Group #91985 — 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	C₄₀	C₄₁	C₄₂	C₄₃	C₄₄	C₄₅	C₄₆	C₄₇	C₄₈	C₄₉	C₅₀	C₅₁	C₅₂	C₅₃	C₅₄	C₅₅	C₅₆	C₅₇	C₅₈	C₅₉	C₆₀
size	1	1	2	2	2	2	2	4	4	4	4	4	4	4	4	4	4	4	4	5	5	10	10	10	10	10	30	30	30	30	1	1	2	2	2	2	2	4	4	4	4	4	4	4	4	4	4	4	4	5	5	10	10	10	10	10	30	30	30	30
order	1	2	3	4	6	12	12	5	10	15	15	20	20	30	30	60	60	60	60	4	4	2	6	6	12	12	8	8	8	8	2	2	6	4	6	12	12	10	10	30	30	20	20	30	30	60	60	60	60	4	4	2	6	6	12	12	8	8	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	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	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	$i$	$i$	$- i$	$- i$	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	-1	-1	-1	-1	-1	-1	-1	$i$	$i$	$- i$	$- i$
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	$- i$	$- i$	$i$	$i$	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	-1	-1	-1	-1	-1	-1	-1	$- i$	$- i$	$i$	$i$
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	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	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	$i$	$- i$	$- i$	$i$	1	1	1	-1	1	-1	-1	1	1	1	1	-1	-1	1	1	-1	-1	-1	-1	-1	-1	1	1	1	-1	-1	$i$	$- i$	$- i$	$i$
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	$- i$	$i$	$i$	$- i$	1	1	1	-1	1	-1	-1	1	1	1	1	-1	-1	1	1	-1	-1	-1	-1	-1	-1	1	1	1	-1	-1	$- i$	$i$	$i$	$- i$
χ₉	2	2	-1	2	-1	-1	-1	2	2	-1	-1	2	2	-1	-1	-1	-1	-1	-1	2	2	2	-1	-1	-1	-1	0	0	0	0	2	2	-1	2	-1	-1	-1	2	2	-1	-1	2	2	-1	-1	-1	-1	-1	-1	2	2	2	-1	-1	-1	-1	0	0	0	0
χ₁₀	2	2	-1	2	-1	-1	-1	2	2	-1	-1	2	2	-1	-1	-1	-1	-1	-1	-2	-2	-2	1	1	1	1	0	0	0	0	2	2	-1	2	-1	-1	-1	2	2	-1	-1	2	2	-1	-1	-1	-1	-1	-1	-2	-2	-2	1	1	1	1	0	0	0	0
χ₁₁	2	2	-1	-2	-1	1	1	2	2	-1	-1	-2	-2	-1	-1	1	1	1	1	2	2	-2	1	1	-1	-1	0	0	0	0	2	2	-1	-2	-1	1	1	2	2	-1	-1	-2	-2	-1	-1	1	1	1	1	2	2	-2	1	1	-1	-1	0	0	0	0
χ₁₂	2	2	-1	-2	-1	1	1	2	2	-1	-1	-2	-2	-1	-1	1	1	1	1	-2	-2	2	-1	-1	1	1	0	0	0	0	2	2	-1	-2	-1	1	1	2	2	-1	-1	-2	-2	-1	-1	1	1	1	1	-2	-2	2	-1	-1	1	1	0	0	0	0
χ₁₃	2	-2	2	0	-2	0	0	2	-2	2	2	0	0	-2	-2	0	0	0	0	$2 i$	$- 2 i$	0	0	0	$2 i$	$- 2 i$	0	0	0	0	2	-2	2	0	-2	0	0	2	-2	2	2	0	0	-2	-2	0	0	0	0	$2 i$	$- 2 i$	0	0	0	$2 i$	$- 2 i$	0	0	0	0
