Group #800 — 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
size	1	1	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	24	24
order	1	2	3	4	6	8	8	12	12	16	16	16	16	24	24	24	24	48	48	48	48	48	48	48	48	2	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
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
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
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
χ₅	2	2	2	2	2	-2	-2	2	2	0	0	0	0	-2	-2	-2	-2	0	0	0	0	0	0	0	0	0	0
χ₆	2	2	2	-2	2	0	0	-2	-2	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	0	0	0	0	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	0	0
χ₇	2	2	2	-2	2	0	0	-2	-2	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	0	0	0	0	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	0	0
χ₈	2	2	-1	2	-1	2	2	-1	-1	2	2	2	2	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	0	0
χ₉	2	2	-1	2	-1	2	2	-1	-1	-2	-2	-2	-2	-1	-1	-1	-1	1	1	1	1	1	1	1	1	0	0
χ₁₀	2	2	-1	2	-1	-2	-2	-1	-1	0	0	0	0	1	1	1	1	$\sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$- \sqrt{3}$	0	0
χ₁₁	2	2	-1	2	-1	-2	-2	-1	-1	0	0	0	0	1	1	1	1	$- \sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$\sqrt{3}$	0	0
χ₁₂	2	2	-1	-2	-1	0	0	1	1	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$- \sqrt{3}$	ζ¹⁰−ζ¹⁴	ζ¹⁰−ζ¹⁴	ζ²⁶−ζ⁴⁶	ζ²⁶−ζ⁴⁶	−ζ¹⁰+ζ¹⁴	−ζ¹⁰+ζ¹⁴	−ζ²⁶+ζ⁴⁶	−ζ²⁶+ζ⁴⁶	0	0
χ₁₃	2	2	-1	-2	-1	0	0	1	1	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$\sqrt{3}$	ζ²⁶−ζ⁴⁶	ζ²⁶−ζ⁴⁶	ζ¹⁰−ζ¹⁴	ζ¹⁰−ζ¹⁴	−ζ²⁶+ζ⁴⁶	−ζ²⁶+ζ⁴⁶	−ζ¹⁰+ζ¹⁴	−ζ¹⁰+ζ¹⁴	0	0
χ₁₄	2	2	-1	-2	-1	0	0	1	1	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$- \sqrt{3}$	−ζ¹⁰+ζ¹⁴	−ζ¹⁰+ζ¹⁴	−ζ²⁶+ζ⁴⁶	−ζ²⁶+ζ⁴⁶	ζ¹⁰−ζ¹⁴	ζ¹⁰−ζ¹⁴	ζ²⁶−ζ⁴⁶	ζ²⁶−ζ⁴⁶	0	0
