Group #88528 — 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
size	1	1	1	1	1	1	2	2	2	2	2	2	2	2	2	6	6	6	6	6	6	6	6	6	6	6	6	6	6	6	6	6	6	6	6	6	6	6	6	6	6	6	6	6	6	6	6	36	36	36	36	36	36
order	1	2	3	3	6	6	4	8	8	12	12	24	24	24	24	3	3	3	3	6	6	6	6	12	12	12	12	12	12	12	12	24	24	24	24	24	24	24	24	24	24	24	24	24	24	24	24	2	4	6	6	12	12
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
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
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
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
χ₅	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	-1	-1	-1	2	-1	-1	-1	2	2	-1	-1	-1	-1	-1	-1	2	2	2	2	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	0	0	0	0	0	0
χ₆	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	-1	2	-1	-1	-1	2	-1	-1	-1	-1	2	2	-1	-1	-1	-1	-1	-1	-1	-1	2	2	2	2	-1	-1	-1	-1	-1	-1	-1	-1	0	0	0	0	0	0
χ₇	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	-1	-1	2	-1	-1	-1	2	-1	-1	-1	-1	-1	2	2	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	2	2	2	2	-1	-1	-1	-1	0	0	0	0	0	0
χ₈	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	-1	-1	-1	2	-1	-1	-1	2	-1	-1	-1	-1	-1	-1	2	2	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	2	2	2	2	0	0	0	0	0	0
χ₉	2	2	2	2	2	2	2	-2	-2	2	2	-2	-2	-2	-2	2	-1	-1	-1	2	-1	-1	-1	2	2	-1	-1	-1	-1	-1	-1	-2	-2	-2	-2	1	1	1	1	1	1	1	1	1	1	1	1	0	0	0	0	0	0
χ₁₀	2	2	2	2	2	2	2	-2	-2	2	2	-2	-2	-2	-2	-1	2	-1	-1	-1	2	-1	-1	-1	-1	2	2	-1	-1	-1	-1	1	1	1	1	-2	-2	-2	-2	1	1	1	1	1	1	1	1	0	0	0	0	0	0
χ₁₁	2	2	2	2	2	2	2	-2	-2	2	2	-2	-2	-2	-2	-1	-1	2	-1	-1	-1	2	-1	-1	-1	-1	-1	2	2	-1	-1	1	1	1	1	1	1	1	1	-2	-2	-2	-2	1	1	1	1	0	0	0	0	0	0
χ₁₂	2	2	2	2	2	2	2	-2	-2	2	2	-2	-2	-2	-2	-1	-1	-1	2	-1	-1	-1	2	-1	-1	-1	-1	-1	-1	2	2	1	1	1	1	1	1	1	1	1	1	1	1	-2	-2	-2	-2	0	0	0	0	0	0
χ₁₃	2	2	2	2	2	2	-2	0	0	-2	-2	0	0	0	0	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
χ₁₄	2	2	2	2	2	2	-2	0	0	-2	-2	0	0	0	0	2	-1	-1	-1	2	-1	-1	-1	-2	-2	1	1	1	1	1	1	0	0	0	0	$\sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$- \sqrt{3}$	0	0	0	0	0	0
χ₁₅	2	2	2	2	2	2	-2	0	0	-2	-2	0	0	0	0	2	-1	-1	-1	2	-1	-1	-1	-2	-2	1	1	1	1	1	1	0	0	0	0	$- \sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$\sqrt{3}$	0	0	0	0	0	0
