Group #4567 — 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
size	1	1	1	1	2	2	2	2	2	2	2	2	2	2	4	4	4	4	4	4	6	6	6	6	6	6	6	6	8	8	8	8	8	8	24	24
order	1	2	4	4	2	3	4	6	8	8	8	8	12	12	6	12	24	24	24	24	16	16	16	16	16	16	16	16	2	4	6	6	12	12	8	8
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
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
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
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
χ₅	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	$i$	$i$	$i$	$i$	$- i$	$- i$	$- i$	$- i$	-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	$- i$	$- i$	$- i$	$- i$	$i$	$i$	$i$	$i$	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	$- i$	$- i$	$- i$	$- i$	$i$	$i$	$i$	$i$	-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	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₁₀	2	2	2	2	2	-1	2	-1	2	2	2	2	-1	-1	-1	-1	-1	-1	-1	-1	0	0	0	0	0	0	0	0	2	2	-1	-1	-1	-1	0	0
χ₁₁	2	2	2	2	2	-1	2	-1	2	2	2	2	-1	-1	-1	-1	-1	-1	-1	-1	0	0	0	0	0	0	0	0	-2	-2	1	1	1	1	0	0
χ₁₂	2	2	2	2	2	-1	2	-1	-2	-2	-2	-2	-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
χ₁₃	2	2	2	2	2	-1	2	-1	-2	-2	-2	-2	-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
χ₁₄	2	2	2	2	-2	2	-2	2	0	0	0	0	2	2	-2	-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
χ₁₅	2	2	2	2	-2	2	-2	2	0	0	0	0	2	2	-2	-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
χ₁₆	2	2	-2	-2	2	2	-2	2	0	0	0	0	-2	-2	2	-2	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
χ₁₇	2	2	-2	-2	2	2	-2	2	0	0	0	0	-2	-2	2	-2	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
χ₁₈	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
χ₁₉	2	2	-2	-2	-2	-1	2	-1	2	2	-2	-2	1	1	1	-1	-1	-1	1	1	0	0	0	0	0	0	0	0	2	-2	-1	-1	1	1	0	0
χ₂₀	2	2	-2	-2	-2	-1	2	-1	2	2	-2	-2	1	1	1	-1	-1	-1	1	1	0	0	0	0	0	0	0	0	-2	2	1	1	-1	-1	0	0
χ₂₁	2	2	-2	-2	-2	-1	2	-1	-2	-2	2	2	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
χ₂₂	2	2	-2	-2	-2	-1	2	-1	-2	-2	2	2	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
χ₂₃	2	-2	$2 i$	$- 2 i$	0	2	0	-2	$\sqrt{2}$	$- \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$2 i$	$- 2 i$	0	0	$\sqrt{2}$	$- \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	ζ¹¹−ζ²⁵−ζ⁴¹+ζ⁴³	−ζ¹¹+ζ²⁵+ζ⁴¹−ζ⁴³	−ζ¹³−ζ²⁹−ζ³¹−ζ⁴⁷	ζ¹³+ζ²⁹+ζ³¹+ζ⁴⁷	−ζ¹³−ζ²⁹+ζ³¹+ζ⁴⁷	ζ¹³+ζ²⁹−ζ³¹−ζ⁴⁷	ζ¹¹+ζ²⁵+ζ⁴¹+ζ⁴³	−ζ¹¹−ζ²⁵−ζ⁴¹−ζ⁴³	0	0	0	0	0	0	0	0
χ₂₄	2	-2	$2 i$	$- 2 i$	0	2	0	-2	$\sqrt{2}$	$- \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$2 i$	$- 2 i$	0	0	$\sqrt{2}$	$- \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	−ζ¹¹+ζ²⁵+ζ⁴¹−ζ⁴³	ζ¹¹−ζ²⁵−ζ⁴¹+ζ⁴³	ζ¹³+ζ²⁹+ζ³¹+ζ⁴⁷	−ζ¹³−ζ²⁹−ζ³¹−ζ⁴⁷	ζ¹³+ζ²⁹−ζ³¹−ζ⁴⁷	−ζ¹³−ζ²⁹+ζ³¹+ζ⁴⁷	−ζ¹¹−ζ²⁵−ζ⁴¹−ζ⁴³	ζ¹¹+ζ²⁵+ζ⁴¹+ζ⁴³	0	0	0	0	0	0	0	0