χ₁₄	2	-2	2	0	-2	0	0	2	-2	2	2	0	0	-2	-2	0	0	0	0	$- 2 i$	$2 i$	0	0	0	$- 2 i$	$2 i$	0	0	0	0	2	-2	2	0	-2	0	0	2	-2	2	2	0	0	-2	-2	0	0	0	0	$- 2 i$	$2 i$	0	0	0	$- 2 i$	$2 i$	0	0	0	0
χ₁₅	2	-2	-1	0	1	$\sqrt{3}$	$- \sqrt{3}$	2	-2	-1	-1	0	0	1	1	$\sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$- \sqrt{3}$	$2 i$	$- 2 i$	0	$- i \sqrt{3}$	$i \sqrt{3}$	$- i$	$i$	0	0	0	0	2	-2	-1	0	1	$\sqrt{3}$	$- \sqrt{3}$	2	-2	-1	-1	0	0	1	1	$\sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$- \sqrt{3}$	$2 i$	$- 2 i$	0	$- i \sqrt{3}$	$i \sqrt{3}$	$- i$	$i$	0	0	0	0
χ₁₆	2	-2	-1	0	1	$\sqrt{3}$	$- \sqrt{3}$	2	-2	-1	-1	0	0	1	1	$\sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$- \sqrt{3}$	$- 2 i$	$2 i$	0	$i \sqrt{3}$	$- i \sqrt{3}$	$i$	$- i$	0	0	0	0	2	-2	-1	0	1	$\sqrt{3}$	$- \sqrt{3}$	2	-2	-1	-1	0	0	1	1	$\sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$- \sqrt{3}$	$- 2 i$	$2 i$	0	$i \sqrt{3}$	$- i \sqrt{3}$	$i$	$- i$	0	0	0	0
χ₁₇	2	-2	-1	0	1	$- \sqrt{3}$	$\sqrt{3}$	2	-2	-1	-1	0	0	1	1	$- \sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$\sqrt{3}$	$2 i$	$- 2 i$	0	$i \sqrt{3}$	$- i \sqrt{3}$	$- i$	$i$	0	0	0	0	2	-2	-1	0	1	$- \sqrt{3}$	$\sqrt{3}$	2	-2	-1	-1	0	0	1	1	$- \sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$\sqrt{3}$	$2 i$	$- 2 i$	0	$i \sqrt{3}$	$- i \sqrt{3}$	$- i$	$i$	0	0	0	0
χ₁₈	2	-2	-1	0	1	$- \sqrt{3}$	$\sqrt{3}$	2	-2	-1	-1	0	0	1	1	$- \sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$\sqrt{3}$	$- 2 i$	$2 i$	0	$- i \sqrt{3}$	$i \sqrt{3}$	$i$	$- i$	0	0	0	0	2	-2	-1	0	1	$- \sqrt{3}$	$\sqrt{3}$	2	-2	-1	-1	0	0	1	1	$- \sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$\sqrt{3}$	$- 2 i$	$2 i$	0	$- i \sqrt{3}$	$i \sqrt{3}$	$i$	$- i$	0	0	0	0
χ₁₉	4	4	4	4	4	4	4	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	0	0	0	0	0	0	0	0	0	0	0	4	4	4	4	4	4	4	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	0	0	0	0	0	0	0	0	0	0	0
χ₂₀	4	4	4	-4	4	-4	-4	-1	-1	-1	-1	1	1	-1	-1	1	1	1	1	0	0	0	0	0	0	0	0	0	0	0	4	4	4	-4	4	-4	-4	-1	-1	-1	-1	1	1	-1	-1	1	1	1	1	0	0	0	0	0	0	0	0	0	0	0