χ₁₆	2	2	2	2	2	2	-2	0	0	-2	-2	0	0	0	0	-1	2	-1	-1	-1	2	-1	-1	1	1	-2	-2	1	1	1	1	$\sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$- \sqrt{3}$	0	0	0	0	$\sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$- \sqrt{3}$	$- \sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$\sqrt{3}$	0	0	0	0	0	0
χ₁₇	2	2	2	2	2	2	-2	0	0	-2	-2	0	0	0	0	-1	2	-1	-1	-1	2	-1	-1	1	1	-2	-2	1	1	1	1	$- \sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$\sqrt{3}$	0	0	0	0	$- \sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$\sqrt{3}$	$\sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$- \sqrt{3}$	0	0	0	0	0	0
χ₁₈	2	2	2	2	2	2	-2	0	0	-2	-2	0	0	0	0	-1	-1	2	-1	-1	-1	2	-1	1	1	1	1	-2	-2	1	1	$\sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$- \sqrt{3}$	$- \sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$\sqrt{3}$	0	0	0	0	$\sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$- \sqrt{3}$	0	0	0	0	0	0
χ₁₉	2	2	2	2	2	2	-2	0	0	-2	-2	0	0	0	0	-1	-1	2	-1	-1	-1	2	-1	1	1	1	1	-2	-2	1	1	$- \sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$\sqrt{3}$	$\sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$- \sqrt{3}$	0	0	0	0	$- \sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$\sqrt{3}$	0	0	0	0	0	0
χ₂₀	2	2	2	2	2	2	-2	0	0	-2	-2	0	0	0	0	-1	-1	-1	2	-1	-1	-1	2	1	1	1	1	1	1	-2	-2	$\sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$- \sqrt{3}$	$- \sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$\sqrt{3}$	0	0	0	0	0	0	0	0	0	0
χ₂₁	2	2	2	2	2	2	-2	0	0	-2	-2	0	0	0	0	-1	-1	-1	2	-1	-1	-1	2	1	1	1	1	1	1	-2	-2	$- \sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$\sqrt{3}$	$\sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$- \sqrt{3}$	0	0	0	0	0	0	0	0	0	0
χ₂₂	2	-2	2	2	-2	-2	0	$- i \sqrt{2}$	$i \sqrt{2}$	0	0	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	2	2	2	2	-2	-2	-2	-2	0	0	0	0	0	0	0	0	$- i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	0	0	0	0	0	0
χ₂₃	2	-2	2	2	-2	-2	0	$- i \sqrt{2}$	$i \sqrt{2}$	0	0	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	2	-1	-1	-1	-2	1	1	1	0	0	$\sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$- i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	ζ⁵+ζ⁷	−ζ⁵−ζ⁷	ζ¹³+ζ²³	−ζ¹³−ζ²³	ζ⁵+ζ⁷	−ζ⁵−ζ⁷	ζ¹³+ζ²³	−ζ¹³−ζ²³	ζ⁵+ζ⁷	−ζ⁵−ζ⁷	ζ¹³+ζ²³	−ζ¹³−ζ²³	0	0	0	0	0	0
