Group #82032 — 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
size	1	1	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	6	6	6	6	8	8	8	8	12	12	12	12	12	12	16	16	16	16	24	24	24	24
order	1	2	2	3	4	4	6	8	8	12	12	16	16	16	16	6	8	12	16	16	24	24	24	24	48	48	48	48	48	48	48	48	2	2	4	4	2	2	4	4	8	8	16	16	16	16	6	6	12	12	2	2	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
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
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
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
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
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
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
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
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	-1	-1	-1	-1	1	-1	1	-1	1	-1	-1	1	1	-1	1	1	-1	-1	1	-1	-1	1	1	-1	1	-1
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	-1	-1	-1	-1	1	-1	1	-1	-1	1	1	-1	1	-1	1	1	-1	-1	-1	1	1	-1	-1	1	-1	1
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	-1	-1	-1	-1	-1	1	-1	1	1	-1	-1	1	-1	1	-1	-1	1	1	1	-1	-1	1	-1	1	-1	1
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	-1	-1	-1	-1	-1	1	-1	1	-1	1	1	-1	-1	1	-1	-1	1	1	-1	1	1	-1	1	-1	1	-1
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	1	1	1	1	1	-1	1	-1	1	1	-1	-1	1	-1	-1	-1	1	1	1	1	-1	-1	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	1	1	1	1	1	-1	1	-1	-1	-1	1	1	1	-1	-1	-1	1	1	-1	-1	1	1	-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	1	1	1	1	-1	1	-1	1	1	1	-1	-1	-1	1	1	1	-1	-1	1	1	-1	-1	-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	1	1	1	1	-1	1	-1	1	-1	-1	1	1	-1	1	1	1	-1	-1	-1	-1	1	1	1	-1	-1	1
χ₁₇	2	2	2	2	2	2	2	-2	-2	2	2	0	0	0	0	2	-2	2	0	0	-2	-2	-2	-2	0	0	0	0	0	0	0	0	2	2	2	2	0	0	0	0	-2	-2	0	0	0	0	0	0	0	0	0	0	0	0
