Group #13686 — 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
size	1	1	1	1	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	16	16	16	16	32	32
order	1	2	2	2	4	4	4	4	8	8	8	8	16	16	16	16	16	16	16	16	4	8	8	16	16	16	16	32	32	32	32	32	32	32	32	32	32	32	32	32	32	32	32	4	4	4	4	2	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	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
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
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
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
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
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
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
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	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₁₀	2	2	2	2	2	2	2	2	-2	-2	-2	-2	0	0	0	0	0	0	0	0	2	-2	-2	0	0	0	0	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	0	0	0	0	0	0
χ₁₁	2	2	2	2	2	2	2	2	-2	-2	-2	-2	0	0	0	0	0	0	0	0	2	-2	-2	0	0	0	0	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	0	0	0	0	0	0
χ₁₂	2	2	2	2	2	2	-2	-2	0	0	0	0	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	-2	0	0	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	ζ²−ζ¹⁴	ζ²−ζ¹⁴	−ζ²+ζ¹⁴	−ζ²+ζ¹⁴	ζ⁶−ζ¹⁰	ζ⁶−ζ¹⁰	−ζ⁶+ζ¹⁰	−ζ⁶+ζ¹⁰	ζ²−ζ¹⁴	ζ²−ζ¹⁴	−ζ²+ζ¹⁴	−ζ²+ζ¹⁴	ζ⁶−ζ¹⁰	ζ⁶−ζ¹⁰	−ζ⁶+ζ¹⁰	−ζ⁶+ζ¹⁰	0	0	0	0	0	0