χ₂₄	2	-2	2	2	-2	-2	0	$- i \sqrt{2}$	$i \sqrt{2}$	0	0	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	2	-1	-1	-1	-2	1	1	1	0	0	$- \sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$- i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	ζ¹³+ζ²³	−ζ¹³−ζ²³	ζ⁵+ζ⁷	−ζ⁵−ζ⁷	ζ¹³+ζ²³	−ζ¹³−ζ²³	ζ⁵+ζ⁷	−ζ⁵−ζ⁷	ζ¹³+ζ²³	−ζ¹³−ζ²³	ζ⁵+ζ⁷	−ζ⁵−ζ⁷	0	0	0	0	0	0
χ₂₅	2	-2	2	2	-2	-2	0	$- i \sqrt{2}$	$i \sqrt{2}$	0	0	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	-1	2	-1	-1	1	-2	1	1	$\sqrt{3}$	$- \sqrt{3}$	0	0	$\sqrt{3}$	$- \sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	ζ⁵+ζ⁷	−ζ⁵−ζ⁷	ζ¹³+ζ²³	−ζ¹³−ζ²³	$- i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	ζ⁵+ζ⁷	−ζ⁵−ζ⁷	ζ¹³+ζ²³	−ζ¹³−ζ²³	ζ¹³+ζ²³	−ζ¹³−ζ²³	ζ⁵+ζ⁷	−ζ⁵−ζ⁷	0	0	0	0	0	0
χ₂₆	2	-2	2	2	-2	-2	0	$- i \sqrt{2}$	$i \sqrt{2}$	0	0	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	-1	2	-1	-1	1	-2	1	1	$- \sqrt{3}$	$\sqrt{3}$	0	0	$- \sqrt{3}$	$\sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	ζ¹³+ζ²³	−ζ¹³−ζ²³	ζ⁵+ζ⁷	−ζ⁵−ζ⁷	$- i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	ζ¹³+ζ²³	−ζ¹³−ζ²³	ζ⁵+ζ⁷	−ζ⁵−ζ⁷	ζ⁵+ζ⁷	−ζ⁵−ζ⁷	ζ¹³+ζ²³	−ζ¹³−ζ²³	0	0	0	0	0	0
χ₂₇	2	-2	2	2	-2	-2	0	$- i \sqrt{2}$	$i \sqrt{2}$	0	0	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	-1	-1	2	-1	1	1	-2	1	$\sqrt{3}$	$- \sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	0	0	$\sqrt{3}$	$- \sqrt{3}$	ζ⁵+ζ⁷	−ζ⁵−ζ⁷	ζ¹³+ζ²³	−ζ¹³−ζ²³	ζ¹³+ζ²³	−ζ¹³−ζ²³	ζ⁵+ζ⁷	−ζ⁵−ζ⁷	$- i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	ζ⁵+ζ⁷	−ζ⁵−ζ⁷	ζ¹³+ζ²³	−ζ¹³−ζ²³	0	0	0	0	0	0
χ₂₈	2	-2	2	2	-2	-2	0	$- i \sqrt{2}$	$i \sqrt{2}$	0	0	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	-1	-1	2	-1	1	1	-2	1	$- \sqrt{3}$	$\sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	0	0	$- \sqrt{3}$	$\sqrt{3}$	ζ¹³+ζ²³	−ζ¹³−ζ²³	ζ⁵+ζ⁷	−ζ⁵−ζ⁷	ζ⁵+ζ⁷	−ζ⁵−ζ⁷	ζ¹³+ζ²³	−ζ¹³−ζ²³	$- i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	ζ¹³+ζ²³	−ζ¹³−ζ²³	ζ⁵+ζ⁷	−ζ⁵−ζ⁷	0	0	0	0	0	0
χ₂₉	2	-2	2	2	-2	-2	0	$- i \sqrt{2}$	$i \sqrt{2}$	0	0	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	-1	-1	-1	2	1	1	1	-2	$\sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	0	0	ζ⁵+ζ⁷	−ζ⁵−ζ⁷	ζ¹³+ζ²³	−ζ¹³−ζ²³	ζ⁵+ζ⁷	−ζ⁵−ζ⁷	ζ¹³+ζ²³	−ζ¹³−ζ²³	ζ¹³+ζ²³	−ζ¹³−ζ²³	ζ⁵+ζ⁷	−ζ⁵−ζ⁷	$- i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	0	0	0	0	0	0
