Group #64868 — 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
size	1	1	1	1	4	4	4	4	4	8	8	8	8	8	8	8	10	10	10	10	20	20	20	20	20	20	20	20	40
order	1	2	2	2	4	5	10	10	10	4	20	20	20	20	20	20	2	2	4	4	4	4	4	4	8	8	8	8	2
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
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
χ₃	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	-1	-1	-1	-1	$i$	$i$	$- i$	$- i$	$i$	$i$	$- i$	$- i$	-1
χ₄	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	-1	-1	-1	-1	$- i$	$- i$	$i$	$i$	$- i$	$- i$	$i$	$i$	-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
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
χ₇	1	1	1	1	1	1	1	1	1	-1	1	1	-1	-1	-1	-1	-1	-1	-1	-1	$i$	$i$	$- i$	$- i$	$- i$	$- i$	$i$	$i$	1
χ₈	1	1	1	1	1	1	1	1	1	-1	1	1	-1	-1	-1	-1	-1	-1	-1	-1	$- i$	$- i$	$i$	$i$	$i$	$i$	$- i$	$- i$	1
χ₉	2	2	2	2	-2	2	2	2	2	0	-2	-2	0	0	0	0	2	2	-2	-2	0	0	0	0	0	0	0	0	0
χ₁₀	2	2	2	2	-2	2	2	2	2	0	-2	-2	0	0	0	0	-2	-2	2	2	0	0	0	0	0	0	0	0	0
χ₁₁	2	2	-2	-2	0	2	2	-2	-2	0	0	0	0	0	0	0	0	0	$2 i$	$- 2 i$	$1 + i$	$- 1 - i$	$1 - i$	$- 1 + i$	0	0	0	0	0
χ₁₂	2	2	-2	-2	0	2	2	-2	-2	0	0	0	0	0	0	0	0	0	$2 i$	$- 2 i$	$- 1 - i$	$1 + i$	$- 1 + i$	$1 - i$	0	0	0	0	0
χ₁₃	2	2	-2	-2	0	2	2	-2	-2	0	0	0	0	0	0	0	0	0	$- 2 i$	$2 i$	$1 - i$	$- 1 + i$	$1 + i$	$- 1 - i$	0	0	0	0	0
χ₁₄	2	2	-2	-2	0	2	2	-2	-2	0	0	0	0	0	0	0	0	0	$- 2 i$	$2 i$	$- 1 + i$	$1 - i$	$- 1 - i$	$1 + i$	0	0	0	0	0
χ₁₅	2	-2	2	-2	0	2	-2	-2	2	0	0	0	0	0	0	0	2	-2	0	0	0	0	0	0	$i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	0
χ₁₆	2	-2	2	-2	0	2	-2	-2	2	0	0	0	0	0	0	0	2	-2	0	0	0	0	0	0	$- i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	0
χ₁₇	2	-2	2	-2	0	2	-2	-2	2	0	0	0	0	0	0	0	-2	2	0	0	0	0	0	0	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	0
χ₁₈	2	-2	2	-2	0	2	-2	-2	2	0	0	0	0	0	0	0	-2	2	0	0	0	0	0	0	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	0
χ₁₉	4	4	4	4	4	-1	-1	-1	-1	4	-1	-1	-1	-1	-1	-1	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₀	4	4	4	4	4	-1	-1	-1	-1	-4	-1	-1	1	1	1	1	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₁	4	4	4	4	-4	-1	-1	-1	-1	0	1	1	$\sqrt{5}$	$\sqrt{5}$	$- \sqrt{5}$	$- \sqrt{5}$	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₂	4	4	4	4	-4	-1	-1	-1	-1	0	1	1	$- \sqrt{5}$	$- \sqrt{5}$	$\sqrt{5}$	$\sqrt{5}$	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₃	4	-4	-4	4	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
χ₂₄	4	-4	-4	4	0	-1	1	-1	1	0	$\sqrt{5}$	$- \sqrt{5}$	−ζ⁶+ζ¹⁴−ζ²²+ζ³⁸	ζ⁶−ζ¹⁴+ζ²²−ζ³⁸	ζ⁶−ζ¹⁴−ζ²²+ζ³⁸	−ζ⁶+ζ¹⁴+ζ²²−ζ³⁸	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₅	4	-4	-4	4	0	-1	1	-1	1	0	$\sqrt{5}$	$- \sqrt{5}$	ζ⁶−ζ¹⁴+ζ²²−ζ³⁸	−ζ⁶+ζ¹⁴−ζ²²+ζ³⁸	−ζ⁶+ζ¹⁴+ζ²²−ζ³⁸	ζ⁶−ζ¹⁴−ζ²²+ζ³⁸	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₆	4	-4	-4	4	0	-1	1	-1	1	0	$- \sqrt{5}$	$\sqrt{5}$	ζ⁶−ζ¹⁴−ζ²²+ζ³⁸	−ζ⁶+ζ¹⁴+ζ²²−ζ³⁸	ζ⁶−ζ¹⁴+ζ²²−ζ³⁸	−ζ⁶+ζ¹⁴−ζ²²+ζ³⁸	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₇	4	-4	-4	4	0	-1	1	-1	1	0	$- \sqrt{5}$	$\sqrt{5}$	−ζ⁶+ζ¹⁴+ζ²²−ζ³⁸	ζ⁶−ζ¹⁴−ζ²²+ζ³⁸	−ζ⁶+ζ¹⁴−ζ²²+ζ³⁸	ζ⁶−ζ¹⁴+ζ²²−ζ³⁸	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₈	8	8	-8	-8	0	-2	-2	2	2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₉	8	-8	8	-8	0	-2	2	2	-2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0

Character table — Group #64868