Group #4520 — 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
size	1	1	2	2	2	2	2	2	2	2	2	4	4	4	4	4	4	4	6	6	6	6	6	6	6	6	16	16	16	48
order	1	2	3	4	6	8	8	16	16	16	16	12	24	24	48	48	48	48	32	32	32	32	32	32	32	32	2	6	6	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
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
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
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
χ₅	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
χ₆	2	2	2	2	2	-2	-2	0	0	0	0	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
χ₇	2	2	2	2	2	-2	-2	0	0	0	0	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
χ₈	2	2	2	-2	2	0	0	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	-2	0	0	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	−ζ⁵⁰+ζ⁶²−ζ⁸²+ζ⁹⁴	−ζ⁵⁰+ζ⁶²−ζ⁸²+ζ⁹⁴	ζ⁵⁰−ζ⁶²+ζ⁸²−ζ⁹⁴	ζ⁵⁰−ζ⁶²+ζ⁸²−ζ⁹⁴	ζ²²−ζ²⁶−ζ⁵⁸+ζ⁸⁶	ζ²²−ζ²⁶−ζ⁵⁸+ζ⁸⁶	−ζ²²+ζ²⁶+ζ⁵⁸−ζ⁸⁶	−ζ²²+ζ²⁶+ζ⁵⁸−ζ⁸⁶	0	0	0	0
χ₉	2	2	2	-2	2	0	0	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	-2	0	0	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	ζ⁵⁰−ζ⁶²+ζ⁸²−ζ⁹⁴	ζ⁵⁰−ζ⁶²+ζ⁸²−ζ⁹⁴	−ζ⁵⁰+ζ⁶²−ζ⁸²+ζ⁹⁴	−ζ⁵⁰+ζ⁶²−ζ⁸²+ζ⁹⁴	−ζ²²+ζ²⁶+ζ⁵⁸−ζ⁸⁶	−ζ²²+ζ²⁶+ζ⁵⁸−ζ⁸⁶	ζ²²−ζ²⁶−ζ⁵⁸+ζ⁸⁶	ζ²²−ζ²⁶−ζ⁵⁸+ζ⁸⁶	0	0	0	0
