Group #33622 — 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	C₅₄	C₅₅	C₅₆	C₅₇	C₅₈
size	1	1	1	1	2	2	2	2	2	2	2	2	4	4	4	4	4	4	4	4	4	4	4	8	8	8	8	16	16	1	1	1	1	2	2	2	2	2	2	2	2	4	4	4	4	4	4	4	4	4	4	4	8	8	8	8	16	16
order	1	2	2	2	4	4	4	4	8	8	8	8	4	8	8	16	16	16	16	16	16	16	16	2	2	4	4	4	4	2	2	2	2	4	4	4	4	8	8	8	8	4	8	8	16	16	16	16	16	16	16	16	2	2	4	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	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	-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	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	-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	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	-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	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	-1	1	1	1	-1
χ₉	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	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	0	0	0	0	-2	0	0	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	0	0	0	0	0	0	2	2	2	2	2	2	-2	-2	0	0	0	0	-2	0	0	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	0	0	0	0	0	0
χ₁₁	2	2	2	2	2	2	-2	-2	0	0	0	0	-2	0	0	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	0	0	0	0	0	0	2	2	2	2	2	2	-2	-2	0	0	0	0	-2	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	-2	-2	-2	-2	2	2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	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
χ₁₃	2	2	2	2	-2	-2	-2	-2	0	0	0	0	2	0	0	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	0	0	0	0	0	0	2	2	2	2	-2	-2	-2	-2	0	0	0	0	2	0	0	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	0	0	0	0	0	0
χ₁₄	2	2	2	2	-2	-2	-2	-2	0	0	0	0	2	0	0	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	0	0	0	0	0	0	2	2	2	2	-2	-2	-2	-2	0	0	0	0	2	0	0	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	0	0	0	0	0	0
χ₁₅	2	2	-2	-2	0	0	2	-2	2	2	-2	-2	0	0	0	0	0	0	0	0	0	0	0	2	-2	0	0	0	0	2	2	-2	-2	0	0	2	-2	2	2	-2	-2	0	0	0	0	0	0	0	0	0	0	0	2	-2	0	0	0	0
χ₁₆	2	2	-2	-2	0	0	2	-2	2	2	-2	-2	0	0	0	0	0	0	0	0	0	0	0	-2	2	0	0	0	0	2	2	-2	-2	0	0	2	-2	2	2	-2	-2	0	0	0	0	0	0	0	0	0	0	0	-2	2	0	0	0	0
χ₁₇	2	2	-2	-2	0	0	2	-2	-2	-2	2	2	0	0	0	0	0	0	0	0	0	0	0	0	0	$2 i$	$- 2 i$	0	0	2	2	-2	-2	0	0	2	-2	-2	-2	2	2	0	0	0	0	0	0	0	0	0	0	0	0	0	$2 i$	$- 2 i$	0	0
χ₁₈	2	2	-2	-2	0	0	2	-2	-2	-2	2	2	0	0	0	0	0	0	0	0	0	0	0	0	0	$- 2 i$	$2 i$	0	0	2	2	-2	-2	0	0	2	-2	-2	-2	2	2	0	0	0	0	0	0	0	0	0	0	0	0	0	$- 2 i$	$2 i$	0	0