χ₁₅	2	2	-1	-2	-1	0	0	1	1	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$\sqrt{3}$	−ζ²⁶+ζ⁴⁶	−ζ²⁶+ζ⁴⁶	−ζ¹⁰+ζ¹⁴	−ζ¹⁰+ζ¹⁴	ζ²⁶−ζ⁴⁶	ζ²⁶−ζ⁴⁶	ζ¹⁰−ζ¹⁴	ζ¹⁰−ζ¹⁴	0	0
χ₁₆	2	-2	2	0	-2	$\sqrt{2}$	$- \sqrt{2}$	0	0	−ζ²⁵−ζ³¹−ζ⁴¹−ζ⁴⁷	ζ²⁵+ζ³¹+ζ⁴¹+ζ⁴⁷	ζ¹¹+ζ¹³+ζ²⁹+ζ⁴³	−ζ¹¹−ζ¹³−ζ²⁹−ζ⁴³	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	−ζ²⁵−ζ³¹−ζ⁴¹−ζ⁴⁷	ζ²⁵+ζ³¹+ζ⁴¹+ζ⁴⁷	−ζ²⁵−ζ³¹−ζ⁴¹−ζ⁴⁷	ζ²⁵+ζ³¹+ζ⁴¹+ζ⁴⁷	ζ¹¹+ζ¹³+ζ²⁹+ζ⁴³	−ζ¹¹−ζ¹³−ζ²⁹−ζ⁴³	ζ¹¹+ζ¹³+ζ²⁹+ζ⁴³	−ζ¹¹−ζ¹³−ζ²⁹−ζ⁴³	0	0
χ₁₇	2	-2	2	0	-2	$\sqrt{2}$	$- \sqrt{2}$	0	0	ζ²⁵+ζ³¹+ζ⁴¹+ζ⁴⁷	−ζ²⁵−ζ³¹−ζ⁴¹−ζ⁴⁷	−ζ¹¹−ζ¹³−ζ²⁹−ζ⁴³	ζ¹¹+ζ¹³+ζ²⁹+ζ⁴³	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	ζ²⁵+ζ³¹+ζ⁴¹+ζ⁴⁷	−ζ²⁵−ζ³¹−ζ⁴¹−ζ⁴⁷	ζ²⁵+ζ³¹+ζ⁴¹+ζ⁴⁷	−ζ²⁵−ζ³¹−ζ⁴¹−ζ⁴⁷	−ζ¹¹−ζ¹³−ζ²⁹−ζ⁴³	ζ¹¹+ζ¹³+ζ²⁹+ζ⁴³	−ζ¹¹−ζ¹³−ζ²⁹−ζ⁴³	ζ¹¹+ζ¹³+ζ²⁹+ζ⁴³	0	0
χ₁₈	2	-2	2	0	-2	$- \sqrt{2}$	$\sqrt{2}$	0	0	ζ¹¹+ζ¹³+ζ²⁹+ζ⁴³	−ζ¹¹−ζ¹³−ζ²⁹−ζ⁴³	ζ²⁵+ζ³¹+ζ⁴¹+ζ⁴⁷	−ζ²⁵−ζ³¹−ζ⁴¹−ζ⁴⁷	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	ζ¹¹+ζ¹³+ζ²⁹+ζ⁴³	−ζ¹¹−ζ¹³−ζ²⁹−ζ⁴³	ζ¹¹+ζ¹³+ζ²⁹+ζ⁴³	−ζ¹¹−ζ¹³−ζ²⁹−ζ⁴³	ζ²⁵+ζ³¹+ζ⁴¹+ζ⁴⁷	−ζ²⁵−ζ³¹−ζ⁴¹−ζ⁴⁷	ζ²⁵+ζ³¹+ζ⁴¹+ζ⁴⁷	−ζ²⁵−ζ³¹−ζ⁴¹−ζ⁴⁷	0	0
χ₁₉	2	-2	2	0	-2	$- \sqrt{2}$	$\sqrt{2}$	0	0	−ζ¹¹−ζ¹³−ζ²⁹−ζ⁴³	ζ¹¹+ζ¹³+ζ²⁹+ζ⁴³	−ζ²⁵−ζ³¹−ζ⁴¹−ζ⁴⁷	ζ²⁵+ζ³¹+ζ⁴¹+ζ⁴⁷	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	−ζ¹¹−ζ¹³−ζ²⁹−ζ⁴³	ζ¹¹+ζ¹³+ζ²⁹+ζ⁴³	−ζ¹¹−ζ¹³−ζ²⁹−ζ⁴³	ζ¹¹+ζ¹³+ζ²⁹+ζ⁴³	−ζ²⁵−ζ³¹−ζ⁴¹−ζ⁴⁷	ζ²⁵+ζ³¹+ζ⁴¹+ζ⁴⁷	−ζ²⁵−ζ³¹−ζ⁴¹−ζ⁴⁷	ζ²⁵+ζ³¹+ζ⁴¹+ζ⁴⁷	0	0
χ₂₀	2	-2	-1	0	1	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{3}$	$- \sqrt{3}$	−ζ²⁵−ζ³¹−ζ⁴¹−ζ⁴⁷	ζ²⁵+ζ³¹+ζ⁴¹+ζ⁴⁷	ζ¹¹+ζ¹³+ζ²⁹+ζ⁴³	−ζ¹¹−ζ¹³−ζ²⁹−ζ⁴³	ζ¹⁰−ζ¹⁴	−ζ¹⁰+ζ¹⁴	ζ²⁶−ζ⁴⁶	−ζ²⁶+ζ⁴⁶	ζ²⁵+ζ⁴⁷	−ζ²⁵−ζ⁴⁷	ζ³¹+ζ⁴¹	−ζ³¹−ζ⁴¹	−ζ¹¹−ζ¹³	ζ¹¹+ζ¹³	−ζ²⁹−ζ⁴³	ζ²⁹+ζ⁴³	0	0