χ₁₀	2	2	2	-2	2	0	0	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	-2	0	0	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	ζ²²−ζ²⁶−ζ⁵⁸+ζ⁸⁶	ζ²²−ζ²⁶−ζ⁵⁸+ζ⁸⁶	−ζ²²+ζ²⁶+ζ⁵⁸−ζ⁸⁶	−ζ²²+ζ²⁶+ζ⁵⁸−ζ⁸⁶	ζ⁵⁰−ζ⁶²+ζ⁸²−ζ⁹⁴	ζ⁵⁰−ζ⁶²+ζ⁸²−ζ⁹⁴	−ζ⁵⁰+ζ⁶²−ζ⁸²+ζ⁹⁴	−ζ⁵⁰+ζ⁶²−ζ⁸²+ζ⁹⁴	0	0	0	0
χ₁₁	2	2	2	-2	2	0	0	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	-2	0	0	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	−ζ²²+ζ²⁶+ζ⁵⁸−ζ⁸⁶	−ζ²²+ζ²⁶+ζ⁵⁸−ζ⁸⁶	ζ²²−ζ²⁶−ζ⁵⁸+ζ⁸⁶	ζ²²−ζ²⁶−ζ⁵⁸+ζ⁸⁶	−ζ⁵⁰+ζ⁶²−ζ⁸²+ζ⁹⁴	−ζ⁵⁰+ζ⁶²−ζ⁸²+ζ⁹⁴	ζ⁵⁰−ζ⁶²+ζ⁸²−ζ⁹⁴	ζ⁵⁰−ζ⁶²+ζ⁸²−ζ⁹⁴	0	0	0	0
χ₁₂	2	2	-1	2	-1	2	2	2	2	2	2	-1	-1	-1	-1	-1	-1	-1	0	0	0	0	0	0	0	0	2	-1	-1	0
χ₁₃	2	2	-1	2	-1	2	2	2	2	2	2	-1	-1	-1	-1	-1	-1	-1	0	0	0	0	0	0	0	0	-2	1	1	0
χ₁₄	2	2	-1	2	-1	2	2	-2	-2	-2	-2	-1	-1	-1	1	1	1	1	0	0	0	0	0	0	0	0	0	$- i \sqrt{3}$	$i \sqrt{3}$	0
χ₁₅	2	2	-1	2	-1	2	2	-2	-2	-2	-2	-1	-1	-1	1	1	1	1	0	0	0	0	0	0	0	0	0	$i \sqrt{3}$	$- i \sqrt{3}$	0
χ₁₆	2	-2	2	0	-2	$\sqrt{2}$	$- \sqrt{2}$	−ζ⁵⁰+ζ⁶²−ζ⁸²+ζ⁹⁴	ζ⁵⁰−ζ⁶²+ζ⁸²−ζ⁹⁴	ζ²²−ζ²⁶−ζ⁵⁸+ζ⁸⁶	−ζ²²+ζ²⁶+ζ⁵⁸−ζ⁸⁶	0	$\sqrt{2}$	$- \sqrt{2}$	−ζ⁵⁰+ζ⁶²−ζ⁸²+ζ⁹⁴	ζ⁵⁰−ζ⁶²+ζ⁸²−ζ⁹⁴	ζ²²−ζ²⁶−ζ⁵⁸+ζ⁸⁶	−ζ²²+ζ²⁶+ζ⁵⁸−ζ⁸⁶	−ζ⁵³−ζ⁵⁹−ζ⁸⁵−ζ⁹¹	ζ⁵³+ζ⁵⁹+ζ⁸⁵+ζ⁹¹	ζ¹⁹+ζ²⁹+ζ⁶¹+ζ⁸³	−ζ¹⁹−ζ²⁹−ζ⁶¹−ζ⁸³	−ζ²³−ζ²⁵−ζ⁵⁵−ζ⁸⁹	ζ²³+ζ²⁵+ζ⁵⁵+ζ⁸⁹	−ζ¹⁷−ζ³¹−ζ⁴⁹−ζ⁹⁵	ζ¹⁷+ζ³¹+ζ⁴⁹+ζ⁹⁵	0	0	0	0
