Group #7232 — 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
size	1	1	1	1	2	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	16	16	16	16	16	16	16	16
order	1	2	2	2	2	2	2	2	4	4	4	4	4	4	8	8	8	8	8	8	8	8	2	4	8	8	8	8	16	16	16	16	16	16	16	16	16	16	16	16	16	16	16	16	4	4	4	4	8	8	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
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
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
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
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	$i$	$i$	$- i$	$- i$	$i$	$i$	$- i$	$- i$
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	-1	$- i$	$- i$	$i$	$i$	$- i$	$- i$	$i$	$i$
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	$i$	$i$	$- i$	$- i$	$- i$	$- i$	$i$	$i$
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	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	1	1	1	1	1	1	1	1	$- i$	$- i$	$i$	$i$	$i$	$i$	$- i$	$- i$
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	$i$	$i$	$i$	$i$	$- i$	$- i$	$- i$	$- i$	$i$	$i$	$i$	$i$	$- i$	$- i$	$- i$	$- i$	1	-1	1	-1	$i$	$- i$	$i$	$- i$
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	$i$	$i$	$i$	$i$	$- i$	$- i$	$- i$	$- i$	$i$	$i$	$i$	$i$	$- i$	$- i$	$- i$	$- i$	-1	1	-1	1	$- i$	$i$	$- i$	$i$
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	$- i$	$- i$	$- i$	$- i$	$i$	$i$	$i$	$i$	$- i$	$- i$	$- i$	$- i$	$i$	$i$	$i$	$i$	1	-1	1	-1	$- i$	$i$	$- i$	$i$
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	$- i$	$- i$	$- i$	$- i$	$i$	$i$	$i$	$i$	$- i$	$- i$	$- i$	$- i$	$i$	$i$	$i$	$i$	-1	1	-1	1	$i$	$- i$	$i$	$- i$
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	$i$	$i$	$i$	$i$	$- i$	$- i$	$- i$	$- i$	$- i$	$- i$	$- i$	$- i$	$i$	$i$	$i$	$i$	$i$	$- i$	$- i$	$i$	-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	$i$	$i$	$i$	$i$	$- i$	$- i$	$- i$	$- i$	$- i$	$- i$	$- i$	$- i$	$i$	$i$	$i$	$i$	$- i$	$i$	$i$	$- i$	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	$- i$	$- i$	$- i$	$- i$	$i$	$i$	$i$	$i$	$i$	$i$	$i$	$i$	$- i$	$- i$	$- i$	$- i$	$i$	$- i$	$- i$	$i$	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	$- i$	$- i$	$- i$	$- i$	$i$	$i$	$i$	$i$	$i$	$i$	$i$	$i$	$- i$	$- i$	$- i$	$- i$	$- i$	$i$	$i$	$- i$	-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	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
χ₁₈	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	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	0	0	0	0	0	0	0	0
