Group #69269 — 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
size	1	1	2	2	2	2	2	2	2	4	4	4	4	4	4	8	8	8	8	8	8	8	8	8	12	12	12	12	12	12	16	16	16	16	16	24	24	24	48
order	1	2	2	3	4	4	6	8	8	6	8	12	12	24	24	4	4	16	16	24	48	48	48	48	2	4	16	16	16	16	8	12	12	24	24	2	4	8	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
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
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
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
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
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
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
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
χ₉	2	2	2	2	2	2	2	-2	-2	2	-2	2	2	-2	-2	0	0	0	0	-2	0	0	0	0	2	2	0	0	0	0	0	0	0	0	0	0	0	-2	0
χ₁₀	2	2	2	2	2	2	2	-2	-2	2	-2	2	2	-2	-2	0	0	0	0	-2	0	0	0	0	-2	-2	0	0	0	0	0	0	0	0	0	0	0	2	0
χ₁₁	2	2	2	-1	2	2	-1	2	2	-1	2	-1	-1	-1	-1	2	2	2	2	-1	-1	-1	-1	-1	0	0	0	0	0	0	2	-1	-1	-1	-1	0	0	0	0
χ₁₂	2	2	2	-1	2	2	-1	2	2	-1	2	-1	-1	-1	-1	2	2	-2	-2	-1	1	1	1	1	0	0	0	0	0	0	-2	-1	-1	1	1	0	0	0	0
χ₁₃	2	2	2	-1	2	2	-1	2	2	-1	2	-1	-1	-1	-1	-2	-2	2	2	-1	-1	-1	-1	-1	0	0	0	0	0	0	-2	1	1	1	1	0	0	0	0
χ₁₄	2	2	2	-1	2	2	-1	2	2	-1	2	-1	-1	-1	-1	-2	-2	-2	-2	-1	1	1	1	1	0	0	0	0	0	0	2	1	1	-1	-1	0	0	0	0
χ₁₅	2	2	-2	2	2	-2	2	0	0	-2	0	-2	2	0	0	0	0	$\sqrt{2}$	$- \sqrt{2}$	0	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	2	-2	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	0	0	0	0	0	0	0	0	0
χ₁₆	2	2	-2	2	2	-2	2	0	0	-2	0	-2	2	0	0	0	0	$\sqrt{2}$	$- \sqrt{2}$	0	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	-2	2	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	0	0	0	0	0	0	0	0	0
χ₁₇	2	2	-2	2	2	-2	2	0	0	-2	0	-2	2	0	0	0	0	$- \sqrt{2}$	$\sqrt{2}$	0	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	2	-2	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	0	0	0	0	0	0	0	0	0
χ₁₈	2	2	-2	2	2	-2	2	0	0	-2	0	-2	2	0	0	0	0	$- \sqrt{2}$	$\sqrt{2}$	0	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	-2	2	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	0	0	0	0	0	0	0	0	0
χ₁₉	2	2	-2	2	-2	2	2	2	2	-2	-2	2	-2	2	2	0	0	0	0	-2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	2	-2	0	0
χ₂₀	2	2	-2	2	-2	2	2	2	2	-2	-2	2	-2	2	2	0	0	0	0	-2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	-2	2	0	0
χ₂₁	2	2	-2	2	-2	2	2	-2	-2	-2	2	2	-2	-2	-2	2	-2	0	0	2	0	0	0	0	0	0	0	0	0	0	0	2	-2	0	0	0	0	0	0
χ₂₂	2	2	-2	2	-2	2	2	-2	-2	-2	2	2	-2	-2	-2	-2	2	0	0	2	0	0	0	0	0	0	0	0	0	0	0	-2	2	0	0	0	0	0	0
χ₂₃	2	2	-2	-1	-2	2	-1	-2	-2	1	2	-1	1	1	1	2	-2	0	0	-1	$\sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	0	0	0	0	0	0	0	-1	1	$\sqrt{3}$	$- \sqrt{3}$	0	0	0	0
