Group #489952 — 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
size	1	1	1	1	2	2	2	2	2	2	2	2	4	4	4	4	4	4	4	8	8	8	8	8	8	8	8	8	8	8	8	8	8	8	8	8	8	16	16	16	16	16	16	16	16	16	16	16	16	32	32	32	32
order	1	2	2	2	4	4	4	4	8	8	8	8	2	4	4	4	4	8	8	2	4	4	4	4	4	4	4	8	8	16	16	16	16	16	16	16	16	4	4	4	4	4	4	8	8	16	16	16	16	2	4	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
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
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
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
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	-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	-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	-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	1	1	-1	-1	1	1
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
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
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
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
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	1	1	1	-1	1	-1	-1	1	1	-1	1	1	-1
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	1	1	1	-1	1	1	1	-1	-1	1	-1	-1	1
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	-1	-1	-1	-1	1	-1	-1	1	1	1	-1	-1	1
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	-1	-1	-1	-1	1	1	1	-1	-1	-1	1	1	-1
χ₁₇	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	0	0	-2	-2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	-2	-2	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	0	0	-2	0	0	-2	-2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	2	2	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	0	0	2	0	0	2	2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	-2	2	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	0	0	-2	0	0	2	2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	2	-2	0	0	0	0	0	0	0	0
χ₂₁	2	2	2	2	2	-2	-2	2	0	0	0	0	2	-2	2	-2	-2	0	0	2	2	-2	0	0	-2	0	0	0	0	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	0	0	0	0	0	0	0	0	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	0	0	0	0
χ₂₂	2	2	2	2	2	-2	-2	2	0	0	0	0	2	-2	2	-2	-2	0	0	2	2	-2	0	0	-2	0	0	0	0	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	0	0	0	0	0	0	0	0	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	0	0	0	0
χ₂₃	2	2	2	2	2	-2	-2	2	0	0	0	0	2	-2	2	-2	-2	0	0	-2	-2	2	0	0	2	0	0	0	0	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	0	0	0	0	0	0	0	0	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	0	0	0	0
χ₂₄	2	2	2	2	2	-2	-2	2	0	0	0	0	2	-2	2	-2	-2	0	0	-2	-2	2	0	0	2	0	0	0	0	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	0	0	0	0	0	0	0	0	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	0	0	0	0
χ₂₅	2	2	2	2	2	-2	-2	2	0	0	0	0	-2	-2	-2	2	2	0	0	2	-2	2	0	0	-2	0	0	0	0	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	0	0	0	0	0	0	0	0	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	0	0	0	0
χ₂₆	2	2	2	2	2	-2	-2	2	0	0	0	0	-2	-2	-2	2	2	0	0	2	-2	2	0	0	-2	0	0	0	0	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	0	0	0	0	0	0	0	0	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	0	0	0	0
χ₂₇	2	2	2	2	2	-2	-2	2	0	0	0	0	-2	-2	-2	2	2	0	0	-2	2	-2	0	0	2	0	0	0	0	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	0	0	0	0	0	0	0	0	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	0	0	0	0
χ₂₈	2	2	2	2	2	-2	-2	2	0	0	0	0	-2	-2	-2	2	2	0	0	-2	2	-2	0	0	2	0	0	0	0	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	0	0	0	0	0	0	0	0	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	0	0	0	0