χ₁₈	2	2	2	2	2	2	2	-2	-2	2	2	0	0	0	0	2	-2	2	0	0	-2	-2	-2	-2	0	0	0	0	0	0	0	0	-2	-2	-2	-2	0	0	0	0	2	2	0	0	0	0	0	0	0	0	0	0	0	0
χ₁₉	2	2	2	2	-2	-2	2	0	0	-2	-2	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	2	0	-2	$\sqrt{2}$	$- \sqrt{2}$	0	0	0	0	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	2	-2	-2	2	0	0	0	0	0	0	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	0	0	0	0	0	0	0	0
χ₂₀	2	2	2	2	-2	-2	2	0	0	-2	-2	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	2	0	-2	$\sqrt{2}$	$- \sqrt{2}$	0	0	0	0	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	-2	2	2	-2	0	0	0	0	0	0	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	0	0	0	0	0	0	0	0
χ₂₁	2	2	2	2	-2	-2	2	0	0	-2	-2	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	2	0	-2	$- \sqrt{2}$	$\sqrt{2}$	0	0	0	0	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	2	-2	-2	2	0	0	0	0	0	0	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	0	0	0	0	0	0	0	0
χ₂₂	2	2	2	2	-2	-2	2	0	0	-2	-2	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	2	0	-2	$- \sqrt{2}$	$\sqrt{2}$	0	0	0	0	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	-2	2	2	-2	0	0	0	0	0	0	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	0	0	0	0	0	0	0	0
χ₂₃	2	2	2	-1	2	2	-1	2	2	-1	-1	2	2	2	2	-1	2	-1	2	2	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	0	0	0	0	2	2	2	2	0	0	0	0	0	0	-1	-1	-1	-1	0	0	0	0
χ₂₄	2	2	2	-1	2	2	-1	2	2	-1	-1	2	2	2	2	-1	2	-1	2	2	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	0	0	0	0	-2	-2	-2	-2	0	0	0	0	0	0	1	1	1	1	0	0	0	0
χ₂₅	2	2	2	-1	2	2	-1	2	2	-1	-1	-2	-2	-2	-2	-1	2	-1	-2	-2	-1	-1	-1	-1	1	1	1	1	1	1	1	1	0	0	0	0	2	-2	2	-2	0	0	0	0	0	0	-1	1	-1	1	0	0	0	0
χ₂₆	2	2	2	-1	2	2	-1	2	2	-1	-1	-2	-2	-2	-2	-1	2	-1	-2	-2	-1	-1	-1	-1	1	1	1	1	1	1	1	1	0	0	0	0	-2	2	-2	2	0	0	0	0	0	0	1	-1	1	-1	0	0	0	0