χ₃₀	2	-2	2	2	-2	-2	0	$- i \sqrt{2}$	$i \sqrt{2}$	0	0	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	-1	-1	-1	2	1	1	1	-2	$- \sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	0	0	ζ¹³+ζ²³	−ζ¹³−ζ²³	ζ⁵+ζ⁷	−ζ⁵−ζ⁷	ζ¹³+ζ²³	−ζ¹³−ζ²³	ζ⁵+ζ⁷	−ζ⁵−ζ⁷	ζ⁵+ζ⁷	−ζ⁵−ζ⁷	ζ¹³+ζ²³	−ζ¹³−ζ²³	$- i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	0	0	0	0	0	0
χ₃₁	2	-2	2	2	-2	-2	0	$i \sqrt{2}$	$- i \sqrt{2}$	0	0	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	2	2	2	2	-2	-2	-2	-2	0	0	0	0	0	0	0	0	$i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	0	0	0	0	0	0
χ₃₂	2	-2	2	2	-2	-2	0	$i \sqrt{2}$	$- i \sqrt{2}$	0	0	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	2	-1	-1	-1	-2	1	1	1	0	0	$\sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	−ζ⁵−ζ⁷	ζ⁵+ζ⁷	−ζ¹³−ζ²³	ζ¹³+ζ²³	−ζ⁵−ζ⁷	ζ⁵+ζ⁷	−ζ¹³−ζ²³	ζ¹³+ζ²³	−ζ⁵−ζ⁷	ζ⁵+ζ⁷	−ζ¹³−ζ²³	ζ¹³+ζ²³	0	0	0	0	0	0
χ₃₃	2	-2	2	2	-2	-2	0	$i \sqrt{2}$	$- i \sqrt{2}$	0	0	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	2	-1	-1	-1	-2	1	1	1	0	0	$- \sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	−ζ¹³−ζ²³	ζ¹³+ζ²³	−ζ⁵−ζ⁷	ζ⁵+ζ⁷	−ζ¹³−ζ²³	ζ¹³+ζ²³	−ζ⁵−ζ⁷	ζ⁵+ζ⁷	−ζ¹³−ζ²³	ζ¹³+ζ²³	−ζ⁵−ζ⁷	ζ⁵+ζ⁷	0	0	0	0	0	0
χ₃₄	2	-2	2	2	-2	-2	0	$i \sqrt{2}$	$- i \sqrt{2}$	0	0	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	-1	2	-1	-1	1	-2	1	1	$\sqrt{3}$	$- \sqrt{3}$	0	0	$\sqrt{3}$	$- \sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	−ζ⁵−ζ⁷	ζ⁵+ζ⁷	−ζ¹³−ζ²³	ζ¹³+ζ²³	$i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	−ζ⁵−ζ⁷	ζ⁵+ζ⁷	−ζ¹³−ζ²³	ζ¹³+ζ²³	−ζ¹³−ζ²³	ζ¹³+ζ²³	−ζ⁵−ζ⁷	ζ⁵+ζ⁷	0	0	0	0	0	0
χ₃₅	2	-2	2	2	-2	-2	0	$i \sqrt{2}$	$- i \sqrt{2}$	0	0	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	-1	2	-1	-1	1	-2	1	1	$- \sqrt{3}$	$\sqrt{3}$	0	0	$- \sqrt{3}$	$\sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	−ζ¹³−ζ²³	ζ¹³+ζ²³	−ζ⁵−ζ⁷	ζ⁵+ζ⁷	$i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	−ζ¹³−ζ²³	ζ¹³+ζ²³	−ζ⁵−ζ⁷	ζ⁵+ζ⁷	−ζ⁵−ζ⁷	ζ⁵+ζ⁷	−ζ¹³−ζ²³	ζ¹³+ζ²³	0	0	0	0	0	0