χ₁₃	2	2	2	2	2	2	-2	-2	0	0	0	0	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	-2	0	0	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	−ζ²+ζ¹⁴	−ζ²+ζ¹⁴	ζ²−ζ¹⁴	ζ²−ζ¹⁴	−ζ⁶+ζ¹⁰	−ζ⁶+ζ¹⁰	ζ⁶−ζ¹⁰	ζ⁶−ζ¹⁰	−ζ²+ζ¹⁴	−ζ²+ζ¹⁴	ζ²−ζ¹⁴	ζ²−ζ¹⁴	−ζ⁶+ζ¹⁰	−ζ⁶+ζ¹⁰	ζ⁶−ζ¹⁰	ζ⁶−ζ¹⁰	0	0	0	0	0	0
χ₁₄	2	2	2	2	2	2	-2	-2	0	0	0	0	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	-2	0	0	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	ζ⁶−ζ¹⁰	ζ⁶−ζ¹⁰	−ζ⁶+ζ¹⁰	−ζ⁶+ζ¹⁰	−ζ²+ζ¹⁴	−ζ²+ζ¹⁴	ζ²−ζ¹⁴	ζ²−ζ¹⁴	ζ⁶−ζ¹⁰	ζ⁶−ζ¹⁰	−ζ⁶+ζ¹⁰	−ζ⁶+ζ¹⁰	−ζ²+ζ¹⁴	−ζ²+ζ¹⁴	ζ²−ζ¹⁴	ζ²−ζ¹⁴	0	0	0	0	0	0
χ₁₅	2	2	2	2	2	2	-2	-2	0	0	0	0	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	-2	0	0	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	−ζ⁶+ζ¹⁰	−ζ⁶+ζ¹⁰	ζ⁶−ζ¹⁰	ζ⁶−ζ¹⁰	ζ²−ζ¹⁴	ζ²−ζ¹⁴	−ζ²+ζ¹⁴	−ζ²+ζ¹⁴	−ζ⁶+ζ¹⁰	−ζ⁶+ζ¹⁰	ζ⁶−ζ¹⁰	ζ⁶−ζ¹⁰	ζ²−ζ¹⁴	ζ²−ζ¹⁴	−ζ²+ζ¹⁴	−ζ²+ζ¹⁴	0	0	0	0	0	0
χ₁₆	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	0	0	0	0	0	0	0	0	0
χ₁₇	2	2	2	2	-2	-2	2	2	-2	-2	-2	-2	0	0	0	0	0	0	0	0	-2	2	2	0	0	0	0	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	0	0	0	0	0	0
χ₁₈	2	2	2	2	-2	-2	2	2	-2	-2	-2	-2	0	0	0	0	0	0	0	0	-2	2	2	0	0	0	0	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	0	0	0	0	0	0
χ₁₉	2	2	2	2	-2	-2	-2	-2	0	0	0	0	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	2	0	0	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	ζ²−ζ¹⁴	ζ²−ζ¹⁴	−ζ²+ζ¹⁴	−ζ²+ζ¹⁴	ζ⁶−ζ¹⁰	ζ⁶−ζ¹⁰	−ζ⁶+ζ¹⁰	−ζ⁶+ζ¹⁰	−ζ²+ζ¹⁴	−ζ²+ζ¹⁴	ζ²−ζ¹⁴	ζ²−ζ¹⁴	−ζ⁶+ζ¹⁰	−ζ⁶+ζ¹⁰	ζ⁶−ζ¹⁰	ζ⁶−ζ¹⁰	0	0	0	0	0	0
χ₂₀	2	2	2	2	-2	-2	-2	-2	0	0	0	0	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	2	0	0	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	−ζ²+ζ¹⁴	−ζ²+ζ¹⁴	ζ²−ζ¹⁴	ζ²−ζ¹⁴	−ζ⁶+ζ¹⁰	−ζ⁶+ζ¹⁰	ζ⁶−ζ¹⁰	ζ⁶−ζ¹⁰	ζ²−ζ¹⁴	ζ²−ζ¹⁴	−ζ²+ζ¹⁴	−ζ²+ζ¹⁴	ζ⁶−ζ¹⁰	ζ⁶−ζ¹⁰	−ζ⁶+ζ¹⁰	−ζ⁶+ζ¹⁰	0	0	0	0	0	0
