$	0	$\sqrt{2}$	$- \sqrt{2}$	0	0	0	0
χ₁₅	4	4	4	4	4	-1	-1	-1	-1	-1	-1	-1	-1	0	0	0	0	0	0	0	0	0	4	4	4	4	4	-1	-1	-1	-1	-1	-1	-1	-1	0	0	0	0	0	0	0	0	0
χ₁₆	4	4	4	-4	-4	-1	-1	-1	-1	1	1	1	1	0	0	0	0	0	0	0	0	0	4	4	4	-4	-4	-1	-1	-1	-1	1	1	1	1	0	0	0	0	0	0	0	0	0
χ₁₇	4	4	-4	0	0	-1	-1	1	1	$i \sqrt{5}$	$- i \sqrt{5}$	$i \sqrt{5}$	$- i \sqrt{5}$	0	0	0	0	0	0	0	0	0	4	4	-4	0	0	-1	-1	1	1	$i \sqrt{5}$	$- i \sqrt{5}$	$i \sqrt{5}$	$- i \sqrt{5}$	0	0	0	0	0	0	0	0	0
χ₁₈	4	4	-4	0	0	-1	-1	1	1	$- i \sqrt{5}$	$i \sqrt{5}$	$- i \sqrt{5}$	$i \sqrt{5}$	0	0	0	0	0	0	0	0	0	4	4	-4	0	0	-1	-1	1	1	$- i \sqrt{5}$	$i \sqrt{5}$	$- i \sqrt{5}$	$i \sqrt{5}$	0	0	0	0	0	0	0	0	0
χ₁₉	4	-4	0	$2 i \sqrt{2}$	$- 2 i \sqrt{2}$	-1	1	$i \sqrt{5}$	$- i \sqrt{5}$	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	4	-4	0	$2 i \sqrt{2}$	$- 2 i \sqrt{2}$	-1	1	$i \sqrt{5}$	$- i \sqrt{5}$	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
χ₂₀	4	-4	0	$2 i \sqrt{2}$	$- 2 i \sqrt{2}$	-1	1	$- i \sqrt{5}$	$i \sqrt{5}$	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	4	-4	0	$2 i \sqrt{2}$	$- 2 i \sqrt{2}$	-1	1	$- i \sqrt{5}$	$i \sqrt{5}$	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
χ₂₁	4	-4	0	$- 2 i \sqrt{2}$	$2 i \sqrt{2}$	-1	1	$i \sqrt{5}$	$- i \sqrt{5}$	−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	4	-4	0	$- 2 i \sqrt{2}$	$2 i \sqrt{2}$	-1	1	$i \sqrt{5}$	$- i \sqrt{5}$	−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
χ₂₂	4	-4	0	$- 2 i \sqrt{2}$	$2 i \sqrt{2}$	-1	1	$- i \sqrt{5}$	$i \sqrt{5}$	−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	4	-4	0	$- 2 i \sqrt{2}$	$2 i \sqrt{2}$	-1	1	$- i \sqrt{5}$	$i \sqrt{5}$	−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
χ₂₃	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1
χ₂₄	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	1	1	1	1
χ₂₅	1	1	1	1	1	1	1	1	1	1	1	1	1	-1	-1	-1	-1	-1	$i$	$i$	$- i$	$- i$	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	1	1	1	1	1	$- i$	$- i$	$i$	$i$
χ₂₆	1	1	1	1	1	1	1	1	1	1	1	1	1	-1	-1	-1	-1	-1	$- i$	$- i$	$i$	$i$	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	1	1	1	1	1	$i$	$i$	$- i$	$- i$
χ₂₇	1	1	1	-1	-1	1	1	1	1	-1	-1	-1	-1	1	1	1	-1	-1	1	-1	1	-1	-1	-1	-1	1	1	-1	-1	-1	-1	1	1	1	1	-1	-1	-1	1	1	-1	1	-1	1
χ₂₈	1	1	1	-1	-1	1	1	1	1	-1	-1	-1	-1	1	1	1	-1	-1	-1	1	-1	1	-1	-1	-1	1	1	-1	-1	-1	-1	1	1	1	1	-1	-1	-1	1	1	1	-1	1	-1
χ₂₉	1	1	1	-1	-1	1	1	1	1	-1	-1	-1	-1	-1	-1	-1	1	1	$i$	$- i$	$- i$	$i$	-1	-1	-1	1	1	-1	-1	-1	-1	1	1	1	1	1	1	1	-1	-1	$- i$	$i$	$i$	$- i$
χ₃₀	1	1	1	-1	-1	1	1	1	1	-1	-1	-1	-1	-1	-1	-1	1	1	$- i$	$i$	$i$	$- i$	-1	-1	-1	1	1	-1	-1	-1	-1	1	1	1	1	1	1	1	-1	-1	$i$	$- i$	$- i$	$i$
χ₃₁	2	2	-2	0	0	2	2	-2	-2	0	0	0	0	2	2	-2	0	0	0	0	0	0	-2	-2	2	0	0	-2	-2	2	2	0	0	0	0	-2	-2	2	0	0	0	0	0	0
χ₃₂	2	2	-2	0	0	2	2	-2	-2	0	0	0	0	-2	-2	2	0	0	0	0	0	0	-2	-2	2	0	0	-2	-2	2	2	0	0	0	0	2	2	-2	0	0	0	0	0	0