χ₁₉	2	-2	2	-2	$2 i$	$- 2 i$	0	0	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	0	$i \sqrt{2}$	$- i \sqrt{2}$	ζ−ζ⁷	−ζ+ζ⁷	ζ³−ζ⁵	−ζ³+ζ⁵	ζ³+ζ⁵	−ζ³−ζ⁵	ζ+ζ⁷	−ζ−ζ⁷	0	0	0	0	0	0	2	-2	2	-2	$2 i$	$- 2 i$	0	0	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	0	$i \sqrt{2}$	$- i \sqrt{2}$	ζ−ζ⁷	−ζ+ζ⁷	ζ³−ζ⁵	−ζ³+ζ⁵	ζ³+ζ⁵	−ζ³−ζ⁵	ζ+ζ⁷	−ζ−ζ⁷	0	0	0	0	0	0
χ₂₀	2	-2	2	-2	$2 i$	$- 2 i$	0	0	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	0	$i \sqrt{2}$	$- i \sqrt{2}$	−ζ+ζ⁷	ζ−ζ⁷	−ζ³+ζ⁵	ζ³−ζ⁵	−ζ³−ζ⁵	ζ³+ζ⁵	−ζ−ζ⁷	ζ+ζ⁷	0	0	0	0	0	0	2	-2	2	-2	$2 i$	$- 2 i$	0	0	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	0	$i \sqrt{2}$	$- i \sqrt{2}$	−ζ+ζ⁷	ζ−ζ⁷	−ζ³+ζ⁵	ζ³−ζ⁵	−ζ³−ζ⁵	ζ³+ζ⁵	−ζ−ζ⁷	ζ+ζ⁷	0	0	0	0	0	0
χ₂₁	2	-2	2	-2	$2 i$	$- 2 i$	0	0	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	0	$- i \sqrt{2}$	$i \sqrt{2}$	ζ³−ζ⁵	−ζ³+ζ⁵	−ζ+ζ⁷	ζ−ζ⁷	ζ+ζ⁷	−ζ−ζ⁷	−ζ³−ζ⁵	ζ³+ζ⁵	0	0	0	0	0	0	2	-2	2	-2	$2 i$	$- 2 i$	0	0	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	0	$- i \sqrt{2}$	$i \sqrt{2}$	ζ³−ζ⁵	−ζ³+ζ⁵	−ζ+ζ⁷	ζ−ζ⁷	ζ+ζ⁷	−ζ−ζ⁷	−ζ³−ζ⁵	ζ³+ζ⁵	0	0	0	0	0	0
χ₂₂	2	-2	2	-2	$2 i$	$- 2 i$	0	0	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	0	$- i \sqrt{2}$	$i \sqrt{2}$	−ζ³+ζ⁵	ζ³−ζ⁵	ζ−ζ⁷	−ζ+ζ⁷	−ζ−ζ⁷	ζ+ζ⁷	ζ³+ζ⁵	−ζ³−ζ⁵	0	0	0	0	0	0	2	-2	2	-2	$2 i$	$- 2 i$	0	0	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	0	$- i \sqrt{2}$	$i \sqrt{2}$	−ζ³+ζ⁵	ζ³−ζ⁵	ζ−ζ⁷	−ζ+ζ⁷	−ζ−ζ⁷	ζ+ζ⁷	ζ³+ζ⁵	−ζ³−ζ⁵	0	0	0	0	0	0
χ₂₃	2	-2	2	-2	$- 2 i$	$2 i$	0	0	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	0	$- i \sqrt{2}$	$i \sqrt{2}$	ζ−ζ⁷	−ζ+ζ⁷	ζ³−ζ⁵	−ζ³+ζ⁵	−ζ³−ζ⁵	ζ³+ζ⁵	−ζ−ζ⁷	ζ+ζ⁷	0	0	0	0	0	0	2	-2	2	-2	$- 2 i$	$2 i$	0	0	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	0	$- i \sqrt{2}$	$i \sqrt{2}$	ζ−ζ⁷	−ζ+ζ⁷	ζ³−ζ⁵	−ζ³+ζ⁵	−ζ³−ζ⁵	ζ³+ζ⁵	−ζ−ζ⁷	ζ+ζ⁷	0	0	0	0	0	0
χ₂₄	2	-2	2	-2	$- 2 i$	$2 i$	0	0	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	0	$- i \sqrt{2}$	$i \sqrt{2}$	−ζ+ζ⁷	ζ−ζ⁷	−ζ³+ζ⁵	ζ³−ζ⁵	ζ³+ζ⁵	−ζ³−ζ⁵	ζ+ζ⁷	−ζ−ζ⁷	0	0	0	0	0	0	2	-2	2	-2	$- 2 i$	$2 i$	0	0	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	0	$- i \sqrt{2}$	$i \sqrt{2}$	−ζ+ζ⁷	ζ−ζ⁷	−ζ³+ζ⁵	ζ³−ζ⁵	ζ³+ζ⁵	−ζ³−ζ⁵	ζ+ζ⁷	−ζ−ζ⁷	0	0	0	0	0	0
χ₂₅	2	-2	2	-2	$- 2 i$	$2 i$	0	0	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	0	$i \sqrt{2}$	$- i \sqrt{2}$	ζ³−ζ⁵	−ζ³+ζ⁵	−ζ+ζ⁷	ζ−ζ⁷	−ζ−ζ⁷	ζ+ζ⁷	ζ³+ζ⁵	−ζ³−ζ⁵	0	0	0	0	0	0	2	-2	2	-2	$- 2 i$	$2 i$	0	0	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	0	$i \sqrt{2}$	$- i \sqrt{2}$	ζ³−ζ⁵	−ζ³+ζ⁵	−ζ+ζ⁷	ζ−ζ⁷	−ζ−ζ⁷	ζ+ζ⁷	ζ³+ζ⁵	−ζ³−ζ⁵	0	0	0	0	0	0