χ₂₇	2	2	-2	2	2	-2	2	0	0	2	2	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	-2	0	-2	$- \sqrt{2}$	$\sqrt{2}$	0	0	0	0	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	2	2	-2	-2	0	0	0	0	0	0	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	0	0	0	0	0	0	0	0
χ₂₈	2	2	-2	2	2	-2	2	0	0	2	2	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	-2	0	-2	$- \sqrt{2}$	$\sqrt{2}$	0	0	0	0	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	-2	-2	2	2	0	0	0	0	0	0	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	0	0	0	0	0	0	0	0
χ₂₉	2	2	-2	2	2	-2	2	0	0	2	2	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	-2	0	-2	$\sqrt{2}$	$- \sqrt{2}$	0	0	0	0	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	2	2	-2	-2	0	0	0	0	0	0	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	0	0	0	0	0	0	0	0
χ₃₀	2	2	-2	2	2	-2	2	0	0	2	2	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	-2	0	-2	$\sqrt{2}$	$- \sqrt{2}$	0	0	0	0	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	-2	-2	2	2	0	0	0	0	0	0	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	0	0	0	0	0	0	0	0
χ₃₁	2	2	-2	2	-2	2	2	-2	-2	-2	-2	0	0	0	0	-2	2	2	0	0	2	2	-2	-2	0	0	0	0	0	0	0	0	2	-2	2	-2	0	0	0	0	-2	2	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₂	2	2	-2	2	-2	2	2	-2	-2	-2	-2	0	0	0	0	-2	2	2	0	0	2	2	-2	-2	0	0	0	0	0	0	0	0	-2	2	-2	2	0	0	0	0	2	-2	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₃	2	2	-2	-1	-2	2	-1	2	2	1	1	2	2	2	2	1	-2	-1	-2	-2	1	1	-1	-1	-1	-1	-1	-1	1	1	1	1	0	0	0	0	2	-2	-2	2	0	0	0	0	0	0	-1	1	1	-1	0	0	0	0
χ₃₄	2	2	-2	-1	-2	2	-1	2	2	1	1	2	2	2	2	1	-2	-1	-2	-2	1	1	-1	-1	-1	-1	-1	-1	1	1	1	1	0	0	0	0	-2	2	2	-2	0	0	0	0	0	0	1	-1	-1	1	0	0	0	0
χ₃₅	2	2	-2	-1	-2	2	-1	2	2	1	1	-2	-2	-2	-2	1	-2	-1	2	2	1	1	-1	-1	1	1	1	1	-1	-1	-1	-1	0	0	0	0	2	2	-2	-2	0	0	0	0	0	0	-1	-1	1	1	0	0	0	0
χ₃₆	2	2	-2	-1	-2	2	-1	2	2	1	1	-2	-2	-2	-2	1	-2	-1	2	2	1	1	-1	-1	1	1	1	1	-1	-1	-1	-1	0	0	0	0	-2	-2	2	2	0	0	0	0	0	0	1	1	-1	-1	0	0	0	0