χ₂₅	2	-2	$2 i$	$- 2 i$	0	2	0	-2	$- \sqrt{2}$	$\sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$2 i$	$- 2 i$	0	0	$- \sqrt{2}$	$\sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	−ζ¹³−ζ²⁹−ζ³¹−ζ⁴⁷	ζ¹³+ζ²⁹+ζ³¹+ζ⁴⁷	−ζ¹¹+ζ²⁵+ζ⁴¹−ζ⁴³	ζ¹¹−ζ²⁵−ζ⁴¹+ζ⁴³	ζ¹¹+ζ²⁵+ζ⁴¹+ζ⁴³	−ζ¹¹−ζ²⁵−ζ⁴¹−ζ⁴³	ζ¹³+ζ²⁹−ζ³¹−ζ⁴⁷	−ζ¹³−ζ²⁹+ζ³¹+ζ⁴⁷	0	0	0	0	0	0	0	0
χ₂₆	2	-2	$2 i$	$- 2 i$	0	2	0	-2	$- \sqrt{2}$	$\sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$2 i$	$- 2 i$	0	0	$- \sqrt{2}$	$\sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	ζ¹³+ζ²⁹+ζ³¹+ζ⁴⁷	−ζ¹³−ζ²⁹−ζ³¹−ζ⁴⁷	ζ¹¹−ζ²⁵−ζ⁴¹+ζ⁴³	−ζ¹¹+ζ²⁵+ζ⁴¹−ζ⁴³	−ζ¹¹−ζ²⁵−ζ⁴¹−ζ⁴³	ζ¹¹+ζ²⁵+ζ⁴¹+ζ⁴³	−ζ¹³−ζ²⁹+ζ³¹+ζ⁴⁷	ζ¹³+ζ²⁹−ζ³¹−ζ⁴⁷	0	0	0	0	0	0	0	0
χ₂₇	2	-2	$- 2 i$	$2 i$	0	2	0	-2	$\sqrt{2}$	$- \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$- 2 i$	$2 i$	0	0	$\sqrt{2}$	$- \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	−ζ¹³−ζ²⁹+ζ³¹+ζ⁴⁷	ζ¹³+ζ²⁹−ζ³¹−ζ⁴⁷	ζ¹¹+ζ²⁵+ζ⁴¹+ζ⁴³	−ζ¹¹−ζ²⁵−ζ⁴¹−ζ⁴³	ζ¹¹−ζ²⁵−ζ⁴¹+ζ⁴³	−ζ¹¹+ζ²⁵+ζ⁴¹−ζ⁴³	−ζ¹³−ζ²⁹−ζ³¹−ζ⁴⁷	ζ¹³+ζ²⁹+ζ³¹+ζ⁴⁷	0	0	0	0	0	0	0	0
χ₂₈	2	-2	$- 2 i$	$2 i$	0	2	0	-2	$\sqrt{2}$	$- \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$- 2 i$	$2 i$	0	0	$\sqrt{2}$	$- \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	ζ¹³+ζ²⁹−ζ³¹−ζ⁴⁷	−ζ¹³−ζ²⁹+ζ³¹+ζ⁴⁷	−ζ¹¹−ζ²⁵−ζ⁴¹−ζ⁴³	ζ¹¹+ζ²⁵+ζ⁴¹+ζ⁴³	−ζ¹¹+ζ²⁵+ζ⁴¹−ζ⁴³	ζ¹¹−ζ²⁵−ζ⁴¹+ζ⁴³	ζ¹³+ζ²⁹+ζ³¹+ζ⁴⁷	−ζ¹³−ζ²⁹−ζ³¹−ζ⁴⁷	0	0	0	0	0	0	0	0
χ₂₉	2	-2	$- 2 i$	$2 i$	0	2	0	-2	$- \sqrt{2}$	$\sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$- 2 i$	$2 i$	0	0	$- \sqrt{2}$	$\sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	ζ¹¹+ζ²⁵+ζ⁴¹+ζ⁴³	−ζ¹¹−ζ²⁵−ζ⁴¹−ζ⁴³	ζ¹³+ζ²⁹−ζ³¹−ζ⁴⁷	−ζ¹³−ζ²⁹+ζ³¹+ζ⁴⁷	−ζ¹³−ζ²⁹−ζ³¹−ζ⁴⁷	ζ¹³+ζ²⁹+ζ³¹+ζ⁴⁷	−ζ¹¹+ζ²⁵+ζ⁴¹−ζ⁴³	ζ¹¹−ζ²⁵−ζ⁴¹+ζ⁴³	0	0	0	0	0	0	0	0
χ₃₀	2	-2	$- 2 i$	$2 i$	0	2	0	-2	$- \sqrt{2}$	$\sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$- 2 i$	$2 i$	0	0	$- \sqrt{2}$	$\sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	−ζ¹¹−ζ²⁵−ζ⁴¹−ζ⁴³	ζ¹¹+ζ²⁵+ζ⁴¹+ζ⁴³	−ζ¹³−ζ²⁹+ζ³¹+ζ⁴⁷	ζ¹³+ζ²⁹−ζ³¹−ζ⁴⁷	ζ¹³+ζ²⁹+ζ³¹+ζ⁴⁷	−ζ¹³−ζ²⁹−ζ³¹−ζ⁴⁷	ζ¹¹−ζ²⁵−ζ⁴¹+ζ⁴³	−ζ¹¹+ζ²⁵+ζ⁴¹−ζ⁴³	0	0	0	0	0	0	0	0
χ₃₁	4	4	4	4	-4	-2	-4	-2	0	0	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
χ₃₂	4	4	-4	-4	4	-2	-4	-2	0	0	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
χ₃₃	4	-4	$4 i$	$- 4 i$	0	-2	0	2	$2 \sqrt{2}$	$- 2 \sqrt{2}$	$- 2 i \sqrt{2}$	$2 i \sqrt{2}$	$- 2 i$	$2 i$	0	0	$- \sqrt{2}$	$\sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₄	4	-4	$4 i$	$- 4 i$	0	-2	0	2	$- 2 \sqrt{2}$	$2 \sqrt{2}$	$2 i \sqrt{2}$	$- 2 i \sqrt{2}$	$- 2 i$	$2 i$	0	0	$\sqrt{2}$	$- \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₅	4	-4	$- 4 i$	$4 i$	0	-2	0	2	$2 \sqrt{2}$	$- 2 \sqrt{2}$	$2 i \sqrt{2}$	$- 2 i \sqrt{2}$	$2 i$	$- 2 i$	0	0	$- \sqrt{2}$	$\sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₆	4	-4	$- 4 i$	$4 i$	0	-2	0	2	$- 2 \sqrt{2}$	$2 \sqrt{2}$	$- 2 i \sqrt{2}$	$2 i \sqrt{2}$	$2 i$	$- 2 i$	0	0	$\sqrt{2}$	$- \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0

Character table — Group #4567