Group #6480 — 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
size	1	1	2	2	2	4	4	2	2	4	4	4	8	8	2	2	4	4	4	8	8	2	2	4	4	4	8	8	7	7	14	14	14	28	28
order	1	2	4	8	8	4	4	7	14	28	56	56	28	28	7	14	28	56	56	28	28	7	14	28	56	56	28	28	2	2	4	8	8	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
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
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
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
χ₅	2	2	-2	0	0	0	0	2	2	-2	0	0	0	0	2	2	-2	0	0	0	0	2	2	-2	0	0	0	0	2	2	-2	0	0	0	0
χ₆	2	-2	0	$\sqrt{2}$	$- \sqrt{2}$	0	0	2	-2	0	$\sqrt{2}$	$- \sqrt{2}$	0	0	2	-2	0	$\sqrt{2}$	$- \sqrt{2}$	0	0	2	-2	0	$\sqrt{2}$	$- \sqrt{2}$	0	0	2	-2	0	$\sqrt{2}$	$- \sqrt{2}$	0	0
χ₇	2	-2	0	$- \sqrt{2}$	$\sqrt{2}$	0	0	2	-2	0	$- \sqrt{2}$	$\sqrt{2}$	0	0	2	-2	0	$- \sqrt{2}$	$\sqrt{2}$	0	0	2	-2	0	$- \sqrt{2}$	$\sqrt{2}$	0	0	2	-2	0	$- \sqrt{2}$	$\sqrt{2}$	0	0
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
χ₉	1	1	1	1	1	-1	-1	1	1	1	1	1	-1	-1	1	1	1	1	1	-1	-1	1	1	1	1	1	-1	-1	-1	-1	-1	-1	-1	1	1
χ₁₀	1	1	1	-1	-1	1	-1	1	1	1	-1	-1	1	-1	1	1	1	-1	-1	1	-1	1	1	1	-1	-1	1	-1	-1	-1	-1	1	1	-1	1
χ₁₁	1	1	1	-1	-1	-1	1	1	1	1	-1	-1	-1	1	1	1	1	-1	-1	-1	1	1	1	1	-1	-1	-1	1	-1	-1	-1	1	1	1	-1