χ₃₇	4	4	4	-2	4	4	-2	-4	-4	-2	-2	0	0	0	0	-2	-4	-2	0	0	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	0	0	0	0	0	0
χ₃₈	4	4	4	-2	-4	-4	-2	0	0	2	2	$2 \sqrt{2}$	$2 \sqrt{2}$	$- 2 \sqrt{2}$	$- 2 \sqrt{2}$	-2	0	2	$2 \sqrt{2}$	$- 2 \sqrt{2}$	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	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₉	4	4	4	-2	-4	-4	-2	0	0	2	2	$- 2 \sqrt{2}$	$- 2 \sqrt{2}$	$2 \sqrt{2}$	$2 \sqrt{2}$	-2	0	2	$- 2 \sqrt{2}$	$2 \sqrt{2}$	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	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₀	4	4	-4	-2	4	-4	-2	0	0	-2	-2	$2 \sqrt{2}$	$2 \sqrt{2}$	$- 2 \sqrt{2}$	$- 2 \sqrt{2}$	2	0	2	$- 2 \sqrt{2}$	$2 \sqrt{2}$	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	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₁	4	4	-4	-2	4	-4	-2	0	0	-2	-2	$- 2 \sqrt{2}$	$- 2 \sqrt{2}$	$2 \sqrt{2}$	$2 \sqrt{2}$	2	0	2	$2 \sqrt{2}$	$- 2 \sqrt{2}$	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	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₂	4	4	-4	-2	-4	4	-2	-4	-4	2	2	0	0	0	0	2	4	-2	0	0	-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	0	0	0	0	0	0
χ₄₃	4	-4	0	4	0	0	-4	$2 \sqrt{2}$	$- 2 \sqrt{2}$	0	0	−2ζ²⁵−2ζ³¹−2ζ⁴¹−2ζ⁴⁷	2ζ²⁵+2ζ³¹+2ζ⁴¹+2ζ⁴⁷	2ζ¹¹+2ζ¹³+2ζ²⁹+2ζ⁴³	−2ζ¹¹−2ζ¹³−2ζ²⁹−2ζ⁴³	0	0	0	0	0	0	0	$2 \sqrt{2}$	$- 2 \sqrt{2}$	−2ζ²⁵−2ζ³¹−2ζ⁴¹−2ζ⁴⁷	2ζ²⁵+2ζ³¹+2ζ⁴¹+2ζ⁴⁷	2ζ¹¹+2ζ¹³+2ζ²⁹+2ζ⁴³	−2ζ¹¹−2ζ¹³−2ζ²⁹−2ζ⁴³	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	4	0	0	-4	$2 \sqrt{2}$	$- 2 \sqrt{2}$	0	0	2ζ²⁵+2ζ³¹+2ζ⁴¹+2ζ⁴⁷	−2ζ²⁵−2ζ³¹−2ζ⁴¹−2ζ⁴⁷	−2ζ¹¹−2ζ¹³−2ζ²⁹−2ζ⁴³	2ζ¹¹+2ζ¹³+2ζ²⁹+2ζ⁴³	0	0	0	0	0	0	0	$2 \sqrt{2}$	$- 2 \sqrt{2}$	2ζ²⁵+2ζ³¹+2ζ⁴¹+2ζ⁴⁷	−2ζ²⁵−2ζ³¹−2ζ⁴¹−2ζ⁴⁷	−2ζ¹¹−2ζ¹³−2ζ²⁹−2ζ⁴³	2ζ¹¹+2ζ¹³+2ζ²⁹+2ζ⁴³	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	4	0	0	-4	$- 2 \sqrt{2}$	$2 \sqrt{2}$	0	0	2ζ¹¹+2ζ¹³+2ζ²⁹+2ζ⁴³	−2ζ¹¹−2ζ¹³−2ζ²⁹−2ζ⁴³	2ζ²⁵+2ζ³¹+2ζ⁴¹+2ζ⁴⁷	