Group #7447 — 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
size	1	1	2	2	2	2	2	2	2	2	2	2	2	4	4	4	4	4	4	4	4	4	4	8	8	8	8	8	8	8	8	16	16	16	16	32	32
order	1	2	2	4	4	8	8	8	8	16	16	16	16	4	4	8	8	16	16	16	16	16	16	32	32	32	32	32	32	32	32	16	16	16	16	2	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
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
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
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
χ₅	1	1	1	1	1	1	1	-1	-1	-1	-1	-1	-1	-1	-1	-1	1	-1	-1	1	1	1	1	$i$	$i$	$i$	$i$	$- i$	$- i$	$- i$	$- i$	$i$	$i$	$- i$	$- i$	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	$i$	$i$	$i$	$i$	$- i$	$- i$	$- i$	$- i$	$- i$	$- i$	$i$	$i$	-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	$- i$	$- i$	$- i$	$- i$	$i$	$i$	$i$	$i$	$i$	$i$	$- i$	$- i$	-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	$- i$	$- i$	$- i$	$- i$	$i$	$i$	$i$	$i$	$- i$	$- i$	$i$	$i$	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	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	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
χ₁₁	2	2	2	2	2	-2	-2	2	2	0	0	0	0	-2	-2	2	-2	0	0	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
χ₁₂	2	2	2	2	2	-2	-2	2	2	0	0	0	0	-2	-2	2	-2	0	0	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
χ₁₃	2	2	2	2	2	-2	-2	-2	-2	0	0	0	0	2	2	-2	-2	0	0	0	0	0	0	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	0	0	0	0	0	0
χ₁₄	2	2	2	2	2	-2	-2	-2	-2	0	0	0	0	2	2	-2	-2	0	0	0	0	0	0	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	0	0	0	0	0	0
χ₁₅	2	2	-2	2	-2	0	0	2	2	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	0	0	-2	0	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	ζ−ζ⁷	−ζ+ζ⁷	ζ³−ζ⁵	−ζ³+ζ⁵	ζ−ζ⁷	−ζ+ζ⁷	ζ³−ζ⁵	−ζ³+ζ⁵	0	0	0	0	0	0
χ₁₆	2	2	-2	2	-2	0	0	2	2	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	0	0	-2	0	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	−ζ+ζ⁷	ζ−ζ⁷	−ζ³+ζ⁵	ζ³−ζ⁵	−ζ+ζ⁷	ζ−ζ⁷	−ζ³+ζ⁵	ζ³−ζ⁵	0	0	0	0	0	0
χ₁₇	2	2	-2	2	-2	0	0	2	2	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	0	0	-2	0	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	ζ³−ζ⁵	−ζ³+ζ⁵	−ζ+ζ⁷	ζ−ζ⁷	ζ³−ζ⁵	−ζ³+ζ⁵	−ζ+ζ⁷	ζ−ζ⁷	0	0	0	0	0	0
χ₁₈	2	2	-2	2	-2	0	0	2	2	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	0	0	-2	0	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	−ζ³+ζ⁵	ζ³−ζ⁵	ζ−ζ⁷	−ζ+ζ⁷	−ζ³+ζ⁵	ζ³−ζ⁵	ζ−ζ⁷	−ζ+ζ⁷	0	0	0	0	0	0
χ₁₉	2	2	-2	2	-2	0	0	-2	-2	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	0	0	2	0	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	ζ+ζ⁷	−ζ−ζ⁷	−ζ³−ζ⁵	ζ³+ζ⁵	−ζ−ζ⁷	ζ+ζ⁷	ζ³+ζ⁵	−ζ³−ζ⁵	0	0	0	0	0	0
χ₂₀	2	2	-2	2	-2	0	0	-2	-2	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	0	0	2	0	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	−ζ−ζ⁷	ζ+ζ⁷	ζ³+ζ⁵	−ζ³−ζ⁵	ζ+ζ⁷	−ζ−ζ⁷	−ζ³−ζ⁵	ζ³+ζ⁵	0	0	0	0	0	0
χ₂₁	2	2	-2	2	-2	0	0	-2	-2	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	0	0	2	0	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	ζ³+ζ⁵	−ζ³−ζ⁵	ζ+ζ⁷	−ζ−ζ⁷	−ζ³−ζ⁵	ζ³+ζ⁵	−ζ−ζ⁷	ζ+ζ⁷	0	0	0	0	0	0