χ₃₆	2	-2	2	2	-2	-2	0	$i \sqrt{2}$	$- i \sqrt{2}$	0	0	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	-1	-1	2	-1	1	1	-2	1	$\sqrt{3}$	$- \sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	0	0	$\sqrt{3}$	$- \sqrt{3}$	−ζ⁵−ζ⁷	ζ⁵+ζ⁷	−ζ¹³−ζ²³	ζ¹³+ζ²³	−ζ¹³−ζ²³	ζ¹³+ζ²³	−ζ⁵−ζ⁷	ζ⁵+ζ⁷	$i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	−ζ⁵−ζ⁷	ζ⁵+ζ⁷	−ζ¹³−ζ²³	ζ¹³+ζ²³	0	0	0	0	0	0
χ₃₇	2	-2	2	2	-2	-2	0	$i \sqrt{2}$	$- i \sqrt{2}$	0	0	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	-1	-1	2	-1	1	1	-2	1	$- \sqrt{3}$	$\sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	0	0	$- \sqrt{3}$	$\sqrt{3}$	−ζ¹³−ζ²³	ζ¹³+ζ²³	−ζ⁵−ζ⁷	ζ⁵+ζ⁷	−ζ⁵−ζ⁷	ζ⁵+ζ⁷	−ζ¹³−ζ²³	ζ¹³+ζ²³	$i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	−ζ¹³−ζ²³	ζ¹³+ζ²³	−ζ⁵−ζ⁷	ζ⁵+ζ⁷	0	0	0	0	0	0
χ₃₈	2	-2	2	2	-2	-2	0	$i \sqrt{2}$	$- i \sqrt{2}$	0	0	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	-1	-1	-1	2	1	1	1	-2	$\sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	0	0	−ζ⁵−ζ⁷	ζ⁵+ζ⁷	−ζ¹³−ζ²³	ζ¹³+ζ²³	−ζ⁵−ζ⁷	ζ⁵+ζ⁷	−ζ¹³−ζ²³	ζ¹³+ζ²³	−ζ¹³−ζ²³	ζ¹³+ζ²³	−ζ⁵−ζ⁷	ζ⁵+ζ⁷	$i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	0	0	0	0	0	0
χ₃₉	2	-2	2	2	-2	-2	0	$i \sqrt{2}$	$- i \sqrt{2}$	0	0	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	-1	-1	-1	2	1	1	1	-2	$- \sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	0	0	−ζ¹³−ζ²³	ζ¹³+ζ²³	−ζ⁵−ζ⁷	ζ⁵+ζ⁷	−ζ¹³−ζ²³	ζ¹³+ζ²³	−ζ⁵−ζ⁷	ζ⁵+ζ⁷	−ζ⁵−ζ⁷	ζ⁵+ζ⁷	−ζ¹³−ζ²³	ζ¹³+ζ²³	$i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	0	0	0	0	0	0
χ₄₀	3	3	$\frac{- 3 - 3 i \sqrt{3}}{2}$	$\frac{- 3 + 3 i \sqrt{3}}{2}$	$\frac{- 3 - 3 i \sqrt{3}}{2}$	$\frac{- 3 + 3 i \sqrt{3}}{2}$	3	3	3	$\frac{- 3 - 3 i \sqrt{3}}{2}$	$\frac{- 3 + 3 i \sqrt{3}}{2}$	$\frac{- 3 - 3 i \sqrt{3}}{2}$	$\frac{- 3 + 3 i \sqrt{3}}{2}$	$\frac{- 3 - 3 i \sqrt{3}}{2}$	$\frac{- 3 + 3 i \sqrt{3}}{2}$	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	0	0	1	1	$\frac{- 1 - i \sqrt{3}}{2}$	$\frac{- 1 + i \sqrt{3}}{2}$	$\frac{- 1 - i \sqrt{3}}{2}$	$\frac{- 1 + i \sqrt{3}}{2}$
χ₄₁	3	3	$\frac{- 3 - 3 i \sqrt{3}}{2}$	$\frac{- 3 + 3 i \sqrt{3}}{2}$	$\frac{- 3 - 3 i \sqrt{3}}{2}$	$\frac{- 3 + 3 i \sqrt{3}}{2}$	3	3	3	$\frac{- 3 - 3 i \sqrt{3}}{2}$	$\frac{- 3 + 3 i \sqrt{3}}{2}$	$\frac{- 3 - 3 i \sqrt{3}}{2}$	$\frac{- 3 + 3 i \sqrt{3}}{2}$	$\frac{- 3 - 3 i \sqrt{3}}{2}$	$\frac{- 3 + 3 i \sqrt{3}}{2}$	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	0	0	-1	-1	$\frac{1 + i \sqrt{3}}{2}$	$\frac{1 - i \sqrt{3}}{2}$	$\frac{1 + i \sqrt{3}}{2}$	$\frac{1 - i \sqrt{3}}{2}$