χ₁₇	2	-2	2	0	-2	$\sqrt{2}$	$- \sqrt{2}$	−ζ⁵⁰+ζ⁶²−ζ⁸²+ζ⁹⁴	ζ⁵⁰−ζ⁶²+ζ⁸²−ζ⁹⁴	ζ²²−ζ²⁶−ζ⁵⁸+ζ⁸⁶	−ζ²²+ζ²⁶+ζ⁵⁸−ζ⁸⁶	0	$\sqrt{2}$	$- \sqrt{2}$	−ζ⁵⁰+ζ⁶²−ζ⁸²+ζ⁹⁴	ζ⁵⁰−ζ⁶²+ζ⁸²−ζ⁹⁴	ζ²²−ζ²⁶−ζ⁵⁸+ζ⁸⁶	−ζ²²+ζ²⁶+ζ⁵⁸−ζ⁸⁶	ζ⁵³+ζ⁵⁹+ζ⁸⁵+ζ⁹¹	−ζ⁵³−ζ⁵⁹−ζ⁸⁵−ζ⁹¹	−ζ¹⁹−ζ²⁹−ζ⁶¹−ζ⁸³	ζ¹⁹+ζ²⁹+ζ⁶¹+ζ⁸³	ζ²³+ζ²⁵+ζ⁵⁵+ζ⁸⁹	−ζ²³−ζ²⁵−ζ⁵⁵−ζ⁸⁹	ζ¹⁷+ζ³¹+ζ⁴⁹+ζ⁹⁵	−ζ¹⁷−ζ³¹−ζ⁴⁹−ζ⁹⁵	0	0	0	0
χ₁₈	2	-2	2	0	-2	$\sqrt{2}$	$- \sqrt{2}$	ζ⁵⁰−ζ⁶²+ζ⁸²−ζ⁹⁴	−ζ⁵⁰+ζ⁶²−ζ⁸²+ζ⁹⁴	−ζ²²+ζ²⁶+ζ⁵⁸−ζ⁸⁶	ζ²²−ζ²⁶−ζ⁵⁸+ζ⁸⁶	0	$\sqrt{2}$	$- \sqrt{2}$	ζ⁵⁰−ζ⁶²+ζ⁸²−ζ⁹⁴	−ζ⁵⁰+ζ⁶²−ζ⁸²+ζ⁹⁴	−ζ²²+ζ²⁶+ζ⁵⁸−ζ⁸⁶	ζ²²−ζ²⁶−ζ⁵⁸+ζ⁸⁶	ζ¹⁹+ζ²⁹+ζ⁶¹+ζ⁸³	−ζ¹⁹−ζ²⁹−ζ⁶¹−ζ⁸³	ζ⁵³+ζ⁵⁹+ζ⁸⁵+ζ⁹¹	−ζ⁵³−ζ⁵⁹−ζ⁸⁵−ζ⁹¹	−ζ¹⁷−ζ³¹−ζ⁴⁹−ζ⁹⁵	ζ¹⁷+ζ³¹+ζ⁴⁹+ζ⁹⁵	ζ²³+ζ²⁵+ζ⁵⁵+ζ⁸⁹	−ζ²³−ζ²⁵−ζ⁵⁵−ζ⁸⁹	0	0	0	0
χ₁₉	2	-2	2	0	-2	$\sqrt{2}$	$- \sqrt{2}$	ζ⁵⁰−ζ⁶²+ζ⁸²−ζ⁹⁴	−ζ⁵⁰+ζ⁶²−ζ⁸²+ζ⁹⁴	−ζ²²+ζ²⁶+ζ⁵⁸−ζ⁸⁶	ζ²²−ζ²⁶−ζ⁵⁸+ζ⁸⁶	0	$\sqrt{2}$	$- \sqrt{2}$	ζ⁵⁰−ζ⁶²+ζ⁸²−ζ⁹⁴	−ζ⁵⁰+ζ⁶²−ζ⁸²+ζ⁹⁴	−ζ²²+ζ²⁶+ζ⁵⁸−ζ⁸⁶	ζ²²−ζ²⁶−ζ⁵⁸+ζ⁸⁶	−ζ¹⁹−ζ²⁹−ζ⁶¹−ζ⁸³	ζ¹⁹+ζ²⁹+ζ⁶¹+ζ⁸³	−ζ⁵³−ζ⁵⁹−ζ⁸⁵−ζ⁹¹	ζ⁵³+ζ⁵⁹+ζ⁸⁵+ζ⁹¹	ζ¹⁷+ζ³¹+ζ⁴⁹+ζ⁹⁵	−ζ¹⁷−ζ³¹−ζ⁴⁹−ζ⁹⁵	−ζ²³−ζ²⁵−ζ⁵⁵−ζ⁸⁹	ζ²³+ζ²⁵+ζ⁵⁵+ζ⁸⁹	0	0	0	0
χ₂₀	2	-2	2	0	-2	$- \sqrt{2}$	$\sqrt{2}$	ζ²²−ζ²⁶−ζ⁵⁸+ζ⁸⁶	−ζ²²+ζ²⁶+ζ⁵⁸−ζ⁸⁶	ζ⁵⁰−ζ⁶²+ζ⁸²−ζ⁹⁴	−ζ⁵⁰+ζ⁶²−ζ⁸²+ζ⁹⁴	0	$- \sqrt{2}$	$\sqrt{2}$	ζ²²−ζ²⁶−ζ⁵⁸+ζ⁸⁶	−ζ²²+ζ²⁶+ζ⁵⁸−ζ⁸⁶	ζ⁵⁰−ζ⁶²+ζ⁸²−ζ⁹⁴	−ζ⁵⁰+ζ⁶²−ζ⁸²+ζ⁹⁴	−ζ²³−ζ²⁵−ζ⁵⁵−ζ⁸⁹	ζ²³+ζ²⁵+ζ⁵⁵+ζ⁸⁹	−ζ¹⁷−ζ³¹−ζ⁴⁹−ζ⁹⁵	ζ¹⁷+ζ³¹+ζ⁴⁹+ζ⁹⁵	ζ¹⁹+ζ²⁹+ζ⁶¹+ζ⁸³	−ζ¹⁹−ζ²⁹−ζ⁶¹−ζ⁸³	ζ⁵³+ζ⁵⁹+ζ⁸⁵+ζ⁹¹	−ζ⁵³−ζ⁵⁹−ζ⁸⁵−ζ⁹¹	0	0	0	0