χ₂₁	2	-2	-1	0	1	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{3}$	$- \sqrt{3}$	ζ²⁵+ζ³¹+ζ⁴¹+ζ⁴⁷	−ζ²⁵−ζ³¹−ζ⁴¹−ζ⁴⁷	−ζ¹¹−ζ¹³−ζ²⁹−ζ⁴³	ζ¹¹+ζ¹³+ζ²⁹+ζ⁴³	ζ¹⁰−ζ¹⁴	−ζ¹⁰+ζ¹⁴	ζ²⁶−ζ⁴⁶	−ζ²⁶+ζ⁴⁶	−ζ²⁵−ζ⁴⁷	ζ²⁵+ζ⁴⁷	−ζ³¹−ζ⁴¹	ζ³¹+ζ⁴¹	ζ¹¹+ζ¹³	−ζ¹¹−ζ¹³	ζ²⁹+ζ⁴³	−ζ²⁹−ζ⁴³	0	0
χ₂₂	2	-2	-1	0	1	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{3}$	$\sqrt{3}$	−ζ²⁵−ζ³¹−ζ⁴¹−ζ⁴⁷	ζ²⁵+ζ³¹+ζ⁴¹+ζ⁴⁷	ζ¹¹+ζ¹³+ζ²⁹+ζ⁴³	−ζ¹¹−ζ¹³−ζ²⁹−ζ⁴³	ζ²⁶−ζ⁴⁶	−ζ²⁶+ζ⁴⁶	ζ¹⁰−ζ¹⁴	−ζ¹⁰+ζ¹⁴	ζ³¹+ζ⁴¹	−ζ³¹−ζ⁴¹	ζ²⁵+ζ⁴⁷	−ζ²⁵−ζ⁴⁷	−ζ²⁹−ζ⁴³	ζ²⁹+ζ⁴³	−ζ¹¹−ζ¹³	ζ¹¹+ζ¹³	0	0
χ₂₃	2	-2	-1	0	1	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{3}$	$\sqrt{3}$	ζ²⁵+ζ³¹+ζ⁴¹+ζ⁴⁷	−ζ²⁵−ζ³¹−ζ⁴¹−ζ⁴⁷	−ζ¹¹−ζ¹³−ζ²⁹−ζ⁴³	ζ¹¹+ζ¹³+ζ²⁹+ζ⁴³	ζ²⁶−ζ⁴⁶	−ζ²⁶+ζ⁴⁶	ζ¹⁰−ζ¹⁴	−ζ¹⁰+ζ¹⁴	−ζ³¹−ζ⁴¹	ζ³¹+ζ⁴¹	−ζ²⁵−ζ⁴⁷	ζ²⁵+ζ⁴⁷	ζ²⁹+ζ⁴³	−ζ²⁹−ζ⁴³	ζ¹¹+ζ¹³	−ζ¹¹−ζ¹³	0	0
χ₂₄	2	-2	-1	0	1	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{3}$	$- \sqrt{3}$	ζ¹¹+ζ¹³+ζ²⁹+ζ⁴³	−ζ¹¹−ζ¹³−ζ²⁹−ζ⁴³	ζ²⁵+ζ³¹+ζ⁴¹+ζ⁴⁷	−ζ²⁵−ζ³¹−ζ⁴¹−ζ⁴⁷	−ζ¹⁰+ζ¹⁴	ζ¹⁰−ζ¹⁴	−ζ²⁶+ζ⁴⁶	ζ²⁶−ζ⁴⁶	−ζ¹¹−ζ¹³	ζ¹¹+ζ¹³	−ζ²⁹−ζ⁴³	ζ²⁹+ζ⁴³	−ζ²⁵−ζ⁴⁷	ζ²⁵+ζ⁴⁷	−ζ³¹−ζ⁴¹	ζ³¹+ζ⁴¹	0	0
χ₂₅	2	-2	-1	0	1	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{3}$	$- \sqrt{3}$	−ζ¹¹−ζ¹³−ζ²⁹−ζ⁴³	ζ¹¹+ζ¹³+ζ²⁹+ζ⁴³	−ζ²⁵−ζ³¹−ζ⁴¹−ζ⁴⁷	ζ²⁵+ζ³¹+ζ⁴¹+ζ⁴⁷	−ζ¹⁰+ζ¹⁴	ζ¹⁰−ζ¹⁴	−ζ²⁶+ζ⁴⁶	ζ²⁶−ζ⁴⁶	ζ¹¹+ζ¹³	−ζ¹¹−ζ¹³	ζ²⁹+ζ⁴³	−ζ²⁹−ζ⁴³	ζ²⁵+ζ⁴⁷	−ζ²⁵−ζ⁴⁷	ζ³¹+ζ⁴¹	−ζ³¹−ζ⁴¹	0	0
χ₂₆	2	-2	-1	0	1	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{3}$	$\sqrt{3}$	ζ¹¹+ζ¹³+ζ²⁹+ζ⁴³	−ζ¹¹−ζ¹³−ζ²⁹−ζ⁴³	ζ²⁵+ζ³¹+ζ⁴¹+ζ⁴⁷	−ζ²⁵−ζ³¹−ζ⁴¹−ζ⁴⁷	−ζ²⁶+ζ⁴⁶	ζ²⁶−ζ⁴⁶	−ζ¹⁰+ζ¹⁴	ζ¹⁰−ζ¹⁴	−ζ²⁹−ζ⁴³	ζ²⁹+ζ⁴³	−ζ¹¹−ζ¹³	ζ¹¹+ζ¹³	−ζ³¹−ζ⁴¹	ζ³¹+ζ⁴¹	−ζ²⁵−ζ⁴⁷	ζ²⁵+ζ⁴⁷	0	0
χ₂₇	2	-2	-1	0	1	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{3}$	$\sqrt{3}$	−ζ¹¹−ζ¹³−ζ²⁹−ζ⁴³	ζ¹¹+ζ¹³+ζ²⁹+ζ⁴³	−ζ²⁵−ζ³¹−ζ⁴¹−ζ⁴⁷	ζ²⁵+ζ³¹+ζ⁴¹+ζ⁴⁷	−ζ²⁶+ζ⁴⁶	ζ²⁶−ζ⁴⁶	−ζ¹⁰+ζ¹⁴	ζ¹⁰−ζ¹⁴	ζ²⁹+ζ⁴³	−ζ²⁹−ζ⁴³	ζ¹¹+ζ¹³	−ζ¹¹−ζ¹³	ζ³¹+ζ⁴¹	−ζ³¹−ζ⁴¹	ζ²⁵+ζ⁴⁷	−ζ²⁵−ζ⁴⁷	0	0

Character table — Group #800