Group #13014568 — 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
size	1	1	2	4	4	4	4	4	4	4	4	4	4	4	8	8	8	8	8	8	8	8	8	8	8	8	8	8	20	20	20	20	20	20	20	20	32	32	32	32	32	80	80	160	160	160	160
order	1	2	2	4	4	4	5	8	8	8	8	10	10	10	20	20	20	20	20	20	40	40	40	40	40	40	40	40	8	8	8	8	8	8	8	8	2	10	10	10	10	2	2	4	4	4	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	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
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	$i$	$i$	$- i$	$- i$
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	$- i$	$- i$	$i$	$i$
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	$i$	$- i$	$i$	$- i$
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	$- i$	$i$	$- i$	$i$
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
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
χ₉	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	2	-2	0	0	0	0
χ₁₀	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	-2	2	0	0	0	0
χ₁₁	4	4	4	4	4	4	-1	4	4	4	4	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	0	0	0	0	0	0	0	0	4	-1	-1	-1	-1	0	0	0	0	0	0
χ₁₂	4	4	4	4	4	4	-1	4	4	4	4	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	0	0	0	0	0	0	0	0	-4	1	1	1	1	0	0	0	0	0	0
χ₁₃	4	4	4	4	4	4	-1	-4	-4	-4	-4	-1	-1	-1	-1	-1	-1	-1	-1	-1	1	1	1	1	1	1	1	1	0	0	0	0	0	0	0	0	0	$\sqrt{5}$	$\sqrt{5}$	$- \sqrt{5}$	$- \sqrt{5}$	0	0	0	0	0	0
χ₁₄	4	4	4	4	4	4	-1	-4	-4	-4	-4	-1	-1	-1	-1	-1	-1	-1	-1	-1	1	1	1	1	1	1	1	1	0	0	0	0	0	0	0	0	0	$- \sqrt{5}$	$- \sqrt{5}$	$\sqrt{5}$	$\sqrt{5}$	0	0	0	0	0	0
χ₁₅	4	4	4	4	-4	-4	4	0	0	0	0	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
χ₁₆	4	4	4	4	-4	-4	-1	0	0	0	0	-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	0	0	0	0	0	0	0	−ζ⁴+ζ¹²−ζ²⁸+ζ³⁶	ζ⁴−ζ¹²+ζ²⁸−ζ³⁶	−ζ⁴−ζ¹²+ζ²⁸+ζ³⁶	ζ⁴+ζ¹²−ζ²⁸−ζ³⁶	0	0	0	0	0	0
χ₁₇	4	4	4	4	-4	-4	-1	0	0	0	0	-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	0	0	0	0	0	0	0	ζ⁴−ζ¹²+ζ²⁸−ζ³⁶	−ζ⁴+ζ¹²−ζ²⁸+ζ³⁶	ζ⁴+ζ¹²−ζ²⁸−ζ³⁶	−ζ⁴−ζ¹²+ζ²⁸+ζ³⁶	0	0	0	0	0	0
χ₁₈	4	4	4	4	-4	-4	-1	0	0	0	0	-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	0	0	0	0	0	0	0	−ζ⁴−ζ¹²+ζ²⁸+ζ³⁶	ζ⁴+ζ¹²−ζ²⁸−ζ³⁶	ζ⁴−ζ¹²+ζ²⁸−ζ³⁶	−ζ⁴+ζ¹²−ζ²⁸+ζ³⁶	0	0	0	0	0	0
χ₁₉	4	4	4	4	-4	-4	-1	0	0	0	0	-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	0	0	0	0	0	0	0	ζ⁴+ζ¹²−ζ²⁸−ζ³⁶	−ζ⁴−ζ¹²+ζ²⁸+ζ³⁶	−ζ⁴+ζ¹²−ζ²⁸+ζ³⁶	ζ⁴−ζ¹²+ζ²⁸−ζ³⁶	0	0	0	0	0	0