χ₂₁	2	-2	2	0	-2	$- \sqrt{2}$	$\sqrt{2}$	ζ²²−ζ²⁶−ζ⁵⁸+ζ⁸⁶	−ζ²²+ζ²⁶+ζ⁵⁸−ζ⁸⁶	ζ⁵⁰−ζ⁶²+ζ⁸²−ζ⁹⁴	−ζ⁵⁰+ζ⁶²−ζ⁸²+ζ⁹⁴	0	$- \sqrt{2}$	$\sqrt{2}$	ζ²²−ζ²⁶−ζ⁵⁸+ζ⁸⁶	−ζ²²+ζ²⁶+ζ⁵⁸−ζ⁸⁶	ζ⁵⁰−ζ⁶²+ζ⁸²−ζ⁹⁴	−ζ⁵⁰+ζ⁶²−ζ⁸²+ζ⁹⁴	ζ²³+ζ²⁵+ζ⁵⁵+ζ⁸⁹	−ζ²³−ζ²⁵−ζ⁵⁵−ζ⁸⁹	ζ¹⁷+ζ³¹+ζ⁴⁹+ζ⁹⁵	−ζ¹⁷−ζ³¹−ζ⁴⁹−ζ⁹⁵	−ζ¹⁹−ζ²⁹−ζ⁶¹−ζ⁸³	ζ¹⁹+ζ²⁹+ζ⁶¹+ζ⁸³	−ζ⁵³−ζ⁵⁹−ζ⁸⁵−ζ⁹¹	ζ⁵³+ζ⁵⁹+ζ⁸⁵+ζ⁹¹	0	0	0	0
χ₂₂	2	-2	2	0	-2	$- \sqrt{2}$	$\sqrt{2}$	−ζ²²+ζ²⁶+ζ⁵⁸−ζ⁸⁶	ζ²²−ζ²⁶−ζ⁵⁸+ζ⁸⁶	−ζ⁵⁰+ζ⁶²−ζ⁸²+ζ⁹⁴	ζ⁵⁰−ζ⁶²+ζ⁸²−ζ⁹⁴	0	$- \sqrt{2}$	$\sqrt{2}$	−ζ²²+ζ²⁶+ζ⁵⁸−ζ⁸⁶	ζ²²−ζ²⁶−ζ⁵⁸+ζ⁸⁶	−ζ⁵⁰+ζ⁶²−ζ⁸²+ζ⁹⁴	ζ⁵⁰−ζ⁶²+ζ⁸²−ζ⁹⁴	−ζ¹⁷−ζ³¹−ζ⁴⁹−ζ⁹⁵	ζ¹⁷+ζ³¹+ζ⁴⁹+ζ⁹⁵	ζ²³+ζ²⁵+ζ⁵⁵+ζ⁸⁹	−ζ²³−ζ²⁵−ζ⁵⁵−ζ⁸⁹	ζ⁵³+ζ⁵⁹+ζ⁸⁵+ζ⁹¹	−ζ⁵³−ζ⁵⁹−ζ⁸⁵−ζ⁹¹	−ζ¹⁹−ζ²⁹−ζ⁶¹−ζ⁸³	ζ¹⁹+ζ²⁹+ζ⁶¹+ζ⁸³	0	0	0	0
χ₂₃	2	-2	2	0	-2	$- \sqrt{2}$	$\sqrt{2}$	−ζ²²+ζ²⁶+ζ⁵⁸−ζ⁸⁶	ζ²²−ζ²⁶−ζ⁵⁸+ζ⁸⁶	−ζ⁵⁰+ζ⁶²−ζ⁸²+ζ⁹⁴	ζ⁵⁰−ζ⁶²+ζ⁸²−ζ⁹⁴	0	$- \sqrt{2}$	$\sqrt{2}$	−ζ²²+ζ²⁶+ζ⁵⁸−ζ⁸⁶	ζ²²−ζ²⁶−ζ⁵⁸+ζ⁸⁶	−ζ⁵⁰+ζ⁶²−ζ⁸²+ζ⁹⁴	ζ⁵⁰−ζ⁶²+ζ⁸²−ζ⁹⁴	ζ¹⁷+ζ³¹+ζ⁴⁹+ζ⁹⁵	−ζ¹⁷−ζ³¹−ζ⁴⁹−ζ⁹⁵	−ζ²³−ζ²⁵−ζ⁵⁵−ζ⁸⁹	ζ²³+ζ²⁵+ζ⁵⁵+ζ⁸⁹	−ζ⁵³−ζ⁵⁹−ζ⁸⁵−ζ⁹¹	ζ⁵³+ζ⁵⁹+ζ⁸⁵+ζ⁹¹	ζ¹⁹+ζ²⁹+ζ⁶¹+ζ⁸³	−ζ¹⁹−ζ²⁹−ζ⁶¹−ζ⁸³	0	0	0	0
χ₂₄	4	4	-2	4	-2	-4	-4	0	0	0	0	-2	2	2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₅	4	4	-2	-4	-2	0	0	$2 \sqrt{2}$	$2 \sqrt{2}$	$- 2 \sqrt{2}$	$- 2 \sqrt{2}$	2	0	0	