χ₄₂	3	3	$\frac{- 3 - 3 i \sqrt{3}}{2}$	$\frac{- 3 + 3 i \sqrt{3}}{2}$	$\frac{- 3 - 3 i \sqrt{3}}{2}$	$\frac{- 3 + 3 i \sqrt{3}}{2}$	3	-3	-3	$\frac{- 3 - 3 i \sqrt{3}}{2}$	$\frac{- 3 + 3 i \sqrt{3}}{2}$	$\frac{3 + 3 i \sqrt{3}}{2}$	$\frac{3 - 3 i \sqrt{3}}{2}$	$\frac{3 + 3 i \sqrt{3}}{2}$	$\frac{3 - 3 i \sqrt{3}}{2}$	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	0	0	1	-1	$\frac{- 1 - i \sqrt{3}}{2}$	$\frac{- 1 + i \sqrt{3}}{2}$	$\frac{1 + i \sqrt{3}}{2}$	$\frac{1 - i \sqrt{3}}{2}$
χ₄₃	3	3	$\frac{- 3 - 3 i \sqrt{3}}{2}$	$\frac{- 3 + 3 i \sqrt{3}}{2}$	$\frac{- 3 - 3 i \sqrt{3}}{2}$	$\frac{- 3 + 3 i \sqrt{3}}{2}$	3	-3	-3	$\frac{- 3 - 3 i \sqrt{3}}{2}$	$\frac{- 3 + 3 i \sqrt{3}}{2}$	$\frac{3 + 3 i \sqrt{3}}{2}$	$\frac{3 - 3 i \sqrt{3}}{2}$	$\frac{3 + 3 i \sqrt{3}}{2}$	$\frac{3 - 3 i \sqrt{3}}{2}$	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	0	0	-1	1	$\frac{1 + i \sqrt{3}}{2}$	$\frac{1 - i \sqrt{3}}{2}$	$\frac{- 1 - i \sqrt{3}}{2}$	$\frac{- 1 + i \sqrt{3}}{2}$
χ₄₄	3	3	$\frac{- 3 + 3 i \sqrt{3}}{2}$	$\frac{- 3 - 3 i \sqrt{3}}{2}$	$\frac{- 3 + 3 i \sqrt{3}}{2}$	$\frac{- 3 - 3 i \sqrt{3}}{2}$	3	3	3	$\frac{- 3 + 3 i \sqrt{3}}{2}$	$\frac{- 3 - 3 i \sqrt{3}}{2}$	$\frac{- 3 + 3 i \sqrt{3}}{2}$	$\frac{- 3 - 3 i \sqrt{3}}{2}$	$\frac{- 3 + 3 i \sqrt{3}}{2}$	$\frac{- 3 - 3 i \sqrt{3}}{2}$	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	0	0	1	1	$\frac{- 1 + i \sqrt{3}}{2}$	$\frac{- 1 - i \sqrt{3}}{2}$	$\frac{- 1 + i \sqrt{3}}{2}$	$\frac{- 1 - i \sqrt{3}}{2}$
χ₄₅	3	3	$\frac{- 3 + 3 i \sqrt{3}}{2}$	$\frac{- 3 - 3 i \sqrt{3}}{2}$	$\frac{- 3 + 3 i \sqrt{3}}{2}$	$\frac{- 3 - 3 i \sqrt{3}}{2}$	3	3	3	$\frac{- 3 + 3 i \sqrt{3}}{2}$	$\frac{- 3 - 3 i \sqrt{3}}{2}$	$\frac{- 3 + 3 i \sqrt{3}}{2}$	$\frac{- 3 - 3 i \sqrt{3}}{2}$	$\frac{- 3 + 3 i \sqrt{3}}{2}$	$\frac{- 3 - 3 i \sqrt{3}}{2}$	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	0	0	-1	-1	$\frac{1 - i \sqrt{3}}{2}$	$\frac{1 + i \sqrt{3}}{2}$	$\frac{1 - i \sqrt{3}}{2}$	$\frac{1 + i \sqrt{3}}{2}$