χ₂₁	2	2	2	2	-2	-2	-2	-2	0	0	0	0	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	2	0	0	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	ζ⁶−ζ¹⁰	ζ⁶−ζ¹⁰	−ζ⁶+ζ¹⁰	−ζ⁶+ζ¹⁰	−ζ²+ζ¹⁴	−ζ²+ζ¹⁴	ζ²−ζ¹⁴	ζ²−ζ¹⁴	−ζ⁶+ζ¹⁰	−ζ⁶+ζ¹⁰	ζ⁶−ζ¹⁰	ζ⁶−ζ¹⁰	ζ²−ζ¹⁴	ζ²−ζ¹⁴	−ζ²+ζ¹⁴	−ζ²+ζ¹⁴	0	0	0	0	0	0
χ₂₂	2	2	2	2	-2	-2	-2	-2	0	0	0	0	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	2	0	0	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	−ζ⁶+ζ¹⁰	−ζ⁶+ζ¹⁰	ζ⁶−ζ¹⁰	ζ⁶−ζ¹⁰	ζ²−ζ¹⁴	ζ²−ζ¹⁴	−ζ²+ζ¹⁴	−ζ²+ζ¹⁴	ζ⁶−ζ¹⁰	ζ⁶−ζ¹⁰	−ζ⁶+ζ¹⁰	−ζ⁶+ζ¹⁰	−ζ²+ζ¹⁴	−ζ²+ζ¹⁴	ζ²−ζ¹⁴	ζ²−ζ¹⁴	0	0	0	0	0	0
χ₂₃	2	2	-2	-2	2	-2	0	0	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	ζ²−ζ¹⁴	−ζ²+ζ¹⁴	ζ⁶−ζ¹⁰	−ζ⁶+ζ¹⁰	ζ²−ζ¹⁴	−ζ²+ζ¹⁴	ζ⁶−ζ¹⁰	−ζ⁶+ζ¹⁰	0	$\sqrt{2}$	$- \sqrt{2}$	ζ²−ζ¹⁴	−ζ²+ζ¹⁴	ζ⁶−ζ¹⁰	−ζ⁶+ζ¹⁰	ζ+ζ¹⁵	−ζ−ζ¹⁵	ζ⁷+ζ⁹	−ζ⁷−ζ⁹	ζ³+ζ¹³	−ζ³−ζ¹³	ζ⁵+ζ¹¹	−ζ⁵−ζ¹¹	ζ+ζ¹⁵	−ζ−ζ¹⁵	ζ⁷+ζ⁹	−ζ⁷−ζ⁹	ζ³+ζ¹³	−ζ³−ζ¹³	ζ⁵+ζ¹¹	−ζ⁵−ζ¹¹	0	0	0	0	0	0
χ₂₄	2	2	-2	-2	2	-2	0	0	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	ζ²−ζ¹⁴	−ζ²+ζ¹⁴	ζ⁶−ζ¹⁰	−ζ⁶+ζ¹⁰	ζ²−ζ¹⁴	−ζ²+ζ¹⁴	ζ⁶−ζ¹⁰	−ζ⁶+ζ¹⁰	0	$\sqrt{2}$	$- \sqrt{2}$	ζ²−ζ¹⁴	−ζ²+ζ¹⁴	ζ⁶−ζ¹⁰	−ζ⁶+ζ¹⁰	−ζ−ζ¹⁵	ζ+ζ¹⁵	−ζ⁷−ζ⁹	ζ⁷+ζ⁹	−ζ³−ζ¹³	ζ³+ζ¹³	−ζ⁵−ζ¹¹	ζ⁵+ζ¹¹	−ζ−ζ¹⁵	ζ+ζ¹⁵	−ζ⁷−ζ⁹	ζ⁷+ζ⁹	−ζ³−ζ¹³	ζ³+ζ¹³	−ζ⁵−ζ¹¹	ζ⁵+ζ¹¹	0	0	0	0	0	0
χ₂₅	2	2	-2	-2	2	-2	0	0	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	−ζ²+ζ¹⁴	ζ²−ζ¹⁴	−ζ⁶+ζ¹⁰	ζ⁶−ζ¹⁰	−ζ²+ζ¹⁴	ζ²−ζ¹⁴	−ζ⁶+ζ¹⁰	ζ⁶−ζ¹⁰	0	$\sqrt{2}$	$- \sqrt{2}$	−ζ²+ζ¹⁴	ζ²−ζ¹⁴	−ζ⁶+ζ¹⁰	ζ⁶−ζ¹⁰	ζ⁷+ζ⁹	−ζ⁷−ζ⁹	−ζ−ζ¹⁵	ζ+ζ¹⁵	−ζ⁵−ζ¹¹	ζ⁵+ζ¹¹	ζ³+ζ¹³	−ζ³−ζ¹³	ζ⁷+ζ⁹	−ζ⁷−ζ⁹	−ζ−ζ¹⁵	ζ+ζ¹⁵	−ζ⁵−ζ¹¹	ζ⁵+ζ¹¹	ζ³+ζ¹³	−ζ³−ζ¹³	0	0	0	0	0	0