χ₁₂	2	2	-2	0	0	0	0	2	2	-2	0	0	0	0	2	2	-2	0	0	0	0	2	2	-2	0	0	0	0	-2	-2	2	0	0	0	0
χ₁₃	2	-2	0	$\sqrt{2}$	$- \sqrt{2}$	0	0	2	-2	0	$\sqrt{2}$	$- \sqrt{2}$	0	0	2	-2	0	$\sqrt{2}$	$- \sqrt{2}$	0	0	2	-2	0	$\sqrt{2}$	$- \sqrt{2}$	0	0	-2	2	0	$- \sqrt{2}$	$\sqrt{2}$	0	0
χ₁₄	2	-2	0	$- \sqrt{2}$	$\sqrt{2}$	0	0	2	-2	0	$- \sqrt{2}$	$\sqrt{2}$	0	0	2	-2	0	$- \sqrt{2}$	$\sqrt{2}$	0	0	2	-2	0	$- \sqrt{2}$	$\sqrt{2}$	0	0	-2	2	0	$\sqrt{2}$	$- \sqrt{2}$	0	0
χ₁₅	2	2	2	2	2	2	2	−ζ²⁰−ζ³⁶	−ζ²⁰−ζ³⁶	−ζ²⁰−ζ³⁶	−ζ²⁰−ζ³⁶	−ζ²⁰−ζ³⁶	−ζ²⁰−ζ³⁶	−ζ²⁰−ζ³⁶	−ζ¹²−ζ⁴⁴	−ζ¹²−ζ⁴⁴	−ζ¹²−ζ⁴⁴	−ζ¹²−ζ⁴⁴	−ζ¹²−ζ⁴⁴	−ζ¹²−ζ⁴⁴	−ζ¹²−ζ⁴⁴	−ζ⁴−ζ⁵²	−ζ⁴−ζ⁵²	−ζ⁴−ζ⁵²	−ζ⁴−ζ⁵²	−ζ⁴−ζ⁵²	−ζ⁴−ζ⁵²	−ζ⁴−ζ⁵²	0	0	0	0	0	0	0
χ₁₆	2	2	2	2	2	-2	-2	−ζ²⁰−ζ³⁶	−ζ²⁰−ζ³⁶	−ζ²⁰−ζ³⁶	−ζ²⁰−ζ³⁶	−ζ²⁰−ζ³⁶	ζ²⁰+ζ³⁶	ζ²⁰+ζ³⁶	−ζ¹²−ζ⁴⁴	−ζ¹²−ζ⁴⁴	−ζ¹²−ζ⁴⁴	−ζ¹²−ζ⁴⁴	−ζ¹²−ζ⁴⁴	ζ¹²+ζ⁴⁴	ζ¹²+ζ⁴⁴	−ζ⁴−ζ⁵²	−ζ⁴−ζ⁵²	−ζ⁴−ζ⁵²	−ζ⁴−ζ⁵²	−ζ⁴−ζ⁵²	ζ⁴+ζ⁵²	ζ⁴+ζ⁵²	0	0	0	0	0	0	0
χ₁₇	2	2	2	-2	-2	2	-2	−ζ²⁰−ζ³⁶	−ζ²⁰−ζ³⁶	−ζ²⁰−ζ³⁶	ζ²⁰+ζ³⁶	ζ²⁰+ζ³⁶	−ζ²⁰−ζ³⁶	ζ²⁰+ζ³⁶	−ζ¹²−ζ⁴⁴	−ζ¹²−ζ⁴⁴	−ζ¹²−ζ⁴⁴	ζ¹²+ζ⁴⁴	ζ¹²+ζ⁴⁴	−ζ¹²−ζ⁴⁴	ζ¹²+ζ⁴⁴	−ζ⁴−ζ⁵²	−ζ⁴−ζ⁵²	−ζ⁴−ζ⁵²	ζ⁴+ζ⁵²	ζ⁴+ζ⁵²	−ζ⁴−ζ⁵²	ζ⁴+ζ⁵²	0	0	0	0	0	0	0
χ₁₈	2	2	2	-2	-2	-2	2	−ζ²⁰−ζ³⁶	−ζ²⁰−ζ³⁶	−ζ²⁰−ζ³⁶	ζ²⁰+ζ³⁶	ζ²⁰+ζ³⁶	ζ²⁰+ζ³⁶	−ζ²⁰−ζ³⁶	−ζ¹²−ζ⁴⁴	−ζ¹²−ζ⁴⁴	−ζ¹²−ζ⁴⁴	ζ¹²+ζ⁴⁴	ζ¹²+ζ⁴⁴	ζ¹²+ζ⁴⁴	−ζ¹²−ζ⁴⁴	−ζ⁴−ζ⁵²	−ζ⁴−ζ⁵²	−ζ⁴−ζ⁵²	ζ⁴+ζ⁵²	ζ⁴+ζ⁵²	ζ⁴+ζ⁵²	−ζ⁴−ζ⁵²	0	0	0	0	0	0	0
