Group #67828 — 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
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	12	12	12	12	12	12	12	12	16	16	16	16	16	16	48	48
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	32	32	32	32	32	32	32	32	2	4	6	6	12	12	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
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
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
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
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	$i$	$i$	$i$	$i$	$- i$	$- i$	$- i$	$- i$	1	-1	1	1	-1	-1	$i$	$- i$
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	$i$	$i$	$i$	$i$	$- i$	$- i$	$- i$	$- i$	-1	1	-1	-1	1	1	$- i$	$i$
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	$- i$	$- i$	$- i$	$- i$	$i$	$i$	$i$	$i$	1	-1	1	1	-1	-1	$- i$	$i$
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	$- i$	$- i$	$- i$	$- i$	$i$	$i$	$i$	$i$	-1	1	-1	-1	1	1	$i$	$- i$
χ₉	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	-2	-2	-2	-2	0	0	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	0	0	0	0	2	-2	2	0	0	-2	-2	-2	-2	0	0	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	0	0
χ₁₁	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	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	0	0	0	0	0	0	0	0
χ₁₂	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	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	−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
χ₁₃	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	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	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
χ₁₄	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	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	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
χ₁₅	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	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	−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
χ₁₆	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	0	0	0	0	2	2	-1	-1	-1	-1	0	0
χ₁₇	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	0	0	0	0	-2	-2	1	1	1	1	0	0
χ₁₈	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	0	0	0	0	0	0	$- i \sqrt{3}$	$i \sqrt{3}$	$- i \sqrt{3}$	$i \sqrt{3}$	0	0
χ₁₉	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	0	0	0	0	0	0	$i \sqrt{3}$	$- i \sqrt{3}$	$i \sqrt{3}$	$- i \sqrt{3}$	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	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	−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
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	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	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
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	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	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
χ₂₃	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	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	−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
χ₂₄	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	2	2	2	2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₅	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	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	0	0	0	0	0	0	0	0
χ₂₆	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	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	0	0	0	0	0	0	0	0
χ₂₇	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	0	0	0	0	0	0	$- i \sqrt{3}$	$i \sqrt{3}$	$i \sqrt{3}$	$- i \sqrt{3}$	0	0
χ₂₈	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	0	0	0	0	0	0	$i \sqrt{3}$	$- i \sqrt{3}$	$- i \sqrt{3}$	$i \sqrt{3}$	0	0
χ₂₉	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	0	0	0	0	2	-2	-1	-1	1	1	0	0
χ₃₀	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	0	0	0	0	-2	2	1	1	-1	-1	0	0
χ₃₁	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
χ₃₂	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
χ₃₃	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
χ₃₄	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
χ₃₅	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
χ₃₆	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
χ₃₇	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	$2 \sqrt{2}$	$- 2 \sqrt{2}$	0	0	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	0	0	0	0	0	0	0	0	0
χ₃₈	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	$2 \sqrt{2}$	$- 2 \sqrt{2}$	0	0	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	0	0	0	0	0	0	0	0	0
χ₃₉	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	$- 2 \sqrt{2}$	$2 \sqrt{2}$	0	0	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	0	0	0	0	0	0	0	0	0
χ₄₀	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	$- 2 \sqrt{2}$	$2 \sqrt{2}$	0	0	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	0	0	0	0	0	0	0	0	0
χ₄₁	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
χ₄₂	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
χ₄₃	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
χ₄₄	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
χ₄₅	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
χ₄₆	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
χ₄₇	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
χ₄₈	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

Character table — Group #67828