χ₂₀	4	4	4	-4	0	0	4	0	0	0	0	4	4	4	0	0	0	0	-4	-4	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
χ₂₁	4	4	4	-4	0	0	4	0	0	0	0	4	4	4	0	0	0	0	-4	-4	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
χ₂₂	4	4	-4	0	0	0	4	2	2	-2	-2	4	-4	-4	0	0	0	0	0	0	2	2	-2	-2	2	2	-2	-2	0	0	0	0	$2 \sqrt{2}$	$2 \sqrt{2}$	$- 2 \sqrt{2}$	$- 2 \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0
χ₂₃	4	4	-4	0	0	0	4	2	2	-2	-2	4	-4	-4	0	0	0	0	0	0	2	2	-2	-2	2	2	-2	-2	0	0	0	0	$- 2 \sqrt{2}$	$- 2 \sqrt{2}$	$2 \sqrt{2}$	$2 \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0
χ₂₄	4	4	-4	0	0	0	4	-2	-2	2	2	4	-4	-4	0	0	0	0	0	0	-2	-2	2	2	-2	-2	2	2	$2 \sqrt{2}$	$2 \sqrt{2}$	$- 2 \sqrt{2}$	$- 2 \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₅	4	4	-4	0	0	0	4	-2	-2	2	2	4	-4	-4	0	0	0	0	0	0	-2	-2	2	2	-2	-2	2	2	$- 2 \sqrt{2}$	$- 2 \sqrt{2}$	$2 \sqrt{2}$	$2 \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₆	4	-4	0	0	2	-2	4	0	0	$2 \sqrt{2}$	$- 2 \sqrt{2}$	-4	0	0	2	2	-2	-2	0	0	0	0	$2 \sqrt{2}$	$- 2 \sqrt{2}$	0	0	$2 \sqrt{2}$	$- 2 \sqrt{2}$	$2 + \sqrt{2}$	$- 2 - \sqrt{2}$	$2 - \sqrt{2}$	$- 2 + \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0
χ₂₇	4	-4	0	0	2	-2	4	0	0	$2 \sqrt{2}$	$- 2 \sqrt{2}$	-4	0	0	2	2	-2	-2	0	0	0	0	$2 \sqrt{2}$	$- 2 \sqrt{2}$	0	0	$2 \sqrt{2}$	$- 2 \sqrt{2}$	$- 2 - \sqrt{2}$	$2 + \sqrt{2}$	$- 2 + \sqrt{2}$	$2 - \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0
χ₂₈	4	-4	0	0	2	-2	4	0	0	$- 2 \sqrt{2}$	$2 \sqrt{2}$	-4	0	0	2	2	-2	-2	0	0	0	0	$- 2 \sqrt{2}$	$2 \sqrt{2}$	0	0	$- 2 \sqrt{2}$	$2 \sqrt{2}$	$2 - \sqrt{2}$	$- 2 + \sqrt{2}$	$2 + \sqrt{2}$	$- 2 - \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0
χ₂₉	4	-4	0	0	2	-2	4	0	0	$- 2 \sqrt{2}$	$2 \sqrt{2}$	-4	0	0	2	2	-2	-2	0	0	0	0	$- 2 \sqrt{2}$	$2 \sqrt{2}$	0	0	$- 2 \sqrt{2}$	$2 \sqrt{2}$	$- 2 + \sqrt{2}$	$2 - \sqrt{2}$	$- 2 - \sqrt{2}$	$2 + \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0
χ₃₀	4	-4	0	0	-2	2	4	$2 \sqrt{2}$	$- 2 \sqrt{2}$	0	0	-4	0	0	-2	-2	2	2	0	0	$2 \sqrt{2}$	$- 2 \sqrt{2}$	0	0	$2 \sqrt{2}$	$- 2 \sqrt{2}$	0	0	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$2 - \sqrt{2}$	$- 2 + \sqrt{2}$	$- 2 - \sqrt{2}$	$2 + \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0
χ₃₁	4	-4	0	0	-2	2	4	$2 \sqrt{2}$	$- 2 \sqrt{2}$	0	0	-4	0	0	-2	-2	2	2	0	0	$2 \sqrt{2}$	$- 2 \sqrt{2}$	0	0	$2 \sqrt{2}$	$- 2 \sqrt{2}$	0	0	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- 2 + \sqrt{2}$	$2 - \sqrt{2}$	$2 + \sqrt{2}$	$- 2 - \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0