χ₂₁	4	4	-2	4	-2	-2	-2	-1	-1	$\frac{1 - i \sqrt{15}}{2}$	$\frac{1 + i \sqrt{15}}{2}$	-1	-1	$\frac{1 - i \sqrt{15}}{2}$	$\frac{1 + i \sqrt{15}}{2}$	$\frac{1 - i \sqrt{15}}{2}$	$\frac{1 + i \sqrt{15}}{2}$	$\frac{1 - i \sqrt{15}}{2}$	$\frac{1 + i \sqrt{15}}{2}$	0	0	0	0	0	0	0	0	0	0	0	4	4	-2	4	-2	-2	-2	-1	-1	$\frac{1 - i \sqrt{15}}{2}$	$\frac{1 + i \sqrt{15}}{2}$	-1	-1	$\frac{1 - i \sqrt{15}}{2}$	$\frac{1 + i \sqrt{15}}{2}$	$\frac{1 - i \sqrt{15}}{2}$	$\frac{1 + i \sqrt{15}}{2}$	$\frac{1 - i \sqrt{15}}{2}$	$\frac{1 + i \sqrt{15}}{2}$	0	0	0	0	0	0	0	0	0	0	0
χ₂₂	4	4	-2	4	-2	-2	-2	-1	-1	$\frac{1 + i \sqrt{15}}{2}$	$\frac{1 - i \sqrt{15}}{2}$	-1	-1	$\frac{1 + i \sqrt{15}}{2}$	$\frac{1 - i \sqrt{15}}{2}$	$\frac{1 + i \sqrt{15}}{2}$	$\frac{1 - i \sqrt{15}}{2}$	$\frac{1 + i \sqrt{15}}{2}$	$\frac{1 - i \sqrt{15}}{2}$	0	0	0	0	0	0	0	0	0	0	0	4	4	-2	4	-2	-2	-2	-1	-1	$\frac{1 + i \sqrt{15}}{2}$	$\frac{1 - i \sqrt{15}}{2}$	-1	-1	$\frac{1 + i \sqrt{15}}{2}$	$\frac{1 - i \sqrt{15}}{2}$	$\frac{1 + i \sqrt{15}}{2}$	$\frac{1 - i \sqrt{15}}{2}$	$\frac{1 + i \sqrt{15}}{2}$	$\frac{1 - i \sqrt{15}}{2}$	0	0	0	0	0	0	0	0	0	0	0
χ₂₃	4	4	-2	-4	-2	2	2	-1	-1	$\frac{1 - i \sqrt{15}}{2}$	$\frac{1 + i \sqrt{15}}{2}$	1	1	$\frac{1 - i \sqrt{15}}{2}$	$\frac{1 + i \sqrt{15}}{2}$	$\frac{- 1 + i \sqrt{15}}{2}$	$\frac{- 1 - i \sqrt{15}}{2}$	$\frac{- 1 + i \sqrt{15}}{2}$	$\frac{- 1 - i \sqrt{15}}{2}$	0	0	0	0	0	0	0	0	0	0	0	4	4	-2	-4	-2	2	2	-1	-1	$\frac{1 - i \sqrt{15}}{2}$	$\frac{1 + i \sqrt{15}}{2}$	1	1	$\frac{1 - i \sqrt{15}}{2}$	$\frac{1 + i \sqrt{15}}{2}$	$\frac{- 1 + i \sqrt{15}}{2}$	$\frac{- 1 - i \sqrt{15}}{2}$	$\frac{- 1 + i \sqrt{15}}{2}$	$\frac{- 1 - i \sqrt{15}}{2}$	0	0	0	0	0	0	0	0	0	0	0