χ₄₆	3	3	$\frac{- 3 + 3 i \sqrt{3}}{2}$	$\frac{- 3 - 3 i \sqrt{3}}{2}$	$\frac{- 3 + 3 i \sqrt{3}}{2}$	$\frac{- 3 - 3 i \sqrt{3}}{2}$	3	-3	-3	$\frac{- 3 + 3 i \sqrt{3}}{2}$	$\frac{- 3 - 3 i \sqrt{3}}{2}$	$\frac{3 - 3 i \sqrt{3}}{2}$	$\frac{3 + 3 i \sqrt{3}}{2}$	$\frac{3 - 3 i \sqrt{3}}{2}$	$\frac{3 + 3 i \sqrt{3}}{2}$	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	0	0	1	-1	$\frac{- 1 + i \sqrt{3}}{2}$	$\frac{- 1 - i \sqrt{3}}{2}$	$\frac{1 - i \sqrt{3}}{2}$	$\frac{1 + i \sqrt{3}}{2}$
χ₄₇	3	3	$\frac{- 3 + 3 i \sqrt{3}}{2}$	$\frac{- 3 - 3 i \sqrt{3}}{2}$	$\frac{- 3 + 3 i \sqrt{3}}{2}$	$\frac{- 3 - 3 i \sqrt{3}}{2}$	3	-3	-3	$\frac{- 3 + 3 i \sqrt{3}}{2}$	$\frac{- 3 - 3 i \sqrt{3}}{2}$	$\frac{3 - 3 i \sqrt{3}}{2}$	$\frac{3 + 3 i \sqrt{3}}{2}$	$\frac{3 - 3 i \sqrt{3}}{2}$	$\frac{3 + 3 i \sqrt{3}}{2}$	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	0	0	-1	1	$\frac{1 - i \sqrt{3}}{2}$	$\frac{1 + i \sqrt{3}}{2}$	$\frac{- 1 + i \sqrt{3}}{2}$	$\frac{- 1 - i \sqrt{3}}{2}$
χ₄₈	6	6	$- 3 - 3 i \sqrt{3}$	$- 3 + 3 i \sqrt{3}$	$- 3 - 3 i \sqrt{3}$	$- 3 + 3 i \sqrt{3}$	-6	0	0	$3 + 3 i \sqrt{3}$	$3 - 3 i \sqrt{3}$	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	0	0	0	0	0
χ₄₉	6	6	$- 3 + 3 i \sqrt{3}$	$- 3 - 3 i \sqrt{3}$	$- 3 + 3 i \sqrt{3}$	$- 3 - 3 i \sqrt{3}$	-6	0	0	$3 - 3 i \sqrt{3}$	$3 + 3 i \sqrt{3}$	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	0	0	0	0	0
χ₅₀	6	-6	$- 3 - 3 i \sqrt{3}$	$- 3 + 3 i \sqrt{3}$	$3 + 3 i \sqrt{3}$	$3 - 3 i \sqrt{3}$	0	$- 3 i \sqrt{2}$	$3 i \sqrt{2}$	0	0	3ζ⁷+3ζ¹³	3ζ⁵+3ζ²³	−3ζ⁷−3ζ¹³	−3ζ⁵−3ζ²³	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	0
χ₅₁	6	-6	$- 3 - 3 i \sqrt{3}$	$- 3 + 3 i \sqrt{3}$	$3 + 3 i \sqrt{3}$	$3 - 3 i \sqrt{3}$	0	$3 i \sqrt{2}$	$- 3 i \sqrt{2}$	0	0	−3ζ⁷−3ζ¹³	−3ζ⁵−3ζ²³	3ζ⁷+3ζ¹³	3ζ⁵+3ζ²³	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	0
χ₅₂	6	-6	$- 3 + 3 i \sqrt{3}$	$- 3 - 3 i \sqrt{3}$	$3 - 3 i \sqrt{3}$	$3 + 3 i \sqrt{3}$	0	$- 3 i \sqrt{2}$	$3 i \sqrt{2}$	0	0	3ζ⁵+3ζ²³	3ζ⁷+3ζ¹³	−3ζ⁵−3ζ²³	−3ζ⁷−3ζ¹³	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	0
χ₅₃	6	-6	$- 3 + 3 i \sqrt{3}$	$- 3 - 3 i \sqrt{3}$	$3 - 3 i \sqrt{3}$	$3 + 3 i \sqrt{3}$	0	$3 i \sqrt{2}$	$- 3 i \sqrt{2}$	0	0	−3ζ⁵−3ζ²³	−3ζ⁷−3ζ¹³	3ζ⁵+3ζ²³	3ζ⁷+3ζ¹³	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	0

Character table — Group #88528