Group #7540 — 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
size	1	1	2	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	32	32	32	32
order	1	2	2	4	4	8	8	16	16	16	16	32	32	32	32	32	32	32	32	8	16	16	32	32	32	32	64	64	64	64	64	64	64	64	64	64	64	64	64	64	64	64	2	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
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
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
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
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	$i$	$i$	$i$	$i$	$i$	$i$	$i$	$i$	$- i$	$- i$	$- i$	$- i$	$- i$	$- i$	$- i$	$- i$	1	-1	$i$	$- i$
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	$i$	$i$	$i$	$i$	$i$	$i$	$i$	$i$	$- i$	$- i$	$- i$	$- i$	$- i$	$- i$	$- i$	$- i$	-1	1	$- i$	$i$
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	$- i$	$- i$	$- i$	$- i$	$- i$	$- i$	$- i$	$- i$	$i$	$i$	$i$	$i$	$i$	$i$	$i$	$i$	1	-1	$- i$	$i$
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	$- i$	$- i$	$- i$	$- i$	$- i$	$- i$	$- i$	$- i$	$i$	$i$	$i$	$i$	$i$	$i$	$i$	$i$	-1	1	$i$	$- i$
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	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	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
χ₁₁	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
χ₁₂	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
χ₁₃	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
χ₁₄	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
χ₁₅	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
χ₁₆	2	2	2	-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	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
χ₁₇	2	2	2	-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	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
χ₁₈	2	2	2	-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	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
χ₁₉	2	2	2	-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	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
χ₂₀	2	2	2	-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	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
χ₂₁	2	2	2	-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	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
χ₂₂	2	2	2	-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	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
χ₂₃	2	2	2	-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	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
χ₂₄	2	2	-2	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	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
χ₂₅	2	2	-2	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	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
χ₂₆	2	2	-2	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	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
χ₂₇	2	2	-2	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	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
χ₂₈	2	2	-2	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	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
χ₂₉	2	2	-2	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	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
χ₃₀	2	2	-2	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	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
χ₃₁	2	2	-2	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	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
χ₃₂	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
χ₃₃	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	$i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	0	0	0	0
χ₃₄	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	$- i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	0	0	0	0
χ₃₅	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
χ₃₆	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
χ₃₇	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
χ₃₈	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
χ₃₉	4	-4	0	0	0	$2 \sqrt{2}$	$- 2 \sqrt{2}$	2ζ²−2ζ¹⁴	−2ζ²+2ζ¹⁴	2ζ⁶−2ζ¹⁰	−2ζ⁶+2ζ¹⁰	2ζ+2ζ¹⁵	−2ζ−2ζ¹⁵	2ζ⁷+2ζ⁹	−2ζ⁷−2ζ⁹	2ζ³+2ζ¹³	−2ζ³−2ζ¹³	2ζ⁵+2ζ¹¹	−2ζ⁵−2ζ¹¹	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
χ₄₀	4	-4	0	0	0	$2 \sqrt{2}$	$- 2 \sqrt{2}$	2ζ²−2ζ¹⁴	−2ζ²+2ζ¹⁴	2ζ⁶−2ζ¹⁰	−2ζ⁶+2ζ¹⁰	−2ζ−2ζ¹⁵	2ζ+2ζ¹⁵	−2ζ⁷−2ζ⁹	2ζ⁷+2ζ⁹	−2ζ³−2ζ¹³	2ζ³+2ζ¹³	−2ζ⁵−2ζ¹¹	2ζ⁵+2ζ¹¹	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
χ₄₁	4	-4	0	0	0	$2 \sqrt{2}$	$- 2 \sqrt{2}$	−2ζ²+2ζ¹⁴	2ζ²−2ζ¹⁴	−2ζ⁶+2ζ¹⁰	2ζ⁶−2ζ¹⁰	2ζ⁷+2ζ⁹	−2ζ⁷−2ζ⁹	−2ζ−2ζ¹⁵	2ζ+2ζ¹⁵	−2ζ⁵−2ζ¹¹	2ζ⁵+2ζ¹¹	2ζ³+2ζ¹³	−2ζ³−2ζ¹³	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
χ₄₂	4	-4	0	0	0	$2 \sqrt{2}$	$- 2 \sqrt{2}$	−2ζ²+2ζ¹⁴	2ζ²−2ζ¹⁴	−2ζ⁶+2ζ¹⁰	2ζ⁶−2ζ¹⁰	−2ζ⁷−2ζ⁹	2ζ⁷+2ζ⁹	2ζ+2ζ¹⁵	−2ζ−2ζ¹⁵	2ζ⁵+2ζ¹¹	−2ζ⁵−2ζ¹¹	−2ζ³−2ζ¹³	2ζ³+2ζ¹³	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
χ₄₃	4	-4	0	0	0	$- 2 \sqrt{2}$	$2 \sqrt{2}$	2ζ⁶−2ζ¹⁰	−2ζ⁶+2ζ¹⁰	−2ζ²+2ζ¹⁴	2ζ²−2ζ¹⁴	2ζ³+2ζ¹³	−2ζ³−2ζ¹³	−2ζ⁵−2ζ¹¹	2ζ⁵+2ζ¹¹	2ζ⁷+2ζ⁹	−2ζ⁷−2ζ⁹	2ζ+2ζ¹⁵	−2ζ−2ζ¹⁵	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	0	0	0	$- 2 \sqrt{2}$	$2 \sqrt{2}$	2ζ⁶−2ζ¹⁰	−2ζ⁶+2ζ¹⁰	−2ζ²+2ζ¹⁴	2ζ²−2ζ¹⁴	−2ζ³−2ζ¹³	2ζ³+2ζ¹³	2ζ⁵+2ζ¹¹	−2ζ⁵−2ζ¹¹	−2ζ⁷−2ζ⁹	2ζ⁷+2ζ⁹	−2ζ−2ζ¹⁵	2ζ+2ζ¹⁵	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	0	0	0	$- 2 \sqrt{2}$	$2 \sqrt{2}$	−2ζ⁶+2ζ¹⁰	2ζ⁶−2ζ¹⁰	2ζ²−2ζ¹⁴	−2ζ²+2ζ¹⁴	2ζ⁵+2ζ¹¹	−2ζ⁵−2ζ¹¹	2ζ³+2ζ¹³	−2ζ³−2ζ¹³	2ζ+2ζ¹⁵	−2ζ−2ζ¹⁵	−2ζ⁷−2ζ⁹	2ζ⁷+2ζ⁹	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	0	0	0	$- 2 \sqrt{2}$	$2 \sqrt{2}$	−2ζ⁶+2ζ¹⁰	2ζ⁶−2ζ¹⁰	2ζ²−2ζ¹⁴	−2ζ²+2ζ¹⁴	−2ζ⁵−2ζ¹¹	2ζ⁵+2ζ¹¹	−2ζ³−2ζ¹³	2ζ³+2ζ¹³	−2ζ−2ζ¹⁵	2ζ+2ζ¹⁵	2ζ⁷+2ζ⁹	−2ζ⁷−2ζ⁹	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 #7540