χ₃₃	2	-2	0	$i \sqrt{2}$	$- i \sqrt{2}$	2	-2	0	0	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$2 i$	$- 2 i$	0	$\sqrt{2}$	$- \sqrt{2}$	0	0	0	0	-2	2	0	$- i \sqrt{2}$	$i \sqrt{2}$	-2	2	0	0	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$- 2 i$	$2 i$	0	$- \sqrt{2}$	$\sqrt{2}$	0	0	0	0
χ₃₄	2	-2	0	$i \sqrt{2}$	$- i \sqrt{2}$	2	-2	0	0	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$- 2 i$	$2 i$	0	$- \sqrt{2}$	$\sqrt{2}$	0	0	0	0	-2	2	0	$- i \sqrt{2}$	$i \sqrt{2}$	-2	2	0	0	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$2 i$	$- 2 i$	0	$\sqrt{2}$	$- \sqrt{2}$	0	0	0	0
χ₃₅	2	-2	0	$- i \sqrt{2}$	$i \sqrt{2}$	2	-2	0	0	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$2 i$	$- 2 i$	0	$- \sqrt{2}$	$\sqrt{2}$	0	0	0	0	-2	2	0	$i \sqrt{2}$	$- i \sqrt{2}$	-2	2	0	0	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$- 2 i$	$2 i$	0	$\sqrt{2}$	$- \sqrt{2}$	0	0	0	0
χ₃₆	2	-2	0	$- i \sqrt{2}$	$i \sqrt{2}$	2	-2	0	0	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$- 2 i$	$2 i$	0	$\sqrt{2}$	$- \sqrt{2}$	0	0	0	0	-2	2	0	$i \sqrt{2}$	$- i \sqrt{2}$	-2	2	0	0	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$2 i$	$- 2 i$	0	$- \sqrt{2}$	$\sqrt{2}$	0	0	0	0
χ₃₇	4	4	4	4	4	-1	-1	-1	-1	-1	-1	-1	-1	0	0	0	0	0	0	0	0	0	-4	-4	-4	-4	-4	1	1	1	1	1	1	1	1	0	0	0	0	0	0	0	0	0
χ₃₈	4	4	4	-4	-4	-1	-1	-1	-1	1	1	1	1	0	0	0	0	0	0	0	0	0	-4	-4	-4	4	4	1	1	1	1	-1	-1	-1	-1	0	0	0	0	0	0	0	0	0
χ₃₉	4	4	-4	0	0	-1	-1	1	1	$i \sqrt{5}$	$- i \sqrt{5}$	$i \sqrt{5}$	$- i \sqrt{5}$	0	0	0	0	0	0	0	0	0	-4	-4	4	0	0	1	1	-1	-1	$- i \sqrt{5}$	$i \sqrt{5}$	$- i \sqrt{5}$	$i \sqrt{5}$	0	0	0	0	0	0	0	0	0
χ₄₀	4	4	-4	0	0	-1	-1	1	1	$- i \sqrt{5}$	$i \sqrt{5}$	$- i \sqrt{5}$	$i \sqrt{5}$	0	0	0	0	0	0	0	0	0	-4	-4	4	0	0	1	1	-1	-1	$i \sqrt{5}$	$- i \sqrt{5}$	$i \sqrt{5}$	$- i \sqrt{5}$	0	0	0	0	0	0	0	0	0
χ₄₁	4	-4	0	$2 i \sqrt{2}$	$- 2 i \sqrt{2}$	-1	1	$i \sqrt{5}$	$- i \sqrt{5}$	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	-4	4	0	$- 2 i \sqrt{2}$	$2 i \sqrt{2}$	1	-1	$- i \sqrt{5}$	$i \sqrt{5}$	−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
χ₄₂	4	-4	0	$2 i \sqrt{2}$	$- 2 i \sqrt{2}$	-1	1	$- i \sqrt{5}$	$i \sqrt{5}$	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	-4	4	0	$- 2 i \sqrt{2}$	$2 i \sqrt{2}$	1	-1	$i \sqrt{5}$	$- i \sqrt{5}$	−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
χ₄₃	4	-4	0	$- 2 i \sqrt{2}$	$2 i \sqrt{2}$	-1	1	$i \sqrt{5}$	$- i \sqrt{5}$	−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	-4	4	0	$2 i \sqrt{2}$	$- 2 i \sqrt{2}$	1	-1	$- i \sqrt{5}$	$i \sqrt{5}$	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
χ₄₄	4	-4	0	$- 2 i \sqrt{2}$	$2 i \sqrt{2}$	-1	1	$- i \sqrt{5}$	$i \sqrt{5}$	−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	-4	4	0	$2 i \sqrt{2}$	$- 2 i \sqrt{2}$	1	-1	$i \sqrt{5}$	$- i \sqrt{5}$	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

Character table — Group #65722