−2ζ²⁵−2ζ³¹−2ζ⁴¹−2ζ⁴⁷	0	0	0	0	0	0	0	$- 2 \sqrt{2}$	$2 \sqrt{2}$	2ζ¹¹+2ζ¹³+2ζ²⁹+2ζ⁴³	−2ζ¹¹−2ζ¹³−2ζ²⁹−2ζ⁴³	2ζ²⁵+2ζ³¹+2ζ⁴¹+2ζ⁴⁷	−2ζ²⁵−2ζ³¹−2ζ⁴¹−2ζ⁴⁷	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	4	0	0	-4	$- 2 \sqrt{2}$	$2 \sqrt{2}$	0	0	−2ζ¹¹−2ζ¹³−2ζ²⁹−2ζ⁴³	2ζ¹¹+2ζ¹³+2ζ²⁹+2ζ⁴³	−2ζ²⁵−2ζ³¹−2ζ⁴¹−2ζ⁴⁷	2ζ²⁵+2ζ³¹+2ζ⁴¹+2ζ⁴⁷	0	0	0	0	0	0	0	$- 2 \sqrt{2}$	$2 \sqrt{2}$	−2ζ¹¹−2ζ¹³−2ζ²⁹−2ζ⁴³	2ζ¹¹+2ζ¹³+2ζ²⁹+2ζ⁴³	−2ζ²⁵−2ζ³¹−2ζ⁴¹−2ζ⁴⁷	2ζ²⁵+2ζ³¹+2ζ⁴¹+2ζ⁴⁷	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	0	-2	0	0	2	$2 \sqrt{2}$	$- 2 \sqrt{2}$	$2 \sqrt{3}$	$- 2 \sqrt{3}$	−2ζ²⁵−2ζ³¹−2ζ⁴¹−2ζ⁴⁷	2ζ²⁵+2ζ³¹+2ζ⁴¹+2ζ⁴⁷	2ζ¹¹+2ζ¹³+2ζ²⁹+2ζ⁴³	−2ζ¹¹−2ζ¹³−2ζ²⁹−2ζ⁴³	0	0	0	0	0	$\sqrt{6}$	$- \sqrt{6}$	$- \sqrt{2}$	$\sqrt{2}$	ζ²⁵+ζ³¹+ζ⁴¹+ζ⁴⁷	−ζ²⁵−ζ³¹−ζ⁴¹−ζ⁴⁷	−ζ¹¹−ζ¹³−ζ²⁹−ζ⁴³	ζ¹¹+ζ¹³+ζ²⁹+ζ⁴³	−ζ²⁵+ζ³¹+ζ⁴¹−ζ⁴⁷	ζ²⁵−ζ³¹−ζ⁴¹+ζ⁴⁷	−ζ¹¹−ζ¹³+ζ²⁹+ζ⁴³	ζ¹¹+ζ¹³−ζ²⁹−ζ⁴³	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	0	-2	0	0	2	$2 \sqrt{2}$	$- 2 \sqrt{2}$	$2 \sqrt{3}$	$- 2 \sqrt{3}$	2ζ²⁵+2ζ³¹+2ζ⁴¹+2ζ⁴⁷	−2ζ²⁵−2ζ³¹−2ζ⁴¹−2ζ⁴⁷	−2ζ¹¹−2ζ¹³−2ζ²⁹−2ζ⁴³	2ζ¹¹+2ζ¹³+2ζ²⁹+2ζ⁴³	0	0	0	0	0	$\sqrt{6}$	$- \sqrt{6}$	$- \sqrt{2}$	$\sqrt{2}$	−ζ²⁵−ζ³¹−ζ⁴¹−ζ⁴⁷	ζ²⁵+ζ³¹+ζ⁴¹+ζ⁴⁷	ζ¹¹+ζ¹³+ζ²⁹+ζ⁴³	−ζ¹¹−ζ¹³−ζ²⁹−ζ⁴³	ζ²⁵−ζ³¹−ζ⁴¹+ζ⁴⁷	−ζ²⁵+ζ³¹+ζ⁴¹−ζ⁴⁷	ζ¹¹+ζ¹³−ζ²⁹−ζ⁴³	−ζ¹¹−ζ¹³+ζ²⁹+ζ⁴³	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	0	-2	0	0	2	$2 \sqrt{2}$	$- 2 \sqrt{2}$	$- 2 \sqrt{3}$	$2 \sqrt{3}$	−2ζ²⁵−2ζ³¹−2ζ⁴¹−2ζ⁴⁷	2ζ²⁵+2ζ³¹+2ζ⁴¹+2ζ⁴⁷	2ζ¹¹+2ζ¹³+2ζ²⁹+2ζ⁴³	−2ζ¹¹−2ζ¹³−2ζ²⁹−2ζ⁴³	0	0	0	0	0	$- \sqrt{6}$	$\sqrt{6}$	$- \sqrt{2}$	$\sqrt{2}$	ζ²⁵+ζ³¹+ζ⁴¹+ζ⁴⁷	−ζ²⁵−ζ³¹−ζ⁴¹−ζ⁴⁷	−ζ¹¹−ζ¹³−ζ²⁹−ζ⁴³	ζ¹¹+ζ¹³+ζ²⁹+ζ⁴³	ζ²⁵−ζ³¹−ζ⁴¹+ζ⁴⁷	−ζ²⁵+ζ³¹+ζ⁴¹−ζ⁴⁷	ζ¹¹+ζ¹³−ζ²⁹−ζ⁴³	−ζ¹¹−ζ¹³+ζ²⁹+ζ⁴³	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	0	-2	0	0	2	$2 \sqrt{2}$	$- 2 \sqrt{2}$	$- 2 \sqrt{3}$	$2 \sqrt{3}$	2ζ²⁵+2ζ³¹+2ζ⁴¹+2ζ⁴⁷	−2ζ²⁵−2ζ³¹−2ζ⁴¹−2ζ⁴⁷	−2ζ¹¹−2ζ¹³−2ζ²⁹−2ζ⁴³	2ζ¹¹+2ζ¹³+2ζ²⁹+2ζ⁴³	0	0	