χ₂₄	4	4	-2	-4	-2	2	2	-1	-1	$\frac{1 + i \sqrt{15}}{2}$	$\frac{1 - i \sqrt{15}}{2}$	1	1	$\frac{1 + i \sqrt{15}}{2}$	$\frac{1 - i \sqrt{15}}{2}$	$\frac{- 1 - i \sqrt{15}}{2}$	$\frac{- 1 + i \sqrt{15}}{2}$	$\frac{- 1 - i \sqrt{15}}{2}$	$\frac{- 1 + i \sqrt{15}}{2}$	0	0	0	0	0	0	0	0	0	0	0	4	4	-2	-4	-2	2	2	-1	-1	$\frac{1 + i \sqrt{15}}{2}$	$\frac{1 - i \sqrt{15}}{2}$	1	1	$\frac{1 + i \sqrt{15}}{2}$	$\frac{1 - i \sqrt{15}}{2}$	$\frac{- 1 - i \sqrt{15}}{2}$	$\frac{- 1 + i \sqrt{15}}{2}$	$\frac{- 1 - i \sqrt{15}}{2}$	$\frac{- 1 + i \sqrt{15}}{2}$	0	0	0	0	0	0	0	0	0	0	0
χ₂₅	4	-4	4	0	-4	0	0	-1	1	-1	-1	$- i \sqrt{5}$	$i \sqrt{5}$	1	1	$- i \sqrt{5}$	$i \sqrt{5}$	$i \sqrt{5}$	$- i \sqrt{5}$	0	0	0	0	0	0	0	0	0	0	0	4	-4	4	0	-4	0	0	-1	1	-1	-1	$- i \sqrt{5}$	$i \sqrt{5}$	1	1	$- i \sqrt{5}$	$i \sqrt{5}$	$i \sqrt{5}$	$- i \sqrt{5}$	0	0	0	0	0	0	0	0	0	0	0
χ₂₆	4	-4	4	0	-4	0	0	-1	1	-1	-1	$i \sqrt{5}$	$- i \sqrt{5}$	1	1	$i \sqrt{5}$	$- i \sqrt{5}$	$- i \sqrt{5}$	$i \sqrt{5}$	0	0	0	0	0	0	0	0	0	0	0	4	-4	4	0	-4	0	0	-1	1	-1	-1	$i \sqrt{5}$	$- i \sqrt{5}$	1	1	$i \sqrt{5}$	$- i \sqrt{5}$	$- i \sqrt{5}$	$i \sqrt{5}$	0	0	0	0	0	0	0	0	0	0	0
χ₂₇	4	-4	-2	0	2	$2 \sqrt{3}$	$- 2 \sqrt{3}$	-1	1	$\frac{1 - i \sqrt{15}}{2}$	$\frac{1 + i \sqrt{15}}{2}$	$i \sqrt{5}$	$- i \sqrt{5}$	$\frac{- 1 + i \sqrt{15}}{2}$	$\frac{- 1 - i \sqrt{15}}{2}$	ζ⁷−ζ¹¹+ζ⁴³−ζ⁵⁹	ζ¹⁹−ζ²³+ζ³¹−ζ⁴⁷	−ζ⁷+ζ¹¹−ζ⁴³+ζ⁵⁹	−ζ¹⁹+ζ²³−ζ³¹+ζ⁴⁷	0	0	0	0	0	0	0	0	0	0	0	4	-4	-2	0	2	$2 \sqrt{3}$	$- 2 \sqrt{3}$	-1	1	$\frac{1 - i \sqrt{15}}{2}$	$\frac{1 + i \sqrt{15}}{2}$	$i \sqrt{5}$	$- i \sqrt{5}$	$\frac{- 1 + i \sqrt{15}}{2}$	$\frac{- 1 - i \sqrt{15}}{2}$	ζ⁷−ζ¹¹+ζ⁴³−ζ⁵⁹	ζ¹⁹−ζ²³+ζ³¹−ζ⁴⁷	−ζ⁷+ζ¹¹−ζ⁴³+ζ⁵⁹	−ζ¹⁹+ζ²³−ζ³¹+ζ⁴⁷	0	0	0	0	0	0	0	0	0	0	0
χ₂₈	4	-4	-2	0	2	$2 \sqrt{3}$	$- 2 \sqrt{3}$	-1	1	$\frac{1 + i \sqrt{15}}{2}$	$\frac{1 - i \sqrt{15}}{2}$	$- i \sqrt{5}$	$i \sqrt{5}$	$\frac{- 1 - i \sqrt{15}}{2}$	$\frac{- 1 + i \sqrt{15}}{2}$	ζ¹⁹−ζ²³+ζ³¹−ζ⁴⁷	ζ⁷−ζ¹¹+ζ⁴³−ζ⁵⁹	−ζ¹⁹+ζ²³−ζ³¹+ζ⁴⁷	−ζ⁷+ζ¹¹−ζ⁴³+ζ⁵⁹	0	0	0	0	0	0	0	0	0	0	0	4	-4	-2	0	2	$2 \sqrt{3}$	$- 2 \sqrt{3}$	-1	1	$\frac{1 + i \sqrt{15}}{2}$	$\frac{1 - i \sqrt{15}}{2}$	$- i \sqrt{5}$	$i \sqrt{5}$	$\frac{- 1 - i \sqrt{15}}{2}$	$\frac{- 1 + i \sqrt{15}}{2}$	ζ¹⁹−ζ²³+ζ³¹−ζ⁴⁷	ζ⁷−ζ¹¹+ζ⁴³−ζ⁵⁹	−ζ¹⁹+ζ²³−ζ³¹+ζ⁴⁷	−ζ⁷+ζ¹¹−ζ⁴³+ζ⁵⁹	0	0	0	0	0	0	0	0	0	0	0