χ₂₆	2	-2	2	-2	$- 2 i$	$2 i$	0	0	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	0	$i \sqrt{2}$	$- i \sqrt{2}$	−ζ³+ζ⁵	ζ³−ζ⁵	ζ−ζ⁷	−ζ+ζ⁷	ζ+ζ⁷	−ζ−ζ⁷	−ζ³−ζ⁵	ζ³+ζ⁵	0	0	0	0	0	0	2	-2	2	-2	$- 2 i$	$2 i$	0	0	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	0	$i \sqrt{2}$	$- i \sqrt{2}$	−ζ³+ζ⁵	ζ³−ζ⁵	ζ−ζ⁷	−ζ+ζ⁷	ζ+ζ⁷	−ζ−ζ⁷	−ζ³−ζ⁵	ζ³+ζ⁵	0	0	0	0	0	0
χ₂₇	4	4	-4	-4	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	4	4	-4	-4	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
χ₂₈	4	-4	-4	4	0	0	0	0	$2 \sqrt{2}$	$- 2 \sqrt{2}$	$- 2 \sqrt{2}$	$2 \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	4	-4	-4	4	0	0	0	0	$2 \sqrt{2}$	$- 2 \sqrt{2}$	$- 2 \sqrt{2}$	$2 \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₉	4	-4	-4	4	0	0	0	0	$- 2 \sqrt{2}$	$2 \sqrt{2}$	$2 \sqrt{2}$	$- 2 \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	4	-4	-4	4	0	0	0	0	$- 2 \sqrt{2}$	$2 \sqrt{2}$	$2 \sqrt{2}$	$- 2 \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₀	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1
χ₃₁	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	1	1	1	1	1	1
χ₃₂	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	-1	-1	-1	-1	-1	-1	-1	-1	1	1	1	1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	1	1	1	1	1	1	1	1	-1	-1	-1	-1	1	1
χ₃₃	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	1	1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	1	1	1	1	1	1	1	1	1	1	1	1	-1	-1
χ₃₄	1	1	1	1	-1	-1	1	1	1	1	1	1	-1	-1	-1	1	1	1	1	-1	-1	-1	-1	1	1	-1	-1	1	-1	-1	-1	-1	-1	1	1	-1	-1	-1	-1	-1	-1	1	1	1	-1	-1	-1	-1	1	1	1	1	-1	-1	1	1	-1	1
χ₃₅	1	1	1	1	-1	-1	1	1	1	1	1	1	-1	-1	-1	1	1	1	1	-1	-1	-1	-1	-1	-1	1	1	-1	1	-1	-1	-1	-1	1	1	-1	-1	-1	-1	-1	-1	1	1	1	-1	-1	-1	-1	1	1	1	1	1	1	-1	-1	1	-1
χ₃₆	1	1	1	1	-1	-1	1	1	1	1	1	1	-1	-1	-1	-1	-1	-1	-1	1	1	1	1	1	1	-1	-1	-1	1	-1	-1	-1	-1	1	1	-1	-1	-1	-1	-1	-1	1	1	1	1	1	1	1	-1	-1	-1	-1	-1	-1	1	1	1	-1
χ₃₇	1	1	1	1	-1	-1	1	1	1	1	1	1	-1	-1	-1	-1	-1	-1	-1	1	1	1	1	-1	-1	1	1	1	-1	-1	-1	-1	-1	1	1	-1	-1	-1	-1	-1	-1	1	1	1	1	1	1	1	-1	-1	-1	-1	1	1	-1	-1	-1	1
χ₃₈	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	-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
χ₃₉	2	2	2	2	2	2	-2	-2	0	0	0	0	-2	0	0	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	0	0	0	0	0	0	-2	-2	-2	-2	-2	-2	2	2	0	0	0	0	2	0	0	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	0	0	0	0	0	0