χ₁₉	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	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	0	0	0	0	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	-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
χ₂₁	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	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	0	0	0	0	0	0	0	0
χ₂₂	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	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	0	0	0	0	0	0	0	0
χ₂₃	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	0	0	0	0	0	0	0	0	0	0	0
χ₂₄	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	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	0	0	0	0	0	0	0	0
χ₂₅	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	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	0	0	0	0	0	0	0	0
χ₂₆	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	0	0	0	0	0	0	0	0	0	0	0
χ₂₇	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	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	0	0	0	0	0	0	0	0
χ₂₈	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	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	0	0	0	0	0	0	0	0
χ₂₉	2	2	-2	-2	0	0	2	-2	0	$2 i$	$- 2 i$	0	$2 i$	$- 2 i$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	0	0	$\sqrt{2}$	$- \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	ζ+ζ³	−ζ−ζ³	ζ⁵−ζ⁷	−ζ⁵+ζ⁷	ζ−ζ³	−ζ+ζ³	ζ⁵+ζ⁷	−ζ⁵−ζ⁷	ζ+ζ³	−ζ−ζ³	ζ⁵−ζ⁷	−ζ⁵+ζ⁷	ζ−ζ³	−ζ+ζ³	ζ⁵+ζ⁷	−ζ⁵−ζ⁷	0	0	0	0	0	0	0	0
χ₃₀	2	2	-2	-2	0	0	2	-2	0	$2 i$	$- 2 i$	0	$2 i$	$- 2 i$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	0	0	$\sqrt{2}$	$- \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	−ζ−ζ³	ζ+ζ³	−ζ⁵+ζ⁷	ζ⁵−ζ⁷	−ζ+ζ³	ζ−ζ³	−ζ⁵−ζ⁷	ζ⁵+ζ⁷	−ζ−ζ³	ζ+ζ³	−ζ⁵+ζ⁷	ζ⁵−ζ⁷	−ζ+ζ³	ζ−ζ³	−ζ⁵−ζ⁷	ζ⁵+ζ⁷	0	0	0	0	0	0	0	0
χ₃₁	2	2	-2	-2	0	0	2	-2	0	$2 i$	$- 2 i$	0	$2 i$	$- 2 i$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	0	0	$- \sqrt{2}$	$\sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	ζ⁵−ζ⁷	−ζ⁵+ζ⁷	−ζ−ζ³	ζ+ζ³	ζ⁵+ζ⁷	−ζ⁵−ζ⁷	−ζ+ζ³	ζ−ζ³	ζ⁵−ζ⁷	−ζ⁵+ζ⁷	−ζ−ζ³	ζ+ζ³	ζ⁵+ζ⁷	−ζ⁵−ζ⁷	−ζ+ζ³	ζ−ζ³	0	0	0	0	0	0	0	0
χ₃₂	2	2	-2	-2	0	0	2	-2	0	$2 i$	$- 2 i$	0	$2 i$	$- 2 i$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	0	0	$- \sqrt{2}$	$\sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	−ζ⁵+ζ⁷	ζ⁵−ζ⁷	ζ+ζ³	−ζ−ζ³	−ζ⁵−ζ⁷	ζ⁵+ζ⁷	ζ−ζ³	−ζ+ζ³	−ζ⁵+ζ⁷	ζ⁵−ζ⁷	ζ+ζ³	−ζ−ζ³	−ζ⁵−ζ⁷	ζ⁵+ζ⁷	ζ−ζ³	−ζ+ζ³	0	0	0	0	0	0	0	0