χ₂₆	2	2	-2	-2	2	-2	0	0	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	−ζ²+ζ¹⁴	ζ²−ζ¹⁴	−ζ⁶+ζ¹⁰	ζ⁶−ζ¹⁰	−ζ²+ζ¹⁴	ζ²−ζ¹⁴	−ζ⁶+ζ¹⁰	ζ⁶−ζ¹⁰	0	$\sqrt{2}$	$- \sqrt{2}$	−ζ²+ζ¹⁴	ζ²−ζ¹⁴	−ζ⁶+ζ¹⁰	ζ⁶−ζ¹⁰	−ζ⁷−ζ⁹	ζ⁷+ζ⁹	ζ+ζ¹⁵	−ζ−ζ¹⁵	ζ⁵+ζ¹¹	−ζ⁵−ζ¹¹	−ζ³−ζ¹³	ζ³+ζ¹³	−ζ⁷−ζ⁹	ζ⁷+ζ⁹	ζ+ζ¹⁵	−ζ−ζ¹⁵	ζ⁵+ζ¹¹	−ζ⁵−ζ¹¹	−ζ³−ζ¹³	ζ³+ζ¹³	0	0	0	0	0	0
χ₂₇	2	2	-2	-2	2	-2	0	0	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	ζ⁶−ζ¹⁰	−ζ⁶+ζ¹⁰	−ζ²+ζ¹⁴	ζ²−ζ¹⁴	ζ⁶−ζ¹⁰	−ζ⁶+ζ¹⁰	−ζ²+ζ¹⁴	ζ²−ζ¹⁴	0	$- \sqrt{2}$	$\sqrt{2}$	ζ⁶−ζ¹⁰	−ζ⁶+ζ¹⁰	−ζ²+ζ¹⁴	ζ²−ζ¹⁴	ζ³+ζ¹³	−ζ³−ζ¹³	−ζ⁵−ζ¹¹	ζ⁵+ζ¹¹	ζ⁷+ζ⁹	−ζ⁷−ζ⁹	ζ+ζ¹⁵	−ζ−ζ¹⁵	ζ³+ζ¹³	−ζ³−ζ¹³	−ζ⁵−ζ¹¹	ζ⁵+ζ¹¹	ζ⁷+ζ⁹	−ζ⁷−ζ⁹	ζ+ζ¹⁵	−ζ−ζ¹⁵	0	0	0	0	0	0
χ₂₈	2	2	-2	-2	2	-2	0	0	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	ζ⁶−ζ¹⁰	−ζ⁶+ζ¹⁰	−ζ²+ζ¹⁴	ζ²−ζ¹⁴	ζ⁶−ζ¹⁰	−ζ⁶+ζ¹⁰	−ζ²+ζ¹⁴	ζ²−ζ¹⁴	0	$- \sqrt{2}$	$\sqrt{2}$	ζ⁶−ζ¹⁰	−ζ⁶+ζ¹⁰	−ζ²+ζ¹⁴	ζ²−ζ¹⁴	−ζ³−ζ¹³	ζ³+ζ¹³	ζ⁵+ζ¹¹	−ζ⁵−ζ¹¹	−ζ⁷−ζ⁹	ζ⁷+ζ⁹	−ζ−ζ¹⁵	ζ+ζ¹⁵	−ζ³−ζ¹³	ζ³+ζ¹³	ζ⁵+ζ¹¹	−ζ⁵−ζ¹¹	−ζ⁷−ζ⁹	ζ⁷+ζ⁹	−ζ−ζ¹⁵	ζ+ζ¹⁵	0	0	0	0	0	0
χ₂₉	2	2	-2	-2	2	-2	0	0	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	−ζ⁶+ζ¹⁰	ζ⁶−ζ¹⁰	ζ²−ζ¹⁴	−ζ²+ζ¹⁴	−ζ⁶+ζ¹⁰	ζ⁶−ζ¹⁰	ζ²−ζ¹⁴	−ζ²+ζ¹⁴	0	$- \sqrt{2}$	$\sqrt{2}$	−ζ⁶+ζ¹⁰	ζ⁶−ζ¹⁰	ζ²−ζ¹⁴	−ζ²+ζ¹⁴	ζ⁵+ζ¹¹	−ζ⁵−ζ¹¹	ζ³+ζ¹³	−ζ³−ζ¹³	ζ+ζ¹⁵	−ζ−ζ¹⁵	−ζ⁷−ζ⁹	ζ⁷+ζ⁹	ζ⁵+ζ¹¹	−ζ⁵−ζ¹¹	ζ³+ζ¹³	−ζ³−ζ¹³	ζ+ζ¹⁵	−ζ−ζ¹⁵	−ζ⁷−ζ⁹	ζ⁷+ζ⁹	0	0	0	0	0	0