χ₂₉	4	-4	-2	0	2	$- 2 \sqrt{3}$	$2 \sqrt{3}$	-1	1	$\frac{1 - i \sqrt{15}}{2}$	$\frac{1 + i \sqrt{15}}{2}$	$- i \sqrt{5}$	$i \sqrt{5}$	$\frac{- 1 + i \sqrt{15}}{2}$	$\frac{- 1 - i \sqrt{15}}{2}$	−ζ⁷+ζ¹¹−ζ⁴³+ζ⁵⁹	−ζ¹⁹+ζ²³−ζ³¹+ζ⁴⁷	ζ⁷−ζ¹¹+ζ⁴³−ζ⁵⁹	ζ¹⁹−ζ²³+ζ³¹−ζ⁴⁷	0	0	0	0	0	0	0	0	0	0	0	4	-4	-2	0	2	$- 2 \sqrt{3}$	$2 \sqrt{3}$	-1	1	$\frac{1 - i \sqrt{15}}{2}$	$\frac{1 + i \sqrt{15}}{2}$	$- i \sqrt{5}$	$i \sqrt{5}$	$\frac{- 1 + i \sqrt{15}}{2}$	$\frac{- 1 - i \sqrt{15}}{2}$	−ζ⁷+ζ¹¹−ζ⁴³+ζ⁵⁹	−ζ¹⁹+ζ²³−ζ³¹+ζ⁴⁷	ζ⁷−ζ¹¹+ζ⁴³−ζ⁵⁹	ζ¹⁹−ζ²³+ζ³¹−ζ⁴⁷	0	0	0	0	0	0	0	0	0	0	0
χ₃₀	4	-4	-2	0	2	$- 2 \sqrt{3}$	$2 \sqrt{3}$	-1	1	$\frac{1 + i \sqrt{15}}{2}$	$\frac{1 - i \sqrt{15}}{2}$	$i \sqrt{5}$	$- i \sqrt{5}$	$\frac{- 1 - i \sqrt{15}}{2}$	$\frac{- 1 + i \sqrt{15}}{2}$	−ζ¹⁹+ζ²³−ζ³¹+ζ⁴⁷	−ζ⁷+ζ¹¹−ζ⁴³+ζ⁵⁹	ζ¹⁹−ζ²³+ζ³¹−ζ⁴⁷	ζ⁷−ζ¹¹+ζ⁴³−ζ⁵⁹	0	0	0	0	0	0	0	0	0	0	0	4	-4	-2	0	2	$- 2 \sqrt{3}$	$2 \sqrt{3}$	-1	1	$\frac{1 + i \sqrt{15}}{2}$	$\frac{1 - i \sqrt{15}}{2}$	$i \sqrt{5}$	$- i \sqrt{5}$	$\frac{- 1 - i \sqrt{15}}{2}$	$\frac{- 1 + i \sqrt{15}}{2}$	−ζ¹⁹+ζ²³−ζ³¹+ζ⁴⁷	−ζ⁷+ζ¹¹−ζ⁴³+ζ⁵⁹	ζ¹⁹−ζ²³+ζ³¹−ζ⁴⁷	ζ⁷−ζ¹¹+ζ⁴³−ζ⁵⁹	0	0	0	0	0	0	0	0	0	0	0
χ₃₁	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1
χ₃₂	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	1	1	1	1
χ₃₃	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	-1	-1	-1	-1	-1	-1	-1	$i$	$i$	$- i$	$- i$	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	1	1	1	1	1	1	1	$- i$	$- i$	$i$	$i$
χ₃₄	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	-1	-1	-1	-1	-1	-1	-1	$- i$	$- i$	$i$	$i$	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	1	1	1	1	1	1	1	$i$	$i$	$- i$	$- i$
χ₃₅	1	1	1	-1	1	-1	-1	1	1	1	1	-1	-1	1	1	-1	-1	-1	-1	1	1	-1	-1	-1	1	1	1	-1	1	-1	-1	-1	-1	1	-1	1	1	-1	-1	-1	-1	1	1	-1	-1	1	1	1	1	-1	-1	1	1	1	-1	-1	-1	1	-1	1
χ₃₆	1	1	1	-1	1	-1	-1	1	1	1	1	-1	-1	1	1	-1	-1	-1	-1	1	1	-1	-1	-1	1	1	-1	1	-1	1	-1	-1	-1	1	-1	1	1	-1	-1	-1	-1	1	1	-1	-1	1	1	1	1	-1	-1	1	1	1	-1	-1	1	-1	1	-1
χ₃₇	1	1	1	-1	1	-1	-1	1	1	1	1	-1	-1	1	1	-1	-1	-1	-1	-1	-1	1	1	1	-1	-1	$i$	$- i$	$- i$	$i$	-1	-1	-1	1	-1	1	1	-1	-1	-1	-1	1	1	-1	-1	1	1	1	1	1	1	-1	-1	-1	1	1	$- i$	$i$	$i$	$- i$