χ₁₉	4	4	-4	0	0	0	0	−2ζ²⁰−2ζ³⁶	−2ζ²⁰−2ζ³⁶	2ζ²⁰+2ζ³⁶	0	0	0	0	−2ζ¹²−2ζ⁴⁴	−2ζ¹²−2ζ⁴⁴	2ζ¹²+2ζ⁴⁴	0	0	0	0	−2ζ⁴−2ζ⁵²	−2ζ⁴−2ζ⁵²	2ζ⁴+2ζ⁵²	0	0	0	0	0	0	0	0	0	0	0
χ₂₀	4	-4	0	$2 \sqrt{2}$	$- 2 \sqrt{2}$	0	0	−2ζ²⁰−2ζ³⁶	2ζ²⁰+2ζ³⁶	0	−ζ¹³+ζ¹⁵−ζ²⁹+ζ⁵⁵	ζ¹³−ζ¹⁵+ζ²⁹−ζ⁵⁵	0	0	−2ζ¹²−2ζ⁴⁴	2ζ¹²+2ζ⁴⁴	0	−ζ⁵+ζ²³−ζ³⁷+ζ⁴⁷	ζ⁵−ζ²³+ζ³⁷−ζ⁴⁷	0	0	−2ζ⁴−2ζ⁵²	2ζ⁴+2ζ⁵²	0	ζ³¹+ζ³⁹−ζ⁴⁵−ζ⁵³	−ζ³¹−ζ³⁹+ζ⁴⁵+ζ⁵³	0	0	0	0	0	0	0	0	0
χ₂₁	4	-4	0	$- 2 \sqrt{2}$	$2 \sqrt{2}$	0	0	−2ζ²⁰−2ζ³⁶	2ζ²⁰+2ζ³⁶	0	ζ¹³−ζ¹⁵+ζ²⁹−ζ⁵⁵	−ζ¹³+ζ¹⁵−ζ²⁹+ζ⁵⁵	0	0	−2ζ¹²−2ζ⁴⁴	2ζ¹²+2ζ⁴⁴	0	ζ⁵−ζ²³+ζ³⁷−ζ⁴⁷	−ζ⁵+ζ²³−ζ³⁷+ζ⁴⁷	0	0	−2ζ⁴−2ζ⁵²	2ζ⁴+2ζ⁵²	0	−ζ³¹−ζ³⁹+ζ⁴⁵+ζ⁵³	ζ³¹+ζ³⁹−ζ⁴⁵−ζ⁵³	0	0	0	0	0	0	0	0	0
χ₂₂	2	2	2	2	2	2	2	−ζ¹²−ζ⁴⁴	−ζ¹²−ζ⁴⁴	−ζ¹²−ζ⁴⁴	−ζ¹²−ζ⁴⁴	−ζ¹²−ζ⁴⁴	−ζ¹²−ζ⁴⁴	−ζ¹²−ζ⁴⁴	−ζ⁴−ζ⁵²	−ζ⁴−ζ⁵²	−ζ⁴−ζ⁵²	−ζ⁴−ζ⁵²	−ζ⁴−ζ⁵²	−ζ⁴−ζ⁵²	−ζ⁴−ζ⁵²	−ζ²⁰−ζ³⁶	−ζ²⁰−ζ³⁶	−ζ²⁰−ζ³⁶	−ζ²⁰−ζ³⁶	−ζ²⁰−ζ³⁶	−ζ²⁰−ζ³⁶	−ζ²⁰−ζ³⁶	0	0	0	0	0	0	0
χ₂₃	2	2	2	2	2	-2	-2	−ζ¹²−ζ⁴⁴	−ζ¹²−ζ⁴⁴	−ζ¹²−ζ⁴⁴	−ζ¹²−ζ⁴⁴	−ζ¹²−ζ⁴⁴	ζ¹²+ζ⁴⁴	ζ¹²+ζ⁴⁴	−ζ⁴−ζ⁵²	−ζ⁴−ζ⁵²	−ζ⁴−ζ⁵²	−ζ⁴−ζ⁵²	−ζ⁴−ζ⁵²	ζ⁴+ζ⁵²	ζ⁴+ζ⁵²	−ζ²⁰−ζ³⁶	−ζ²⁰−ζ³⁶	−ζ²⁰−ζ³⁶	−ζ²⁰−ζ³⁶	−ζ²⁰−ζ³⁶	ζ²⁰+ζ³⁶	ζ²⁰+ζ³⁶	0	0	0	0	0	0	0