χ₃₃	2	2	-2	-2	0	0	2	-2	0	$- 2 i$	$2 i$	0	$- 2 i$	$2 i$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	0	0	$\sqrt{2}$	$- \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	ζ⁵+ζ⁷	−ζ⁵−ζ⁷	−ζ+ζ³	ζ−ζ³	−ζ⁵+ζ⁷	ζ⁵−ζ⁷	ζ+ζ³	−ζ−ζ³	ζ⁵+ζ⁷	−ζ⁵−ζ⁷	−ζ+ζ³	ζ−ζ³	−ζ⁵+ζ⁷	ζ⁵−ζ⁷	ζ+ζ³	−ζ−ζ³	0	0	0	0	0	0	0	0
χ₃₄	2	2	-2	-2	0	0	2	-2	0	$- 2 i$	$2 i$	0	$- 2 i$	$2 i$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	0	0	$\sqrt{2}$	$- \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	−ζ⁵−ζ⁷	ζ⁵+ζ⁷	ζ−ζ³	−ζ+ζ³	ζ⁵−ζ⁷	−ζ⁵+ζ⁷	−ζ−ζ³	ζ+ζ³	−ζ⁵−ζ⁷	ζ⁵+ζ⁷	ζ−ζ³	−ζ+ζ³	ζ⁵−ζ⁷	−ζ⁵+ζ⁷	−ζ−ζ³	ζ+ζ³	0	0	0	0	0	0	0	0
χ₃₅	2	2	-2	-2	0	0	2	-2	0	$- 2 i$	$2 i$	0	$- 2 i$	$2 i$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	0	0	$- \sqrt{2}$	$\sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	ζ−ζ³	−ζ+ζ³	ζ⁵+ζ⁷	−ζ⁵−ζ⁷	−ζ−ζ³	ζ+ζ³	−ζ⁵+ζ⁷	ζ⁵−ζ⁷	ζ−ζ³	−ζ+ζ³	ζ⁵+ζ⁷	−ζ⁵−ζ⁷	−ζ−ζ³	ζ+ζ³	−ζ⁵+ζ⁷	ζ⁵−ζ⁷	0	0	0	0	0	0	0	0
χ₃₆	2	2	-2	-2	0	0	2	-2	0	$- 2 i$	$2 i$	0	$- 2 i$	$2 i$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	0	0	$- \sqrt{2}$	$\sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	−ζ+ζ³	ζ−ζ³	−ζ⁵−ζ⁷	ζ⁵+ζ⁷	ζ+ζ³	−ζ−ζ³	ζ⁵−ζ⁷	−ζ⁵+ζ⁷	−ζ+ζ³	ζ−ζ³	−ζ⁵−ζ⁷	ζ⁵+ζ⁷	ζ+ζ³	−ζ−ζ³	ζ⁵−ζ⁷	−ζ⁵+ζ⁷	0	0	0	0	0	0	0	0
χ₃₇	2	2	-2	-2	0	0	-2	2	0	$2 i$	$- 2 i$	0	$- 2 i$	$2 i$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	0	0	$- \sqrt{2}$	$\sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	ζ+ζ³	−ζ−ζ³	ζ⁵−ζ⁷	−ζ⁵+ζ⁷	ζ−ζ³	−ζ+ζ³	ζ⁵+ζ⁷	−ζ⁵−ζ⁷	−ζ−ζ³	ζ+ζ³	−ζ⁵+ζ⁷	ζ⁵−ζ⁷	−ζ+ζ³	ζ−ζ³	−ζ⁵−ζ⁷	ζ⁵+ζ⁷	0	0	0	0	0	0	0	0
χ₃₈	2	2	-2	-2	0	0	-2	2	0	$2 i$	$- 2 i$	0	$- 2 i$	$2 i$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	0	0	$- \sqrt{2}$	$\sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	−ζ−ζ³	ζ+ζ³	−ζ⁵+ζ⁷	ζ⁵−ζ⁷	−ζ+ζ³	ζ−ζ³	−ζ⁵−ζ⁷	ζ⁵+ζ⁷	ζ+ζ³	−ζ−ζ³	ζ⁵−ζ⁷	−ζ⁵+ζ⁷	ζ−ζ³	−ζ+ζ³	ζ⁵+ζ⁷	−ζ⁵−ζ⁷	0	0	0	0	0	0	0	0
χ₃₉	2	2	-2	-2	0	0	-2	2	0	$2 i$	$- 2 i$	0	$- 2 i$	$2 i$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	0	0	$\sqrt{2}$	$- \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	ζ⁵−ζ⁷	−ζ⁵+ζ⁷	−ζ−ζ³	ζ+ζ³	ζ⁵+ζ⁷	−ζ⁵−ζ⁷	−ζ+ζ³	ζ−ζ³	−ζ⁵+ζ⁷	ζ⁵−ζ⁷	ζ+ζ³	−ζ−ζ³	−ζ⁵−ζ⁷	ζ⁵+ζ⁷	ζ−ζ³	−ζ+ζ³	0	0	0	0	0	0	0	0
χ₄₀	2	2	-2	-2	0	0	-2	2	0	$2 i$	$- 2 i$	0	$- 2 i$	$2 i$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	0	0	$\sqrt{2}$	$- \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	−ζ⁵+ζ⁷	ζ⁵−ζ⁷	ζ+ζ³	−ζ−ζ³	−ζ⁵−ζ⁷	ζ⁵+ζ⁷	ζ−ζ³	−ζ+ζ³	ζ⁵−ζ⁷	−ζ⁵+ζ⁷	−ζ−ζ³	ζ+ζ³	ζ⁵+ζ⁷	−ζ⁵−ζ⁷	−ζ+ζ³	ζ−ζ³	0	0	0	0	0	0	0	0