χ₂₉	2	2	2	2	-2	2	2	-2	2	2	2	2	2	-2	-2	-2	2	-2	-2	0	0	0	2	2	0	-2	-2	2	-2	0	0	0	0	0	0	0	0	2	0	0	-2	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₀	2	2	2	2	-2	2	2	-2	2	2	2	2	2	-2	-2	-2	2	-2	-2	0	0	0	-2	-2	0	2	2	2	-2	0	0	0	0	0	0	0	0	-2	0	0	2	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₁	2	2	2	2	-2	2	2	-2	2	2	2	2	-2	-2	2	2	-2	-2	-2	0	0	0	2	2	0	2	2	-2	2	0	0	0	0	0	0	0	0	-2	0	0	-2	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₂	2	2	2	2	-2	2	2	-2	2	2	2	2	-2	-2	2	2	-2	-2	-2	0	0	0	-2	-2	0	-2	-2	-2	2	0	0	0	0	0	0	0	0	2	0	0	2	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₃	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	-2	2	0	0	0	0	0	0	0	0	0	2	-2	0	2	-2	0	0	0	0	0	0	0	0	0	0
χ₃₄	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	-2	2	0	0	0	0	0	0	0	0	0	-2	2	0	-2	2	0	0	0	0	0	0	0	0	0	0
χ₃₅	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	2	-2	0	0	0	0	0	0	0	0	0	2	-2	0	-2	2	0	0	0	0	0	0	0	0	0	0
χ₃₆	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	2	-2	0	0	0	0	0	0	0	0	0	-2	2	0	2	-2	0	0	0	0	0	0	0	0	0	0
χ₃₇	4	4	4	4	-4	-4	-4	-4	0	0	0	0	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	0	0	0	0	0	0	0	0	0
χ₃₈	4	4	4	4	-4	-4	-4	-4	0	0	0	0	-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	0	0	0	0	0	0	0	0	0
χ₃₉	4	4	-4	-4	4	0	0	-4	$2 \sqrt{2}$	$- 2 \sqrt{2}$	$2 \sqrt{2}$	$- 2 \sqrt{2}$	0	0	0	0	0	$2 \sqrt{2}$	$- 2 \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	2ζ−2ζ⁷	−2ζ+2ζ⁷	2ζ³−2ζ⁵	−2ζ³+2ζ⁵	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₀	4	4	-4	-4	4	0	0	-4	$2 \sqrt{2}$	$- 2 \sqrt{2}$	$2 \sqrt{2}$	$- 2 \sqrt{2}$	0	0	0	0	0	$2 \sqrt{2}$	$- 2 \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	−2ζ+2ζ⁷	2ζ−2ζ⁷	−2ζ³+2ζ⁵	2ζ³−2ζ⁵	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₁	4	4	-4	-4	4	0	0	-4	$- 2 \sqrt{2}$	$2 \sqrt{2}$	$- 2 \sqrt{2}$	$2 \sqrt{2}$	0	0	0	0	0	$- 2 \sqrt{2}$	$2 \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	2ζ³−2ζ⁵	−2ζ³+2ζ⁵	−2ζ+2ζ⁷	2ζ−2ζ⁷	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	0	0	-4	$- 2 \sqrt{2}$	$2 \sqrt{2}$	$- 2 \sqrt{2}$	$2 \sqrt{2}$	0	0	0	0	0	$- 2 \sqrt{2}$	$2 \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	−2ζ³+2ζ⁵	2ζ³−2ζ⁵	2ζ−2ζ⁷	−2ζ+2ζ⁷	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	0	0	4	$2 \sqrt{2}$	$- 2 \sqrt{2}$	$2 \sqrt{2}$	$- 2 \sqrt{2}$	0	0	0	0	0	$- 2 \sqrt{2}$	$2 \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	2ζ³+2ζ⁵	−2ζ³−2ζ⁵	2ζ+2ζ⁷	−2ζ−2ζ⁷	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₄	4	4	-4	-4	-4	0	0	4	$2 \sqrt{2}$	$- 2 \sqrt{2}$	$2 \sqrt{2}$	$- 2 \sqrt{2}$	0	0	0	0	0	$- 2 \sqrt{2}$	$2 \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	−2ζ³−2ζ⁵	2ζ³+2ζ⁵	−2ζ−2ζ⁷	2ζ+2ζ⁷	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₅	4	4	-4	-4	-4	0	0	4	$- 2 \sqrt{2}$	$2 \sqrt{2}$	$- 2 \sqrt{2}$	$2 \sqrt{2}$	0	0	0	0	0	$2 \sqrt{2}$	$- 2 \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	2ζ+2ζ⁷	−2ζ−2ζ⁷	−2ζ³−2ζ⁵	2ζ³+2ζ⁵	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₆	4	4	-4	-4	-4	0	0	4	$- 2 \sqrt{2}$	$2 \sqrt{2}$	$- 2 \sqrt{2}$	$2 \sqrt{2}$	0	0	0	0	0	$2 \sqrt{2}$	$- 2 \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	−2ζ−2ζ⁷	2ζ+2ζ⁷	2ζ³+2ζ⁵	−2ζ³−2ζ⁵	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₇	4	-4	-4	4	0	4	-4	0	4	4	-4	-4	0	0	0	0	0	0	0	0	0	0	$4 i$	$- 4 i$	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
χ₄₈	4	-4	-4	4	0	4	-4	0	4	4	-4	-4	0	0	0	0	0	0	0	0	0	0	$- 4 i$	$4 i$	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
χ₄₉	4	-4	-4	4	0	4	-4	0	-4	-4	4	4	0	0	0	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	0	0	0	0	0	0	0
χ₅₀	4	-4	-4	4	0	4	-4	0	-4	-4	4	4	0	0	0	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	0	0	0	0	0	0	0
χ₅₁	8	-8	8	-8	0	0	0	0	$4 \sqrt{2}$	$- 4 \sqrt{2}$	$- 4 \sqrt{2}$	$4 \sqrt{2}$	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	0	0	0	0	0	0	0	0	0	0	0	0
χ₅₂	8	-8	8	-8	0	0	0	0	$- 4 \sqrt{2}$	$4 \sqrt{2}$	$4 \sqrt{2}$	$- 4 \sqrt{2}$	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	0	0	0	0	0	0	0	0	0	0	0	0
χ₅₃	8	-8	-8	8	0	-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	0	0

Character table — Group #489952