χ₃₈	1	1	1	-1	1	-1	-1	1	1	1	1	-1	-1	1	1	-1	-1	-1	-1	-1	-1	1	1	1	-1	-1	$- i$	$i$	$i$	$- i$	-1	-1	-1	1	-1	1	1	-1	-1	-1	-1	1	1	-1	-1	1	1	1	1	1	1	-1	-1	-1	1	1	$i$	$- i$	$- i$	$i$
χ₃₉	2	2	-1	2	-1	-1	-1	2	2	-1	-1	2	2	-1	-1	-1	-1	-1	-1	2	2	2	-1	-1	-1	-1	0	0	0	0	-2	-2	1	-2	1	1	1	-2	-2	1	1	-2	-2	1	1	1	1	1	1	-2	-2	-2	1	1	1	1	0	0	0	0
χ₄₀	2	2	-1	2	-1	-1	-1	2	2	-1	-1	2	2	-1	-1	-1	-1	-1	-1	-2	-2	-2	1	1	1	1	0	0	0	0	-2	-2	1	-2	1	1	1	-2	-2	1	1	-2	-2	1	1	1	1	1	1	2	2	2	-1	-1	-1	-1	0	0	0	0
χ₄₁	2	2	-1	-2	-1	1	1	2	2	-1	-1	-2	-2	-1	-1	1	1	1	1	2	2	-2	1	1	-1	-1	0	0	0	0	-2	-2	1	2	1	-1	-1	-2	-2	1	1	2	2	1	1	-1	-1	-1	-1	-2	-2	2	-1	-1	1	1	0	0	0	0
χ₄₂	2	2	-1	-2	-1	1	1	2	2	-1	-1	-2	-2	-1	-1	1	1	1	1	-2	-2	2	-1	-1	1	1	0	0	0	0	-2	-2	1	2	1	-1	-1	-2	-2	1	1	2	2	1	1	-1	-1	-1	-1	2	2	-2	1	1	-1	-1	0	0	0	0
χ₄₃	2	-2	2	0	-2	0	0	2	-2	2	2	0	0	-2	-2	0	0	0	0	$2 i$	$- 2 i$	0	0	0	$2 i$	$- 2 i$	0	0	0	0	-2	2	-2	0	2	0	0	-2	2	-2	-2	0	0	2	2	0	0	0	0	$- 2 i$	$2 i$	0	0	0	$- 2 i$	$2 i$	0	0	0	0
χ₄₄	2	-2	2	0	-2	0	0	2	-2	2	2	0	0	-2	-2	0	0	0	0	$- 2 i$	$2 i$	0	0	0	$- 2 i$	$2 i$	0	0	0	0	-2	2	-2	0	2	0	0	-2	2	-2	-2	0	0	2	2	0	0	0	0	$2 i$	$- 2 i$	0	0	0	$2 i$	$- 2 i$	0	0	0	0
χ₄₅	2	-2	-1	0	1	$\sqrt{3}$	$- \sqrt{3}$	2	-2	-1	-1	0	0	1	1	$\sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$- \sqrt{3}$	$2 i$	$- 2 i$	0	$- i \sqrt{3}$	$i \sqrt{3}$	$- i$	$i$	0	0	0	0	-2	2	1	0	-1	$- \sqrt{3}$	$\sqrt{3}$	-2	2	1	1	0	0	-1	-1	$- \sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$\sqrt{3}$	$- 2 i$	$2 i$	0	$i \sqrt{3}$	$- i \sqrt{3}$	$i$	$- i$	0	0	0	0
χ₄₆	2	-2	-1	0	1	$\sqrt{3}$	$- \sqrt{3}$	2	-2	-1	-1	0	0	1	1	$\sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$- \sqrt{3}$	$- 2 i$	$2 i$	0	$i \sqrt{3}$	$- i \sqrt{3}$	$i$	$- i$	0	0	0	0	-2	2	1	0	-1	$- \sqrt{3}$	$\sqrt{3}$	-2	2	1	1	0	0	-1	-1	$- \sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$\sqrt{3}$	$2 i$	$- 2 i$	0	$- i \sqrt{3}$	$i \sqrt{3}$	$- i$	$i$	0	0	0	0