χ₃₀	2	2	-2	-2	2	-2	0	0	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	−ζ⁶+ζ¹⁰	ζ⁶−ζ¹⁰	ζ²−ζ¹⁴	−ζ²+ζ¹⁴	−ζ⁶+ζ¹⁰	ζ⁶−ζ¹⁰	ζ²−ζ¹⁴	−ζ²+ζ¹⁴	0	$- \sqrt{2}$	$\sqrt{2}$	−ζ⁶+ζ¹⁰	ζ⁶−ζ¹⁰	ζ²−ζ¹⁴	−ζ²+ζ¹⁴	−ζ⁵−ζ¹¹	ζ⁵+ζ¹¹	−ζ³−ζ¹³	ζ³+ζ¹³	−ζ−ζ¹⁵	ζ+ζ¹⁵	ζ⁷+ζ⁹	−ζ⁷−ζ⁹	−ζ⁵−ζ¹¹	ζ⁵+ζ¹¹	−ζ³−ζ¹³	ζ³+ζ¹³	−ζ−ζ¹⁵	ζ+ζ¹⁵	ζ⁷+ζ⁹	−ζ⁷−ζ⁹	0	0	0	0	0	0
χ₃₁	2	2	-2	-2	-2	2	0	0	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	ζ²−ζ¹⁴	−ζ²+ζ¹⁴	ζ⁶−ζ¹⁰	−ζ⁶+ζ¹⁰	ζ²−ζ¹⁴	−ζ²+ζ¹⁴	ζ⁶−ζ¹⁰	−ζ⁶+ζ¹⁰	0	$- \sqrt{2}$	$\sqrt{2}$	−ζ²+ζ¹⁴	ζ²−ζ¹⁴	−ζ⁶+ζ¹⁰	ζ⁶−ζ¹⁰	ζ+ζ¹⁵	−ζ−ζ¹⁵	ζ⁷+ζ⁹	−ζ⁷−ζ⁹	ζ³+ζ¹³	−ζ³−ζ¹³	ζ⁵+ζ¹¹	−ζ⁵−ζ¹¹	−ζ−ζ¹⁵	ζ+ζ¹⁵	−ζ⁷−ζ⁹	ζ⁷+ζ⁹	−ζ³−ζ¹³	ζ³+ζ¹³	−ζ⁵−ζ¹¹	ζ⁵+ζ¹¹	0	0	0	0	0	0
χ₃₂	2	2	-2	-2	-2	2	0	0	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	ζ²−ζ¹⁴	−ζ²+ζ¹⁴	ζ⁶−ζ¹⁰	−ζ⁶+ζ¹⁰	ζ²−ζ¹⁴	−ζ²+ζ¹⁴	ζ⁶−ζ¹⁰	−ζ⁶+ζ¹⁰	0	$- \sqrt{2}$	$\sqrt{2}$	−ζ²+ζ¹⁴	ζ²−ζ¹⁴	−ζ⁶+ζ¹⁰	ζ⁶−ζ¹⁰	−ζ−ζ¹⁵	ζ+ζ¹⁵	−ζ⁷−ζ⁹	ζ⁷+ζ⁹	−ζ³−ζ¹³	ζ³+ζ¹³	−ζ⁵−ζ¹¹	ζ⁵+ζ¹¹	ζ+ζ¹⁵	−ζ−ζ¹⁵	ζ⁷+ζ⁹	−ζ⁷−ζ⁹	ζ³+ζ¹³	−ζ³−ζ¹³	ζ⁵+ζ¹¹	−ζ⁵−ζ¹¹	0	0	0	0	0	0
χ₃₃	2	2	-2	-2	-2	2	0	0	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	−ζ²+ζ¹⁴	ζ²−ζ¹⁴	−ζ⁶+ζ¹⁰	ζ⁶−ζ¹⁰	−ζ²+ζ¹⁴	ζ²−ζ¹⁴	−ζ⁶+ζ¹⁰	ζ⁶−ζ¹⁰	0	$- \sqrt{2}$	$\sqrt{2}$	ζ²−ζ¹⁴	−ζ²+ζ¹⁴	ζ⁶−ζ¹⁰	−ζ⁶+ζ¹⁰	ζ⁷+ζ⁹	−ζ⁷−ζ⁹	−ζ−ζ¹⁵	ζ+ζ¹⁵	−ζ⁵−ζ¹¹	ζ⁵+ζ¹¹	ζ³+ζ¹³	−ζ³−ζ¹³	−ζ⁷−ζ⁹	ζ⁷+ζ⁹	ζ+ζ¹⁵	−ζ−ζ¹⁵	ζ⁵+ζ¹¹	−ζ⁵−ζ¹¹	−ζ³−ζ¹³	ζ³+ζ¹³	0	0	0	0	0	0
χ₃₄	2	2	-2	-2	-2	2	0	0	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	−ζ²+ζ¹⁴	ζ²−ζ¹⁴	−ζ⁶+ζ¹⁰	ζ⁶−ζ¹⁰	−ζ²+ζ¹⁴	ζ²−ζ¹⁴	−ζ⁶+ζ¹⁰	ζ⁶−ζ¹⁰	0	$- \sqrt{2}$	$\sqrt{2}$	ζ²−ζ¹⁴	−ζ²+ζ¹⁴	ζ⁶−ζ¹⁰	−ζ⁶+ζ¹⁰	−ζ⁷−ζ⁹	ζ⁷+ζ⁹	ζ+ζ¹⁵	−ζ−ζ¹⁵	ζ⁵+ζ¹¹	−ζ⁵−ζ¹¹	−ζ³−ζ¹³	ζ³+ζ¹³	ζ⁷+ζ⁹	−ζ⁷−ζ⁹	−ζ−ζ¹⁵	ζ+ζ¹⁵	−ζ⁵−ζ¹¹	ζ⁵+ζ¹¹	ζ³+ζ¹³	−ζ³−ζ¹³	0	0	0	0	0	0