χ₃₂	4	-4	0	0	-2	2	4	$- 2 \sqrt{2}$	$2 \sqrt{2}$	0	0	-4	0	0	-2	-2	2	2	0	0	$- 2 \sqrt{2}$	$2 \sqrt{2}$	0	0	$- 2 \sqrt{2}$	$2 \sqrt{2}$	0	0	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$- 2 - \sqrt{2}$	$2 + \sqrt{2}$	$2 - \sqrt{2}$	$- 2 + \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0
χ₃₃	4	-4	0	0	-2	2	4	$- 2 \sqrt{2}$	$2 \sqrt{2}$	0	0	-4	0	0	-2	-2	2	2	0	0	$- 2 \sqrt{2}$	$2 \sqrt{2}$	0	0	$- 2 \sqrt{2}$	$2 \sqrt{2}$	0	0	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$2 + \sqrt{2}$	$- 2 - \sqrt{2}$	$- 2 + \sqrt{2}$	$2 - \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0
χ₃₄	8	8	8	-8	0	0	-2	0	0	0	0	-2	-2	-2	$2 \sqrt{5}$	$- 2 \sqrt{5}$	$2 \sqrt{5}$	$- 2 \sqrt{5}$	2	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
χ₃₅	8	8	8	-8	0	0	-2	0	0	0	0	-2	-2	-2	$- 2 \sqrt{5}$	$2 \sqrt{5}$	$- 2 \sqrt{5}$	$2 \sqrt{5}$	2	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
χ₃₆	8	8	-8	0	0	0	-2	4	4	-4	-4	-2	2	2	0	0	0	0	$2 \sqrt{5}$	$- 2 \sqrt{5}$	$- 1 + \sqrt{5}$	$- 1 + \sqrt{5}$	$1 - \sqrt{5}$	$1 - \sqrt{5}$	$- 1 - \sqrt{5}$	$- 1 - \sqrt{5}$	$1 + \sqrt{5}$	$1 + \sqrt{5}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₇	8	8	-8	0	0	0	-2	4	4	-4	-4	-2	2	2	0	0	0	0	$- 2 \sqrt{5}$	$2 \sqrt{5}$	$- 1 - \sqrt{5}$	$- 1 - \sqrt{5}$	$1 + \sqrt{5}$	$1 + \sqrt{5}$	$- 1 + \sqrt{5}$	$- 1 + \sqrt{5}$	$1 - \sqrt{5}$	$1 - \sqrt{5}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₈	8	8	-8	0	0	0	-2	-4	-4	4	4	-2	2	2	0	0	0	0	$2 \sqrt{5}$	$- 2 \sqrt{5}$	$1 - \sqrt{5}$	$1 - \sqrt{5}$	$- 1 + \sqrt{5}$	$- 1 + \sqrt{5}$	$1 + \sqrt{5}$	$1 + \sqrt{5}$	$- 1 - \sqrt{5}$	$- 1 - \sqrt{5}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₉	8	8	-8	0	0	0	-2	-4	-4	4	4	-2	2	2	0	0	0	0	$- 2 \sqrt{5}$	$2 \sqrt{5}$	$1 + \sqrt{5}$	$1 + \sqrt{5}$	$- 1 - \sqrt{5}$	$- 1 - \sqrt{5}$	$1 - \sqrt{5}$	$1 - \sqrt{5}$	$- 1 + \sqrt{5}$	$- 1 + \sqrt{5}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₀	8	-8	0	0	4	-4	-2	0	0	$4 \sqrt{2}$	$- 4 \sqrt{2}$	2	$2 \sqrt{5}$	$- 2 \sqrt{5}$	$- 1 + \sqrt{5}$	$- 1 - \sqrt{5}$	$1 - \sqrt{5}$	$1 + \sqrt{5}$	0	0	$\sqrt{10}$	$- \sqrt{10}$	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{10}$	$\sqrt{10}$	$- \sqrt{2}$	$\sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₁	8	-8	0	0	4	-4	-2	