0	0	0	$- \sqrt{6}$	$\sqrt{6}$	$- \sqrt{2}$	$\sqrt{2}$	−ζ²⁵−ζ³¹−ζ⁴¹−ζ⁴⁷	ζ²⁵+ζ³¹+ζ⁴¹+ζ⁴⁷	ζ¹¹+ζ¹³+ζ²⁹+ζ⁴³	−ζ¹¹−ζ¹³−ζ²⁹−ζ⁴³	−ζ²⁵+ζ³¹+ζ⁴¹−ζ⁴⁷	ζ²⁵−ζ³¹−ζ⁴¹+ζ⁴⁷	−ζ¹¹−ζ¹³+ζ²⁹+ζ⁴³	ζ¹¹+ζ¹³−ζ²⁹−ζ⁴³	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	0	-2	0	0	2	$- 2 \sqrt{2}$	$2 \sqrt{2}$	$2 \sqrt{3}$	$- 2 \sqrt{3}$	2ζ¹¹+2ζ¹³+2ζ²⁹+2ζ⁴³	−2ζ¹¹−2ζ¹³−2ζ²⁹−2ζ⁴³	2ζ²⁵+2ζ³¹+2ζ⁴¹+2ζ⁴⁷	−2ζ²⁵−2ζ³¹−2ζ⁴¹−2ζ⁴⁷	0	0	0	0	0	$- \sqrt{6}$	$\sqrt{6}$	$\sqrt{2}$	$- \sqrt{2}$	−ζ¹¹−ζ¹³−ζ²⁹−ζ⁴³	ζ¹¹+ζ¹³+ζ²⁹+ζ⁴³	−ζ²⁵−ζ³¹−ζ⁴¹−ζ⁴⁷	ζ²⁵+ζ³¹+ζ⁴¹+ζ⁴⁷	ζ¹¹+ζ¹³−ζ²⁹−ζ⁴³	−ζ¹¹−ζ¹³+ζ²⁹+ζ⁴³	−ζ²⁵+ζ³¹+ζ⁴¹−ζ⁴⁷	ζ²⁵−ζ³¹−ζ⁴¹+ζ⁴⁷	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	0	-2	0	0	2	$- 2 \sqrt{2}$	$2 \sqrt{2}$	$2 \sqrt{3}$	$- 2 \sqrt{3}$	−2ζ¹¹−2ζ¹³−2ζ²⁹−2ζ⁴³	2ζ¹¹+2ζ¹³+2ζ²⁹+2ζ⁴³	−2ζ²⁵−2ζ³¹−2ζ⁴¹−2ζ⁴⁷	2ζ²⁵+2ζ³¹+2ζ⁴¹+2ζ⁴⁷	0	0	0	0	0	$- \sqrt{6}$	$\sqrt{6}$	$\sqrt{2}$	$- \sqrt{2}$	ζ¹¹+ζ¹³+ζ²⁹+ζ⁴³	−ζ¹¹−ζ¹³−ζ²⁹−ζ⁴³	ζ²⁵+ζ³¹+ζ⁴¹+ζ⁴⁷	−ζ²⁵−ζ³¹−ζ⁴¹−ζ⁴⁷	−ζ¹¹−ζ¹³+ζ²⁹+ζ⁴³	ζ¹¹+ζ¹³−ζ²⁹−ζ⁴³	ζ²⁵−ζ³¹−ζ⁴¹+ζ⁴⁷	−ζ²⁵+ζ³¹+ζ⁴¹−ζ⁴⁷	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₅₃	4	-4	0	-2	0	0	2	$- 2 \sqrt{2}$	$2 \sqrt{2}$	$- 2 \sqrt{3}$	$2 \sqrt{3}$	2ζ¹¹+2ζ¹³+2ζ²⁹+2ζ⁴³	−2ζ¹¹−2ζ¹³−2ζ²⁹−2ζ⁴³	2ζ²⁵+2ζ³¹+2ζ⁴¹+2ζ⁴⁷	−2ζ²⁵−2ζ³¹−2ζ⁴¹−2ζ⁴⁷	0	0	0	0	0	$\sqrt{6}$	$- \sqrt{6}$	$\sqrt{2}$	$- \sqrt{2}$	−ζ¹¹−ζ¹³−ζ²⁹−ζ⁴³	ζ¹¹+ζ¹³+ζ²⁹+ζ⁴³	−ζ²⁵−ζ³¹−ζ⁴¹−ζ⁴⁷	ζ²⁵+ζ³¹+ζ⁴¹+ζ⁴⁷	−ζ¹¹−ζ¹³+ζ²⁹+ζ⁴³	ζ¹¹+ζ¹³−ζ²⁹−ζ⁴³	ζ²⁵−ζ³¹−ζ⁴¹+ζ⁴⁷	−ζ²⁵+ζ³¹+ζ⁴¹−ζ⁴⁷	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₅₄	4	-4	0	-2	0	0	2	$- 2 \sqrt{2}$	$2 \sqrt{2}$	$- 2 \sqrt{3}$	$2 \sqrt{3}$	−2ζ¹¹−2ζ¹³−2ζ²⁹−2ζ⁴³	2ζ¹¹+2ζ¹³+2ζ²⁹+2ζ⁴³	−2ζ²⁵−2ζ³¹−2ζ⁴¹−2ζ⁴⁷	2ζ²⁵+2ζ³¹+2ζ⁴¹+2ζ⁴⁷	0	0	0	0	0	$\sqrt{6}$	$- \sqrt{6}$	$\sqrt{2}$	$- \sqrt{2}$	ζ¹¹+ζ¹³+ζ²⁹+ζ⁴³	−ζ¹¹−ζ¹³−ζ²⁹−ζ⁴³	ζ²⁵+ζ³¹+ζ⁴¹+ζ⁴⁷	−ζ²⁵−ζ³¹−ζ⁴¹−ζ⁴⁷	ζ¹¹+ζ¹³−ζ²⁹−ζ⁴³	−ζ¹¹−ζ¹³+ζ²⁹+ζ⁴³	−ζ²⁵+ζ³¹+ζ⁴¹−ζ⁴⁷	ζ²⁵−ζ³¹−ζ⁴¹+ζ⁴⁷	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 #82032