χ₃₅	2	2	-2	-2	-2	2	0	0	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	ζ⁶−ζ¹⁰	−ζ⁶+ζ¹⁰	−ζ²+ζ¹⁴	ζ²−ζ¹⁴	ζ⁶−ζ¹⁰	−ζ⁶+ζ¹⁰	−ζ²+ζ¹⁴	ζ²−ζ¹⁴	0	$\sqrt{2}$	$- \sqrt{2}$	−ζ⁶+ζ¹⁰	ζ⁶−ζ¹⁰	ζ²−ζ¹⁴	−ζ²+ζ¹⁴	ζ³+ζ¹³	−ζ³−ζ¹³	−ζ⁵−ζ¹¹	ζ⁵+ζ¹¹	ζ⁷+ζ⁹	−ζ⁷−ζ⁹	ζ+ζ¹⁵	−ζ−ζ¹⁵	−ζ³−ζ¹³	ζ³+ζ¹³	ζ⁵+ζ¹¹	−ζ⁵−ζ¹¹	−ζ⁷−ζ⁹	ζ⁷+ζ⁹	−ζ−ζ¹⁵	ζ+ζ¹⁵	0	0	0	0	0	0
χ₃₆	2	2	-2	-2	-2	2	0	0	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	ζ⁶−ζ¹⁰	−ζ⁶+ζ¹⁰	−ζ²+ζ¹⁴	ζ²−ζ¹⁴	ζ⁶−ζ¹⁰	−ζ⁶+ζ¹⁰	−ζ²+ζ¹⁴	ζ²−ζ¹⁴	0	$\sqrt{2}$	$- \sqrt{2}$	−ζ⁶+ζ¹⁰	ζ⁶−ζ¹⁰	ζ²−ζ¹⁴	−ζ²+ζ¹⁴	−ζ³−ζ¹³	ζ³+ζ¹³	ζ⁵+ζ¹¹	−ζ⁵−ζ¹¹	−ζ⁷−ζ⁹	ζ⁷+ζ⁹	−ζ−ζ¹⁵	ζ+ζ¹⁵	ζ³+ζ¹³	−ζ³−ζ¹³	−ζ⁵−ζ¹¹	ζ⁵+ζ¹¹	ζ⁷+ζ⁹	−ζ⁷−ζ⁹	ζ+ζ¹⁵	−ζ−ζ¹⁵	0	0	0	0	0	0
χ₃₇	2	2	-2	-2	-2	2	0	0	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	−ζ⁶+ζ¹⁰	ζ⁶−ζ¹⁰	ζ²−ζ¹⁴	−ζ²+ζ¹⁴	−ζ⁶+ζ¹⁰	ζ⁶−ζ¹⁰	ζ²−ζ¹⁴	−ζ²+ζ¹⁴	0	$\sqrt{2}$	$- \sqrt{2}$	ζ⁶−ζ¹⁰	−ζ⁶+ζ¹⁰	−ζ²+ζ¹⁴	ζ²−ζ¹⁴	ζ⁵+ζ¹¹	−ζ⁵−ζ¹¹	ζ³+ζ¹³	−ζ³−ζ¹³	ζ+ζ¹⁵	−ζ−ζ¹⁵	−ζ⁷−ζ⁹	ζ⁷+ζ⁹	−ζ⁵−ζ¹¹	ζ⁵+ζ¹¹	−ζ³−ζ¹³	ζ³+ζ¹³	−ζ−ζ¹⁵	ζ+ζ¹⁵	ζ⁷+ζ⁹	−ζ⁷−ζ⁹	0	0	0	0	0	0
χ₃₈	2	2	-2	-2	-2	2	0	0	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	−ζ⁶+ζ¹⁰	ζ⁶−ζ¹⁰	ζ²−ζ¹⁴	−ζ²+ζ¹⁴	−ζ⁶+ζ¹⁰	ζ⁶−ζ¹⁰	ζ²−ζ¹⁴	−ζ²+ζ¹⁴	0	$\sqrt{2}$	$- \sqrt{2}$	ζ⁶−ζ¹⁰	−ζ⁶+ζ¹⁰	−ζ²+ζ¹⁴	ζ²−ζ¹⁴	−ζ⁵−ζ¹¹	ζ⁵+ζ¹¹	−ζ³−ζ¹³	ζ³+ζ¹³	−ζ−ζ¹⁵	ζ+ζ¹⁵	ζ⁷+ζ⁹	−ζ⁷−ζ⁹	ζ⁵+ζ¹¹	−ζ⁵−ζ¹¹	ζ³+ζ¹³	−ζ³−ζ¹³	ζ+ζ¹⁵	−ζ−ζ¹⁵	−ζ⁷−ζ⁹	ζ⁷+ζ⁹	0	0	0	0	0	0
χ₃₉	2	-2	2	-2	0	0	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	0	0	0	0	0	0	0	0	0	0	0	0	$2 i$	$- 2 i$	0	0
χ₄₀	2	-2	2	-2	0	0	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	0	0	0	0	0	0	0	0	0	0	0	0	$- 2 i$	$2 i$	0	0