χ₂₄	2	2	-2	-1	-2	2	-1	-2	-2	1	2	-1	1	1	1	2	-2	0	0	-1	$- \sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	0	0	0	0	0	0	0	-1	1	$- \sqrt{3}$	$\sqrt{3}$	0	0	0	0
χ₂₅	2	2	-2	-1	-2	2	-1	-2	-2	1	2	-1	1	1	1	-2	2	0	0	-1	$\sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	0	0	0	0	0	0	0	1	-1	$- \sqrt{3}$	$\sqrt{3}$	0	0	0	0
χ₂₆	2	2	-2	-1	-2	2	-1	-2	-2	1	2	-1	1	1	1	-2	2	0	0	-1	$- \sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	0	0	0	0	0	0	0	1	-1	$\sqrt{3}$	$- \sqrt{3}$	0	0	0	0
χ₂₇	4	4	4	4	-4	-4	4	0	0	4	0	-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
χ₂₈	4	4	4	-2	4	4	-2	-4	-4	-2	-4	-2	-2	2	2	0	0	0	0	2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₉	4	4	4	-2	-4	-4	-2	0	0	-2	0	2	2	0	0	0	0	0	0	0	$\sqrt{6}$	$- \sqrt{6}$	$- \sqrt{6}$	$\sqrt{6}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₀	4	4	4	-2	-4	-4	-2	0	0	-2	0	2	2	0	0	0	0	0	0	0	$- \sqrt{6}$	$\sqrt{6}$	$\sqrt{6}$	$- \sqrt{6}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₁	4	4	-4	-2	4	-4	-2	0	0	2	0	2	-2	0	0	0	0	$2 \sqrt{2}$	$- 2 \sqrt{2}$	0	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	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	0	2	-2	0	0	0	0	$- 2 \sqrt{2}$	$2 \sqrt{2}$	0	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₃	4	4	-4	-2	-4	4	-2	4	4	2	-4	-2	2	-2	-2	0	0	0	0	2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₄	4	-4	0	4	0	0	-4	$2 \sqrt{2}$	$- 2 \sqrt{2}$	0	0	0	0	$2 \sqrt{2}$	$- 2 \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0	ζ¹¹−ζ¹³−ζ²⁵−ζ²⁹+ζ³¹−ζ⁴¹+ζ⁴³+ζ⁴⁷	−ζ¹¹+ζ¹³+ζ²⁵+ζ²⁹−ζ³¹+ζ⁴¹−ζ⁴³−ζ⁴⁷	ζ¹¹−ζ¹³+ζ²⁵−ζ²⁹−ζ³¹+ζ⁴¹+ζ⁴³−ζ⁴⁷	−ζ¹¹+ζ¹³−ζ²⁵+ζ²⁹+ζ³¹−ζ⁴¹−ζ⁴³+ζ⁴⁷	0	0	0	0	0	0	0	0	0
χ₃₅	4	-4	0	4	0	0	-4	$2 \sqrt{2}$	$- 2 \sqrt{2}$	0	0	0	0	$2 \sqrt{2}$	$- 2 \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0	−ζ¹¹+ζ¹³+ζ²⁵+ζ²⁹−ζ³¹+ζ⁴¹−ζ⁴³−ζ⁴⁷	ζ¹¹−ζ¹³−ζ²⁵−ζ²⁹+ζ³¹−ζ⁴¹+ζ⁴³+ζ⁴⁷	−ζ¹¹+ζ¹³−ζ²⁵+ζ²⁹+ζ³¹−ζ⁴¹−ζ⁴³+ζ⁴⁷	ζ¹¹−ζ¹³+ζ²⁵−ζ²⁹−ζ³¹+ζ⁴¹+ζ⁴³−ζ⁴⁷	0	0	0	0	0	0	0	0	0
χ₃₆	4	-4	0	4	0	0	-4	$- 2 \sqrt{2}$	$2 \sqrt{2}$	0	0	0	0	$- 2 \sqrt{2}$	$2 \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0	ζ¹¹−ζ¹³+ζ²⁵−ζ²⁹−ζ³¹+ζ⁴¹+ζ⁴³−ζ⁴⁷	−ζ¹¹+ζ¹³−ζ²⁵+ζ²⁹+ζ³¹−ζ⁴¹−ζ⁴³+ζ⁴⁷	−ζ¹¹+ζ¹³+ζ²⁵+ζ²⁹−ζ³¹+ζ⁴¹−ζ⁴³−ζ⁴⁷	ζ¹¹−ζ¹³−ζ²⁵−ζ²⁹+ζ³¹−ζ⁴¹+ζ⁴³+ζ⁴⁷	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	0	0	$- 2 \sqrt{2}$	$2 \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0	−ζ¹¹+ζ¹³−ζ²⁵+ζ²⁹+ζ³¹−ζ⁴¹−ζ⁴³+ζ⁴⁷	ζ¹¹−ζ¹³+ζ²⁵−ζ²⁹−ζ³¹+ζ⁴¹+ζ⁴³−ζ⁴⁷	ζ¹¹−ζ¹³−ζ²⁵−ζ²⁹+ζ³¹−ζ⁴¹+ζ⁴³+ζ⁴⁷	−ζ¹¹+ζ¹³+ζ²⁵+ζ²⁹−ζ³¹+ζ⁴¹−ζ⁴³−ζ⁴⁷	0	0	0	0	0	0	0	0	0
χ₃₈	8	-8	0	-4	0	0	4	$4 \sqrt{2}$	$- 4 \sqrt{2}$	0	0	0	0	$- 2 \sqrt{2}$	$2 \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₉	8	-8	0	-4	0	0	4	$- 4 \sqrt{2}$	$4 \sqrt{2}$	0	0	0	0	$2 \sqrt{2}$	$- 2 \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0

Character table — Group #69269