χ₄₀	2	2	2	2	2	2	-2	-2	0	0	0	0	-2	0	0	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	0	0	0	0	0	0	-2	-2	-2	-2	-2	-2	2	2	0	0	0	0	2	0	0	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	0	0	0	0	0	0
χ₄₁	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	-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
χ₄₂	2	2	2	2	-2	-2	-2	-2	0	0	0	0	2	0	0	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	0	0	0	0	0	0	-2	-2	-2	-2	2	2	2	2	0	0	0	0	-2	0	0	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	0	0	0	0	0	0
χ₄₃	2	2	2	2	-2	-2	-2	-2	0	0	0	0	2	0	0	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	0	0	0	0	0	0	-2	-2	-2	-2	2	2	2	2	0	0	0	0	-2	0	0	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	0	0	0	0	0	0
χ₄₄	2	2	-2	-2	0	0	2	-2	2	2	-2	-2	0	0	0	0	0	0	0	0	0	0	0	2	-2	0	0	0	0	-2	-2	2	2	0	0	-2	2	-2	-2	2	2	0	0	0	0	0	0	0	0	0	0	0	-2	2	0	0	0	0
χ₄₅	2	2	-2	-2	0	0	2	-2	2	2	-2	-2	0	0	0	0	0	0	0	0	0	0	0	-2	2	0	0	0	0	-2	-2	2	2	0	0	-2	2	-2	-2	2	2	0	0	0	0	0	0	0	0	0	0	0	2	-2	0	0	0	0
χ₄₆	2	2	-2	-2	0	0	2	-2	-2	-2	2	2	0	0	0	0	0	0	0	0	0	0	0	0	0	$2 i$	$- 2 i$	0	0	-2	-2	2	2	0	0	-2	2	2	2	-2	-2	0	0	0	0	0	0	0	0	0	0	0	0	0	$- 2 i$	$2 i$	0	0
χ₄₇	2	2	-2	-2	0	0	2	-2	-2	-2	2	2	0	0	0	0	0	0	0	0	0	0	0	0	0	$- 2 i$	$2 i$	0	0	-2	-2	2	2	0	0	-2	2	2	2	-2	-2	0	0	0	0	0	0	0	0	0	0	0	0	0	$2 i$	$- 2 i$	0	0
χ₄₈	2	-2	2	-2	$2 i$	$- 2 i$	0	0	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	0	$i \sqrt{2}$	$- i \sqrt{2}$	ζ−ζ⁷	−ζ+ζ⁷	ζ³−ζ⁵	−ζ³+ζ⁵	ζ³+ζ⁵	−ζ³−ζ⁵	ζ+ζ⁷	−ζ−ζ⁷	0	0	0	0	0	0	-2	2	-2	2	$- 2 i$	$2 i$	0	0	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	0	$- i \sqrt{2}$	$i \sqrt{2}$	−ζ+ζ⁷	ζ−ζ⁷	−ζ³+ζ⁵	ζ³−ζ⁵	−ζ³−ζ⁵	ζ³+ζ⁵	−ζ−ζ⁷	ζ+ζ⁷	0	0	0	0	0	0
χ₄₉	2	-2	2	-2	$2 i$	$- 2 i$	0	0	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	0	$i \sqrt{2}$	$- i \sqrt{2}$	−ζ+ζ⁷	ζ−ζ⁷	−ζ³+ζ⁵	ζ³−ζ⁵	−ζ³−ζ⁵	ζ³+ζ⁵	−ζ−ζ⁷	ζ+ζ⁷	0	0	0	0	0	0	-2	2	-2	2	$- 2 i$	$2 i$	0	0	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	0	$- i \sqrt{2}$	$i \sqrt{2}$	ζ−ζ⁷	−ζ+ζ⁷	ζ³−ζ⁵	−ζ³+ζ⁵	ζ³+ζ⁵	−ζ³−ζ⁵	ζ+ζ⁷	−ζ−ζ⁷	0	0	0	0	0	0
χ₅₀	2	-2	2	-2	$2 i$	$- 2 i$	0	0	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	0	$- i \sqrt{2}$	$i \sqrt{2}$	ζ³−ζ⁵	−ζ³+ζ⁵	−ζ+ζ⁷	ζ−ζ⁷	ζ+ζ⁷	−ζ−ζ⁷	−ζ³−ζ⁵	ζ³+ζ⁵	0	0	0	0	0	0	-2	2	-2	2	$- 2 i$	$2 i$	0	0	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	0	$i \sqrt{2}$	$- i \sqrt{2}$	−ζ³+ζ⁵	ζ³−ζ⁵	ζ−ζ⁷	−ζ+ζ⁷	−ζ−ζ⁷	ζ+ζ⁷	ζ³+ζ⁵	−ζ³−ζ⁵	0	0	0	0	0	0