χ₄₇	2	-2	-1	0	1	$- \sqrt{3}$	$\sqrt{3}$	2	-2	-1	-1	0	0	1	1	$- \sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$\sqrt{3}$	$2 i$	$- 2 i$	0	$i \sqrt{3}$	$- i \sqrt{3}$	$- i$	$i$	0	0	0	0	-2	2	1	0	-1	$\sqrt{3}$	$- \sqrt{3}$	-2	2	1	1	0	0	-1	-1	$\sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$- \sqrt{3}$	$- 2 i$	$2 i$	0	$- i \sqrt{3}$	$i \sqrt{3}$	$i$	$- i$	0	0	0	0
χ₄₈	2	-2	-1	0	1	$- \sqrt{3}$	$\sqrt{3}$	2	-2	-1	-1	0	0	1	1	$- \sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$\sqrt{3}$	$- 2 i$	$2 i$	0	$- i \sqrt{3}$	$i \sqrt{3}$	$i$	$- i$	0	0	0	0	-2	2	1	0	-1	$\sqrt{3}$	$- \sqrt{3}$	-2	2	1	1	0	0	-1	-1	$\sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$- \sqrt{3}$	$2 i$	$- 2 i$	0	$i \sqrt{3}$	$- i \sqrt{3}$	$- i$	$i$	0	0	0	0
χ₄₉	4	4	4	4	4	4	4	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	0	0	0	0	0	0	0	0	0	0	0	-4	-4	-4	-4	-4	-4	-4	1	1	1	1	1	1	1	1	1	1	1	1	0	0	0	0	0	0	0	0	0	0	0
χ₅₀	4	4	4	-4	4	-4	-4	-1	-1	-1	-1	1	1	-1	-1	1	1	1	1	0	0	0	0	0	0	0	0	0	0	0	-4	-4	-4	4	-4	4	4	1	1	1	1	-1	-1	1	1	-1	-1	-1	-1	0	0	0	0	0	0	0	0	0	0	0
χ₅₁	4	4	-2	4	-2	-2	-2	-1	-1	$\frac{1 - i \sqrt{15}}{2}$	$\frac{1 + i \sqrt{15}}{2}$	-1	-1	$\frac{1 - i \sqrt{15}}{2}$	$\frac{1 + i \sqrt{15}}{2}$	$\frac{1 - i \sqrt{15}}{2}$	$\frac{1 + i \sqrt{15}}{2}$	$\frac{1 - i \sqrt{15}}{2}$	$\frac{1 + i \sqrt{15}}{2}$	0	0	0	0	0	0	0	0	0	0	0	-4	-4	2	-4	2	2	2	1	1	$\frac{- 1 + i \sqrt{15}}{2}$	$\frac{- 1 - i \sqrt{15}}{2}$	1	1	$\frac{- 1 + i \sqrt{15}}{2}$	$\frac{- 1 - i \sqrt{15}}{2}$	$\frac{- 1 + i \sqrt{15}}{2}$	$\frac{- 1 - i \sqrt{15}}{2}$	$\frac{- 1 + i \sqrt{15}}{2}$	$\frac{- 1 - i \sqrt{15}}{2}$	0	0	0	0	0	0	0	0	0	0	0
χ₅₂	4	4	-2	4	-2	-2	-2	-1	-1	$\frac{1 + i \sqrt{15}}{2}$	$\frac{1 - i \sqrt{15}}{2}$	-1	-1	$\frac{1 + i \sqrt{15}}{2}$	$\frac{1 - i \sqrt{15}}{2}$	$\frac{1 + i \sqrt{15}}{2}$	$\frac{1 - i \sqrt{15}}{2}$	$\frac{1 + i \sqrt{15}}{2}$	$\frac{1 - i \sqrt{15}}{2}$	0	0	0	0	0	0	0	0	0	0	0	-4	-4	2	-4	2	2	2	1	1	$\frac{- 1 - i \sqrt{15}}{2}$	$\frac{- 1 + i \sqrt{15}}{2}$	1	1	$\frac{- 1 - i \sqrt{15}}{2}$	$\frac{- 1 + i \sqrt{15}}{2}$	$\frac{- 1 - i \sqrt{15}}{2}$	$\frac{- 1 + i \sqrt{15}}{2}$	$\frac{- 1 - i \sqrt{15}}{2}$	$\frac{- 1 + i \sqrt{15}}{2}$	0	0	0	0	0	0	0	0	0	0	0