χ₄₁	2	-2	2	-2	0	0	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	0	0	0	0	0	0	0	0	0	0	2	-2	0	0	0	0
χ₄₂	2	-2	2	-2	0	0	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	0	0	0	0	0	0	0	0	0	0	-2	2	0	0	0	0
χ₄₃	4	-4	4	-4	0	0	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	0	0	0	0	0	0	0	0	0	0
χ₄₄	4	-4	4	-4	0	0	-4	4	0	0	0	0	$2 \sqrt{2}$	$2 \sqrt{2}$	$- 2 \sqrt{2}$	$- 2 \sqrt{2}$	$- 2 \sqrt{2}$	$- 2 \sqrt{2}$	$2 \sqrt{2}$	$2 \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₅	4	-4	4	-4	0	0	-4	4	0	0	0	0	$- 2 \sqrt{2}$	$- 2 \sqrt{2}$	$2 \sqrt{2}$	$2 \sqrt{2}$	$2 \sqrt{2}$	$2 \sqrt{2}$	$- 2 \sqrt{2}$	$- 2 \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₆	4	-4	-4	4	0	0	0	0	$2 \sqrt{2}$	$- 2 \sqrt{2}$	$- 2 \sqrt{2}$	$2 \sqrt{2}$	2ζ²−2ζ¹⁴	−2ζ²+2ζ¹⁴	2ζ⁶−2ζ¹⁰	−2ζ⁶+2ζ¹⁰	−2ζ²+2ζ¹⁴	2ζ²−2ζ¹⁴	−2ζ⁶+2ζ¹⁰	2ζ⁶−2ζ¹⁰	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
χ₄₇	4	-4	-4	4	0	0	0	0	$2 \sqrt{2}$	$- 2 \sqrt{2}$	$- 2 \sqrt{2}$	$2 \sqrt{2}$	−2ζ²+2ζ¹⁴	2ζ²−2ζ¹⁴	−2ζ⁶+2ζ¹⁰	2ζ⁶−2ζ¹⁰	2ζ²−2ζ¹⁴	−2ζ²+2ζ¹⁴	2ζ⁶−2ζ¹⁰	−2ζ⁶+2ζ¹⁰	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	0	0	0	$- 2 \sqrt{2}$	$2 \sqrt{2}$	$2 \sqrt{2}$	$- 2 \sqrt{2}$	2ζ⁶−2ζ¹⁰	−2ζ⁶+2ζ¹⁰	−2ζ²+2ζ¹⁴	2ζ²−2ζ¹⁴	−2ζ⁶+2ζ¹⁰	2ζ⁶−2ζ¹⁰	2ζ²−2ζ¹⁴	−2ζ²+2ζ¹⁴	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	0	0	0	$- 2 \sqrt{2}$	$2 \sqrt{2}$	$2 \sqrt{2}$	$- 2 \sqrt{2}$	−2ζ⁶+2ζ¹⁰	2ζ⁶−2ζ¹⁰	2ζ²−2ζ¹⁴	−2ζ²+2ζ¹⁴	2ζ⁶−2ζ¹⁰	−2ζ⁶+2ζ¹⁰	−2ζ²+2ζ¹⁴	2ζ²−2ζ¹⁴	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 #13686