χ₂₂	2	2	-2	2	-2	0	0	-2	-2	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	0	0	2	0	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	−ζ³−ζ⁵	ζ³+ζ⁵	−ζ−ζ⁷	ζ+ζ⁷	ζ³+ζ⁵	−ζ³−ζ⁵	ζ+ζ⁷	−ζ−ζ⁷	0	0	0	0	0	0
χ₂₃	2	2	-2	-2	2	2	2	0	0	2	2	2	2	0	0	0	-2	-2	-2	0	0	0	0	0	0	0	0	0	0	0	0	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	0	0
χ₂₄	2	2	-2	-2	2	2	2	0	0	2	2	2	2	0	0	0	-2	-2	-2	0	0	0	0	0	0	0	0	0	0	0	0	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	0	0
χ₂₅	2	2	-2	-2	2	2	2	0	0	-2	-2	-2	-2	0	0	0	-2	2	2	0	0	0	0	0	0	0	0	0	0	0	0	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	0	0
χ₂₆	2	2	-2	-2	2	2	2	0	0	-2	-2	-2	-2	0	0	0	-2	2	2	0	0	0	0	0	0	0	0	0	0	0	0	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	0	0
χ₂₇	4	4	4	-4	-4	0	0	0	0	$2 \sqrt{2}$	$2 \sqrt{2}$	$- 2 \sqrt{2}$	$- 2 \sqrt{2}$	0	0	0	0	$- 2 \sqrt{2}$	$2 \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₈	4	4	4	-4	-4	0	0	0	0	$- 2 \sqrt{2}$	$- 2 \sqrt{2}$	$2 \sqrt{2}$	$2 \sqrt{2}$	0	0	0	0	$2 \sqrt{2}$	$- 2 \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₉	4	4	-4	-4	4	-4	-4	0	0	0	0	0	0	0	0	0	4	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₀	4	-4	0	0	0	$2 \sqrt{2}$	$- 2 \sqrt{2}$	$2 i \sqrt{2}$	$- 2 i \sqrt{2}$	2ζ+2ζ⁷	−2ζ−2ζ⁷	2ζ³+2ζ⁵	−2ζ³−2ζ⁵	$2 i$	$- 2 i$	0	0	0	0	ζ−ζ³+ζ⁵−ζ⁷	−ζ+ζ³−ζ⁵+ζ⁷	ζ+ζ³−ζ⁵−ζ⁷	−ζ−ζ³+ζ⁵+ζ⁷	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₁	4	-4	0	0	0	$2 \sqrt{2}$	$- 2 \sqrt{2}$	$2 i \sqrt{2}$	$- 2 i \sqrt{2}$	−2ζ−2ζ⁷	2ζ+2ζ⁷	−2ζ³−2ζ⁵	2ζ³+2ζ⁵	$2 i$	$- 2 i$	0	0	0	0	−ζ+ζ³−ζ⁵+ζ⁷	ζ−ζ³+ζ⁵−ζ⁷	−ζ−ζ³+ζ⁵+ζ⁷	ζ+ζ³−ζ⁵−ζ⁷	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₂	4	-4	0	0	0	$2 \sqrt{2}$	$- 2 \sqrt{2}$	$- 2 i \sqrt{2}$	$2 i \sqrt{2}$	2ζ+2ζ⁷	−2ζ−2ζ⁷	2ζ³+2ζ⁵	−2ζ³−2ζ⁵	$- 2 i$	$2 i$	0	0	0	0	−ζ+ζ³−ζ⁵+ζ⁷	ζ−ζ³+ζ⁵−ζ⁷	−ζ−ζ³+ζ⁵+ζ⁷	ζ+ζ³−ζ⁵−ζ⁷	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₃	4	-4	0	0	0	$2 \sqrt{2}$	$- 2 \sqrt{2}$	$- 2 i \sqrt{2}$	$2 i \sqrt{2}$	−2ζ−2ζ⁷	2ζ+2ζ⁷	−2ζ³−2ζ⁵	2ζ³+2ζ⁵	$- 2 i$	$2 i$	0	0	0	0	ζ−ζ³+ζ⁵−ζ⁷	−ζ+ζ³−ζ⁵+ζ⁷	ζ+ζ³−ζ⁵−ζ⁷	−ζ−ζ³+ζ⁵+ζ⁷	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₄	4	-4	0	0	0	$- 2 \sqrt{2}$	$2 \sqrt{2}$	$2 i \sqrt{2}$	$- 2 i \sqrt{2}$	2ζ³+2ζ⁵	−2ζ³−2ζ⁵	−2ζ−2ζ⁷	2ζ+2ζ⁷	$- 2 i$	$2 i$	0	0	0	0	ζ+ζ³−ζ⁵−ζ⁷	−ζ−ζ³+ζ⁵+ζ⁷	−ζ+ζ³−ζ⁵+ζ⁷	ζ−ζ³+ζ⁵−ζ⁷	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₅	4	-4	0	0	0	$- 2 \sqrt{2}$	$2 \sqrt{2}$	$2 i \sqrt{2}$	$- 2 i \sqrt{2}$	−2ζ³−2ζ⁵	2ζ³+2ζ⁵	2ζ+2ζ⁷	−2ζ−2ζ⁷	$- 2 i$	$2 i$	0	0	0	0	−ζ−ζ³+ζ⁵+ζ⁷	ζ+ζ³−ζ⁵−ζ⁷	ζ−ζ³+ζ⁵−ζ⁷	−ζ+ζ³−ζ⁵+ζ⁷	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₆	4	-4	0	0	0	$- 2 \sqrt{2}$	$2 \sqrt{2}$	$- 2 i \sqrt{2}$	$2 i \sqrt{2}$	2ζ³+2ζ⁵	−2ζ³−2ζ⁵	−2ζ−2ζ⁷	2ζ+2ζ⁷	$2 i$	$- 2 i$	0	0	0	0	−ζ−ζ³+ζ⁵+ζ⁷	ζ+ζ³−ζ⁵−ζ⁷	ζ−ζ³+ζ⁵−ζ⁷	−ζ+ζ³−ζ⁵+ζ⁷	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₇	4	-4	0	0	0	$- 2 \sqrt{2}$	$2 \sqrt{2}$	$- 2 i \sqrt{2}$	$2 i \sqrt{2}$	−2ζ³−2ζ⁵	2ζ³+2ζ⁵	2ζ+2ζ⁷	−2ζ−2ζ⁷	$2 i$	$- 2 i$	0	0	0	0	ζ+ζ³−ζ⁵−ζ⁷	−ζ−ζ³+ζ⁵+ζ⁷	−ζ+ζ³−ζ⁵+ζ⁷	ζ−ζ³+ζ⁵−ζ⁷	0	0	0	0	0	0	0	0	0	0	0	0	0	0

Character table — Group #7447