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₆	4	4	-2	-4	-2	0	0	$- 2 \sqrt{2}$	$- 2 \sqrt{2}$	$2 \sqrt{2}$	$2 \sqrt{2}$	2	0	0	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₇	4	-4	-2	0	2	$2 \sqrt{2}$	$- 2 \sqrt{2}$	−2ζ⁵⁰+2ζ⁶²−2ζ⁸²+2ζ⁹⁴	2ζ⁵⁰−2ζ⁶²+2ζ⁸²−2ζ⁹⁴	2ζ²²−2ζ²⁶−2ζ⁵⁸+2ζ⁸⁶	−2ζ²²+2ζ²⁶+2ζ⁵⁸−2ζ⁸⁶	0	$- \sqrt{2}$	$\sqrt{2}$	ζ⁵⁰−ζ⁶²+ζ⁸²−ζ⁹⁴	−ζ⁵⁰+ζ⁶²−ζ⁸²+ζ⁹⁴	−ζ²²+ζ²⁶+ζ⁵⁸−ζ⁸⁶	ζ²²−ζ²⁶−ζ⁵⁸+ζ⁸⁶	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₈	4	-4	-2	0	2	$2 \sqrt{2}$	$- 2 \sqrt{2}$	2ζ⁵⁰−2ζ⁶²+2ζ⁸²−2ζ⁹⁴	−2ζ⁵⁰+2ζ⁶²−2ζ⁸²+2ζ⁹⁴	−2ζ²²+2ζ²⁶+2ζ⁵⁸−2ζ⁸⁶	2ζ²²−2ζ²⁶−2ζ⁵⁸+2ζ⁸⁶	0	$- \sqrt{2}$	$\sqrt{2}$	−ζ⁵⁰+ζ⁶²−ζ⁸²+ζ⁹⁴	ζ⁵⁰−ζ⁶²+ζ⁸²−ζ⁹⁴	ζ²²−ζ²⁶−ζ⁵⁸+ζ⁸⁶	−ζ²²+ζ²⁶+ζ⁵⁸−ζ⁸⁶	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₉	4	-4	-2	0	2	$- 2 \sqrt{2}$	$2 \sqrt{2}$	2ζ²²−2ζ²⁶−2ζ⁵⁸+2ζ⁸⁶	−2ζ²²+2ζ²⁶+2ζ⁵⁸−2ζ⁸⁶	2ζ⁵⁰−2ζ⁶²+2ζ⁸²−2ζ⁹⁴	−2ζ⁵⁰+2ζ⁶²−2ζ⁸²+2ζ⁹⁴	0	$\sqrt{2}$	$- \sqrt{2}$	−ζ²²+ζ²⁶+ζ⁵⁸−ζ⁸⁶	ζ²²−ζ²⁶−ζ⁵⁸+ζ⁸⁶	−ζ⁵⁰+ζ⁶²−ζ⁸²+ζ⁹⁴	ζ⁵⁰−ζ⁶²+ζ⁸²−ζ⁹⁴	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₀	4	-4	-2	0	2	$- 2 \sqrt{2}$	$2 \sqrt{2}$	−2ζ²²+2ζ²⁶+2ζ⁵⁸−2ζ⁸⁶	2ζ²²−2ζ²⁶−2ζ⁵⁸+2ζ⁸⁶	−2ζ⁵⁰+2ζ⁶²−2ζ⁸²+2ζ⁹⁴	2ζ⁵⁰−2ζ⁶²+2ζ⁸²−2ζ⁹⁴	0	$\sqrt{2}$	$- \sqrt{2}$	ζ²²−ζ²⁶−ζ⁵⁸+ζ⁸⁶	−ζ²²+ζ²⁶+ζ⁵⁸−ζ⁸⁶	ζ⁵⁰−ζ⁶²+ζ⁸²−ζ⁹⁴	−ζ⁵⁰+ζ⁶²−ζ⁸²+ζ⁹⁴	0	0	0	0	0	0	0	0	0	0	0	0

Character table — Group #4520