0	0	$4 \sqrt{2}$	$- 4 \sqrt{2}$	2	$- 2 \sqrt{5}$	$2 \sqrt{5}$	$- 1 - \sqrt{5}$	$- 1 + \sqrt{5}$	$1 + \sqrt{5}$	$1 - \sqrt{5}$	0	0	$- \sqrt{10}$	$\sqrt{10}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{10}$	$- \sqrt{10}$	$- \sqrt{2}$	$\sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₂	8	-8	0	0	4	-4	-2	0	0	$- 4 \sqrt{2}$	$4 \sqrt{2}$	2	$2 \sqrt{5}$	$- 2 \sqrt{5}$	$- 1 + \sqrt{5}$	$- 1 - \sqrt{5}$	$1 - \sqrt{5}$	$1 + \sqrt{5}$	0	0	$- \sqrt{10}$	$\sqrt{10}$	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{10}$	$- \sqrt{10}$	$\sqrt{2}$	$- \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₃	8	-8	0	0	4	-4	-2	0	0	$- 4 \sqrt{2}$	$4 \sqrt{2}$	2	$- 2 \sqrt{5}$	$2 \sqrt{5}$	$- 1 - \sqrt{5}$	$- 1 + \sqrt{5}$	$1 + \sqrt{5}$	$1 - \sqrt{5}$	0	0	$\sqrt{10}$	$- \sqrt{10}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{10}$	$\sqrt{10}$	$\sqrt{2}$	$- \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₄	8	-8	0	0	-4	4	-2	$4 \sqrt{2}$	$- 4 \sqrt{2}$	0	0	2	$2 \sqrt{5}$	$- 2 \sqrt{5}$	$1 - \sqrt{5}$	$1 + \sqrt{5}$	$- 1 + \sqrt{5}$	$- 1 - \sqrt{5}$	0	0	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{10}$	$- \sqrt{10}$	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{10}$	$\sqrt{10}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₅	8	-8	0	0	-4	4	-2	$4 \sqrt{2}$	$- 4 \sqrt{2}$	0	0	2	$- 2 \sqrt{5}$	$2 \sqrt{5}$	$1 + \sqrt{5}$	$1 - \sqrt{5}$	$- 1 - \sqrt{5}$	$- 1 + \sqrt{5}$	0	0	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{10}$	$\sqrt{10}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{10}$	$- \sqrt{10}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₆	8	-8	0	0	-4	4	-2	$- 4 \sqrt{2}$	$4 \sqrt{2}$	0	0	2	$2 \sqrt{5}$	$- 2 \sqrt{5}$	$1 - \sqrt{5}$	$1 + \sqrt{5}$	$- 1 + \sqrt{5}$	$- 1 - \sqrt{5}$	0	0	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{10}$	$\sqrt{10}$	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{10}$	$- \sqrt{10}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₇	8	-8	0	0	-4	4	-2	$- 4 \sqrt{2}$	$4 \sqrt{2}$	0	0	2	$- 2 \sqrt{5}$	$2 \sqrt{5}$	$1 + \sqrt{5}$	$1 - \sqrt{5}$	$- 1 - \sqrt{5}$	$- 1 + \sqrt{5}$	0	0	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{10}$	$- \sqrt{10}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{10}$	$\sqrt{10}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0

Character table — Group #13014568