χ₂₄	2	2	2	-2	-2	2	-2	−ζ¹²−ζ⁴⁴	−ζ¹²−ζ⁴⁴	−ζ¹²−ζ⁴⁴	ζ¹²+ζ⁴⁴	ζ¹²+ζ⁴⁴	−ζ¹²−ζ⁴⁴	ζ¹²+ζ⁴⁴	−ζ⁴−ζ⁵²	−ζ⁴−ζ⁵²	−ζ⁴−ζ⁵²	ζ⁴+ζ⁵²	ζ⁴+ζ⁵²	−ζ⁴−ζ⁵²	ζ⁴+ζ⁵²	−ζ²⁰−ζ³⁶	−ζ²⁰−ζ³⁶	−ζ²⁰−ζ³⁶	ζ²⁰+ζ³⁶	ζ²⁰+ζ³⁶	−ζ²⁰−ζ³⁶	ζ²⁰+ζ³⁶	0	0	0	0	0	0	0
χ₂₅	2	2	2	-2	-2	-2	2	−ζ¹²−ζ⁴⁴	−ζ¹²−ζ⁴⁴	−ζ¹²−ζ⁴⁴	ζ¹²+ζ⁴⁴	ζ¹²+ζ⁴⁴	ζ¹²+ζ⁴⁴	−ζ¹²−ζ⁴⁴	−ζ⁴−ζ⁵²	−ζ⁴−ζ⁵²	−ζ⁴−ζ⁵²	ζ⁴+ζ⁵²	ζ⁴+ζ⁵²	ζ⁴+ζ⁵²	−ζ⁴−ζ⁵²	−ζ²⁰−ζ³⁶	−ζ²⁰−ζ³⁶	−ζ²⁰−ζ³⁶	ζ²⁰+ζ³⁶	ζ²⁰+ζ³⁶	ζ²⁰+ζ³⁶	−ζ²⁰−ζ³⁶	0	0	0	0	0	0	0
χ₂₆	4	4	-4	0	0	0	0	−2ζ¹²−2ζ⁴⁴	−2ζ¹²−2ζ⁴⁴	2ζ¹²+2ζ⁴⁴	0	0	0	0	−2ζ⁴−2ζ⁵²	−2ζ⁴−2ζ⁵²	2ζ⁴+2ζ⁵²	0	0	0	0	−2ζ²⁰−2ζ³⁶	−2ζ²⁰−2ζ³⁶	2ζ²⁰+2ζ³⁶	0	0	0	0	0	0	0	0	0	0	0
χ₂₇	4	-4	0	$2 \sqrt{2}$	$- 2 \sqrt{2}$	0	0	−2ζ¹²−2ζ⁴⁴	2ζ¹²+2ζ⁴⁴	0	−ζ⁵+ζ²³−ζ³⁷+ζ⁴⁷	ζ⁵−ζ²³+ζ³⁷−ζ⁴⁷	0	0	−2ζ⁴−2ζ⁵²	2ζ⁴+2ζ⁵²	0	ζ³¹+ζ³⁹−ζ⁴⁵−ζ⁵³	−ζ³¹−ζ³⁹+ζ⁴⁵+ζ⁵³	0	0	−2ζ²⁰−2ζ³⁶	2ζ²⁰+2ζ³⁶	0	−ζ¹³+ζ¹⁵−ζ²⁹+ζ⁵⁵	ζ¹³−ζ¹⁵+ζ²⁹−ζ⁵⁵	0	0	0	0	0	0	0	0	0
χ₂₈	4	-4	0	$- 2 \sqrt{2}$	$2 \sqrt{2}$	0	0	−2ζ¹²−2ζ⁴⁴	2ζ¹²+2ζ⁴⁴	0	ζ⁵−ζ²³+ζ³⁷−ζ⁴⁷	−ζ⁵+ζ²³−ζ³⁷+ζ⁴⁷	0	0	−2ζ⁴−2ζ⁵²	2ζ⁴+2ζ⁵²	0	−ζ³¹−ζ³⁹+ζ⁴⁵+ζ⁵³	ζ³¹+ζ³⁹−ζ⁴⁵−ζ⁵³	0	0	−2ζ²⁰−2ζ³⁶	2ζ²⁰+2ζ³⁶	0	ζ¹³−ζ¹⁵+ζ²⁹−ζ⁵⁵	−ζ¹³+ζ¹⁵−ζ²⁹+ζ⁵⁵	0	0	0	0	0	0	0	0	0
χ₂₉	2	2	2	2	2	2	2	−ζ⁴−ζ⁵²	−ζ⁴−ζ⁵²	−ζ⁴−ζ⁵²	−ζ⁴−ζ⁵²	−ζ⁴−ζ⁵²	−ζ⁴−ζ⁵²	−ζ⁴−ζ⁵²	−ζ²⁰−ζ³⁶	−ζ²⁰−ζ³⁶	−ζ²⁰−ζ³⁶	−ζ²⁰−ζ³⁶	−ζ²⁰−ζ³⁶	−ζ²⁰−ζ³⁶	−ζ²⁰−ζ³⁶	−ζ¹²−ζ⁴⁴	−ζ¹²−ζ⁴⁴	−ζ¹²−ζ⁴⁴	−ζ¹²−ζ⁴⁴	−ζ¹²−ζ⁴⁴	−ζ¹²−ζ⁴⁴	−ζ¹²−ζ⁴⁴	0	0	0	0	0	0	0