χ₅₁	2	-2	2	-2	$2 i$	$- 2 i$	0	0	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	0	$- i \sqrt{2}$	$i \sqrt{2}$	−ζ³+ζ⁵	ζ³−ζ⁵	ζ−ζ⁷	−ζ+ζ⁷	−ζ−ζ⁷	ζ+ζ⁷	ζ³+ζ⁵	−ζ³−ζ⁵	0	0	0	0	0	0	-2	2	-2	2	$- 2 i$	$2 i$	0	0	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	0	$i \sqrt{2}$	$- i \sqrt{2}$	ζ³−ζ⁵	−ζ³+ζ⁵	−ζ+ζ⁷	ζ−ζ⁷	ζ+ζ⁷	−ζ−ζ⁷	−ζ³−ζ⁵	ζ³+ζ⁵	0	0	0	0	0	0
χ₅₂	2	-2	2	-2	$- 2 i$	$2 i$	0	0	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	0	$- i \sqrt{2}$	$i \sqrt{2}$	ζ−ζ⁷	−ζ+ζ⁷	ζ³−ζ⁵	−ζ³+ζ⁵	−ζ³−ζ⁵	ζ³+ζ⁵	−ζ−ζ⁷	ζ+ζ⁷	0	0	0	0	0	0	-2	2	-2	2	$2 i$	$- 2 i$	0	0	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	0	$i \sqrt{2}$	$- i \sqrt{2}$	−ζ+ζ⁷	ζ−ζ⁷	−ζ³+ζ⁵	ζ³−ζ⁵	ζ³+ζ⁵	−ζ³−ζ⁵	ζ+ζ⁷	−ζ−ζ⁷	0	0	0	0	0	0
χ₅₃	2	-2	2	-2	$- 2 i$	$2 i$	0	0	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	0	$- i \sqrt{2}$	$i \sqrt{2}$	−ζ+ζ⁷	ζ−ζ⁷	−ζ³+ζ⁵	ζ³−ζ⁵	ζ³+ζ⁵	−ζ³−ζ⁵	ζ+ζ⁷	−ζ−ζ⁷	0	0	0	0	0	0	-2	2	-2	2	$2 i$	$- 2 i$	0	0	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	0	$i \sqrt{2}$	$- i \sqrt{2}$	ζ−ζ⁷	−ζ+ζ⁷	ζ³−ζ⁵	−ζ³+ζ⁵	−ζ³−ζ⁵	ζ³+ζ⁵	−ζ−ζ⁷	ζ+ζ⁷	0	0	0	0	0	0
χ₅₄	2	-2	2	-2	$- 2 i$	$2 i$	0	0	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	0	$i \sqrt{2}$	$- i \sqrt{2}$	ζ³−ζ⁵	−ζ³+ζ⁵	−ζ+ζ⁷	ζ−ζ⁷	−ζ−ζ⁷	ζ+ζ⁷	ζ³+ζ⁵	−ζ³−ζ⁵	0	0	0	0	0	0	-2	2	-2	2	$2 i$	$- 2 i$	0	0	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	0	$- i \sqrt{2}$	$i \sqrt{2}$	−ζ³+ζ⁵	ζ³−ζ⁵	ζ−ζ⁷	−ζ+ζ⁷	ζ+ζ⁷	−ζ−ζ⁷	−ζ³−ζ⁵	ζ³+ζ⁵	0	0	0	0	0	0
χ₅₅	2	-2	2	-2	$- 2 i$	$2 i$	0	0	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	0	$i \sqrt{2}$	$- i \sqrt{2}$	−ζ³+ζ⁵	ζ³−ζ⁵	ζ−ζ⁷	−ζ+ζ⁷	ζ+ζ⁷	−ζ−ζ⁷	−ζ³−ζ⁵	ζ³+ζ⁵	0	0	0	0	0	0	-2	2	-2	2	$2 i$	$- 2 i$	0	0	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	0	$- i \sqrt{2}$	$i \sqrt{2}$	ζ³−ζ⁵	−ζ³+ζ⁵	−ζ+ζ⁷	ζ−ζ⁷	−ζ−ζ⁷	ζ+ζ⁷	ζ³+ζ⁵	−ζ³−ζ⁵	0	0	0	0	0	0
χ₅₆	4	4	-4	-4	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	-4	-4	4	4	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
χ₅₇	4	-4	-4	4	0	0	0	0	$2 \sqrt{2}$	$- 2 \sqrt{2}$	$- 2 \sqrt{2}$	$2 \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	-4	4	4	-4	0	0	0	0	$- 2 \sqrt{2}$	$2 \sqrt{2}$	$2 \sqrt{2}$	$- 2 \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₅₈	4	-4	-4	4	0	0	0	0	$- 2 \sqrt{2}$	$2 \sqrt{2}$	$2 \sqrt{2}$	$- 2 \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	-4	4	4	-4	0	0	0	0	$2 \sqrt{2}$	$- 2 \sqrt{2}$	$- 2 \sqrt{2}$	$2 \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0

Character table — Group #33622