χ₄₁	2	2	-2	-2	0	0	-2	2	0	$- 2 i$	$2 i$	0	$2 i$	$- 2 i$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	0	0	$- \sqrt{2}$	$\sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	ζ⁵+ζ⁷	−ζ⁵−ζ⁷	−ζ+ζ³	ζ−ζ³	−ζ⁵+ζ⁷	ζ⁵−ζ⁷	ζ+ζ³	−ζ−ζ³	−ζ⁵−ζ⁷	ζ⁵+ζ⁷	ζ−ζ³	−ζ+ζ³	ζ⁵−ζ⁷	−ζ⁵+ζ⁷	−ζ−ζ³	ζ+ζ³	0	0	0	0	0	0	0	0
χ₄₂	2	2	-2	-2	0	0	-2	2	0	$- 2 i$	$2 i$	0	$2 i$	$- 2 i$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	0	0	$- \sqrt{2}$	$\sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	−ζ⁵−ζ⁷	ζ⁵+ζ⁷	ζ−ζ³	−ζ+ζ³	ζ⁵−ζ⁷	−ζ⁵+ζ⁷	−ζ−ζ³	ζ+ζ³	ζ⁵+ζ⁷	−ζ⁵−ζ⁷	−ζ+ζ³	ζ−ζ³	−ζ⁵+ζ⁷	ζ⁵−ζ⁷	ζ+ζ³	−ζ−ζ³	0	0	0	0	0	0	0	0
χ₄₃	2	2	-2	-2	0	0	-2	2	0	$- 2 i$	$2 i$	0	$2 i$	$- 2 i$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	0	0	$\sqrt{2}$	$- \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	ζ−ζ³	−ζ+ζ³	ζ⁵+ζ⁷	−ζ⁵−ζ⁷	−ζ−ζ³	ζ+ζ³	−ζ⁵+ζ⁷	ζ⁵−ζ⁷	−ζ+ζ³	ζ−ζ³	−ζ⁵−ζ⁷	ζ⁵+ζ⁷	ζ+ζ³	−ζ−ζ³	ζ⁵−ζ⁷	−ζ⁵+ζ⁷	0	0	0	0	0	0	0	0
χ₄₄	2	2	-2	-2	0	0	-2	2	0	$- 2 i$	$2 i$	0	$2 i$	$- 2 i$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	0	0	$\sqrt{2}$	$- \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	−ζ+ζ³	ζ−ζ³	−ζ⁵−ζ⁷	ζ⁵+ζ⁷	ζ+ζ³	−ζ−ζ³	ζ⁵−ζ⁷	−ζ⁵+ζ⁷	ζ−ζ³	−ζ+ζ³	ζ⁵+ζ⁷	−ζ⁵−ζ⁷	−ζ−ζ³	ζ+ζ³	−ζ⁵+ζ⁷	ζ⁵−ζ⁷	0	0	0	0	0	0	0	0
χ₄₅	4	-4	4	-4	4	-4	0	0	0	0	0	0	0	0	$2 i \sqrt{2}$	$- 2 i \sqrt{2}$	$2 i \sqrt{2}$	$- 2 i \sqrt{2}$	$2 i \sqrt{2}$	$- 2 i \sqrt{2}$	$2 i \sqrt{2}$	$- 2 i \sqrt{2}$	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
χ₄₆	4	-4	4	-4	4	-4	0	0	0	0	0	0	0	0	$- 2 i \sqrt{2}$	$2 i \sqrt{2}$	$- 2 i \sqrt{2}$	$2 i \sqrt{2}$	$- 2 i \sqrt{2}$	$2 i \sqrt{2}$	$- 2 i \sqrt{2}$	$2 i \sqrt{2}$	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
χ₄₇	4	-4	4	-4	-4	4	0	0	0	0	0	0	0	0	$2 i \sqrt{2}$	$- 2 i \sqrt{2}$	$2 i \sqrt{2}$	$- 2 i \sqrt{2}$	$- 2 i \sqrt{2}$	$2 i \sqrt{2}$	$- 2 i \sqrt{2}$	$2 i \sqrt{2}$	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
χ₄₈	4	-4	4	-4	-4	4	0	0	0	0	0	0	0	0	$- 2 i \sqrt{2}$	$2 i \sqrt{2}$	$- 2 i \sqrt{2}$	$2 i \sqrt{2}$	$2 i \sqrt{2}$	$- 2 i \sqrt{2}$	$2 i \sqrt{2}$	$- 2 i \sqrt{2}$	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
χ₄₉	4	-4	-4	4	0	0	0	0	4	0	0	-4	0	0	$4 i$	$- 4 i$	$- 4 i$	$4 i$	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	0	0	0	0	0
χ₅₀	4	-4	-4	4	0	0	0	0	4	0	0	-4	0	0	$- 4 i$	$4 i$	$4 i$	$- 4 i$	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	0	0	0	0	0
χ₅₁	4	-4	-4	4	0	0	0	0	-4	0	0	4	0	0	0	0	0	0	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
χ₅₂	4	-4	-4	4	0	0	0	0	-4	0	0	4	0	0	0	0	0	0	-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

Character table — Group #7232