χ₃₀	2	2	2	2	2	-2	-2	−ζ⁴−ζ⁵²	−ζ⁴−ζ⁵²	−ζ⁴−ζ⁵²	−ζ⁴−ζ⁵²	−ζ⁴−ζ⁵²	ζ⁴+ζ⁵²	ζ⁴+ζ⁵²	−ζ²⁰−ζ³⁶	−ζ²⁰−ζ³⁶	−ζ²⁰−ζ³⁶	−ζ²⁰−ζ³⁶	−ζ²⁰−ζ³⁶	ζ²⁰+ζ³⁶	ζ²⁰+ζ³⁶	−ζ¹²−ζ⁴⁴	−ζ¹²−ζ⁴⁴	−ζ¹²−ζ⁴⁴	−ζ¹²−ζ⁴⁴	−ζ¹²−ζ⁴⁴	ζ¹²+ζ⁴⁴	ζ¹²+ζ⁴⁴	0	0	0	0	0	0	0
χ₃₁	2	2	2	-2	-2	2	-2	−ζ⁴−ζ⁵²	−ζ⁴−ζ⁵²	−ζ⁴−ζ⁵²	ζ⁴+ζ⁵²	ζ⁴+ζ⁵²	−ζ⁴−ζ⁵²	ζ⁴+ζ⁵²	−ζ²⁰−ζ³⁶	−ζ²⁰−ζ³⁶	−ζ²⁰−ζ³⁶	ζ²⁰+ζ³⁶	ζ²⁰+ζ³⁶	−ζ²⁰−ζ³⁶	ζ²⁰+ζ³⁶	−ζ¹²−ζ⁴⁴	−ζ¹²−ζ⁴⁴	−ζ¹²−ζ⁴⁴	ζ¹²+ζ⁴⁴	ζ¹²+ζ⁴⁴	−ζ¹²−ζ⁴⁴	ζ¹²+ζ⁴⁴	0	0	0	0	0	0	0
χ₃₂	2	2	2	-2	-2	-2	2	−ζ⁴−ζ⁵²	−ζ⁴−ζ⁵²	−ζ⁴−ζ⁵²	ζ⁴+ζ⁵²	ζ⁴+ζ⁵²	ζ⁴+ζ⁵²	−ζ⁴−ζ⁵²	−ζ²⁰−ζ³⁶	−ζ²⁰−ζ³⁶	−ζ²⁰−ζ³⁶	ζ²⁰+ζ³⁶	ζ²⁰+ζ³⁶	ζ²⁰+ζ³⁶	−ζ²⁰−ζ³⁶	−ζ¹²−ζ⁴⁴	−ζ¹²−ζ⁴⁴	−ζ¹²−ζ⁴⁴	ζ¹²+ζ⁴⁴	ζ¹²+ζ⁴⁴	ζ¹²+ζ⁴⁴	−ζ¹²−ζ⁴⁴	0	0	0	0	0	0	0
χ₃₃	4	4	-4	0	0	0	0	−2ζ⁴−2ζ⁵²	−2ζ⁴−2ζ⁵²	2ζ⁴+2ζ⁵²	0	0	0	0	−2ζ²⁰−2ζ³⁶	−2ζ²⁰−2ζ³⁶	2ζ²⁰+2ζ³⁶	0	0	0	0	−2ζ¹²−2ζ⁴⁴	−2ζ¹²−2ζ⁴⁴	2ζ¹²+2ζ⁴⁴	0	0	0	0	0	0	0	0	0	0	0
χ₃₄	4	-4	0	$2 \sqrt{2}$	$- 2 \sqrt{2}$	0	0	−2ζ⁴−2ζ⁵²	2ζ⁴+2ζ⁵²	0	ζ³¹+ζ³⁹−ζ⁴⁵−ζ⁵³	−ζ³¹−ζ³⁹+ζ⁴⁵+ζ⁵³	0	0	−2ζ²⁰−2ζ³⁶	2ζ²⁰+2ζ³⁶	0	−ζ¹³+ζ¹⁵−ζ²⁹+ζ⁵⁵	ζ¹³−ζ¹⁵+ζ²⁹−ζ⁵⁵	0	0	−2ζ¹²−2ζ⁴⁴	2ζ¹²+2ζ⁴⁴	0	−ζ⁵+ζ²³−ζ³⁷+ζ⁴⁷	ζ⁵−ζ²³+ζ³⁷−ζ⁴⁷	0	0	0	0	0	0	0	0	0
χ₃₅	4	-4	0	$- 2 \sqrt{2}$	$2 \sqrt{2}$	0	0	−2ζ⁴−2ζ⁵²	2ζ⁴+2ζ⁵²	0	−ζ³¹−ζ³⁹+ζ⁴⁵+ζ⁵³	ζ³¹+ζ³⁹−ζ⁴⁵−ζ⁵³	0	0	−2ζ²⁰−2ζ³⁶	2ζ²⁰+2ζ³⁶	0	ζ¹³−ζ¹⁵+ζ²⁹−ζ⁵⁵	−ζ¹³+ζ¹⁵−ζ²⁹+ζ⁵⁵	0	0	−2ζ¹²−2ζ⁴⁴	2ζ¹²+2ζ⁴⁴	0	ζ⁵−ζ²³+ζ³⁷−ζ⁴⁷	−ζ⁵+ζ²³−ζ³⁷+ζ⁴⁷	0	0	0	0	0	0	0	0	0

Character table — Group #6480