χ₅₃	4	4	-2	-4	-2	2	2	-1	-1	$\frac{1 - i \sqrt{15}}{2}$	$\frac{1 + i \sqrt{15}}{2}$	1	1	$\frac{1 - i \sqrt{15}}{2}$	$\frac{1 + i \sqrt{15}}{2}$	$\frac{- 1 + i \sqrt{15}}{2}$	$\frac{- 1 - i \sqrt{15}}{2}$	$\frac{- 1 + i \sqrt{15}}{2}$	$\frac{- 1 - i \sqrt{15}}{2}$	0	0	0	0	0	0	0	0	0	0	0	-4	-4	2	4	2	-2	-2	1	1	$\frac{- 1 + i \sqrt{15}}{2}$	$\frac{- 1 - i \sqrt{15}}{2}$	-1	-1	$\frac{- 1 + i \sqrt{15}}{2}$	$\frac{- 1 - i \sqrt{15}}{2}$	$\frac{1 - i \sqrt{15}}{2}$	$\frac{1 + i \sqrt{15}}{2}$	$\frac{1 - i \sqrt{15}}{2}$	$\frac{1 + i \sqrt{15}}{2}$	0	0	0	0	0	0	0	0	0	0	0
χ₅₄	4	4	-2	-4	-2	2	2	-1	-1	$\frac{1 + i \sqrt{15}}{2}$	$\frac{1 - i \sqrt{15}}{2}$	1	1	$\frac{1 + i \sqrt{15}}{2}$	$\frac{1 - i \sqrt{15}}{2}$	$\frac{- 1 - i \sqrt{15}}{2}$	$\frac{- 1 + i \sqrt{15}}{2}$	$\frac{- 1 - i \sqrt{15}}{2}$	$\frac{- 1 + i \sqrt{15}}{2}$	0	0	0	0	0	0	0	0	0	0	0	-4	-4	2	4	2	-2	-2	1	1	$\frac{- 1 - i \sqrt{15}}{2}$	$\frac{- 1 + i \sqrt{15}}{2}$	-1	-1	$\frac{- 1 - i \sqrt{15}}{2}$	$\frac{- 1 + i \sqrt{15}}{2}$	$\frac{1 + i \sqrt{15}}{2}$	$\frac{1 - i \sqrt{15}}{2}$	$\frac{1 + i \sqrt{15}}{2}$	$\frac{1 - i \sqrt{15}}{2}$	0	0	0	0	0	0	0	0	0	0	0
χ₅₅	4	-4	4	0	-4	0	0	-1	1	-1	-1	$- i \sqrt{5}$	$i \sqrt{5}$	1	1	$- i \sqrt{5}$	$i \sqrt{5}$	$i \sqrt{5}$	$- i \sqrt{5}$	0	0	0	0	0	0	0	0	0	0	0	-4	4	-4	0	4	0	0	1	-1	1	1	$i \sqrt{5}$	$- i \sqrt{5}$	-1	-1	$i \sqrt{5}$	$- i \sqrt{5}$	$- i \sqrt{5}$	$i \sqrt{5}$	0	0	0	0	0	0	0	0	0	0	0
χ₅₆	4	-4	4	0	-4	0	0	-1	1	-1	-1	$i \sqrt{5}$	$- i \sqrt{5}$	1	1	$i \sqrt{5}$	$- i \sqrt{5}$	$- i \sqrt{5}$	$i \sqrt{5}$	0	0	0	0	0	0	0	0	0	0	0	-4	4	-4	0	4	0	0	1	-1	1	1	$- i \sqrt{5}$	$i \sqrt{5}$	-1	-1	$- i \sqrt{5}$	$i \sqrt{5}$	$i \sqrt{5}$	$- i \sqrt{5}$	0	0	0	0	0	0	0	0	0	0	0
χ₅₇	4	-4	-2	0	2	$2 \sqrt{3}$	$- 2 \sqrt{3}$	-1	1	$\frac{1 - i \sqrt{15}}{2}$	$\frac{1 + i \sqrt{15}}{2}$	$i \sqrt{5}$	$- i \sqrt{5}$	$\frac{- 1 + i \sqrt{15}}{2}$	$\frac{- 1 - i \sqrt{15}}{2}$	ζ⁷−ζ¹¹+ζ⁴³−ζ⁵⁹	ζ¹⁹−ζ²³+ζ³¹−ζ⁴⁷	−ζ⁷+ζ¹¹−ζ⁴³+ζ⁵⁹	−ζ¹⁹+ζ²³−ζ³¹+ζ⁴⁷	0	0	0	0	0	0	0	0	0	0	0	-4	4	2	0	-2	$- 2 \sqrt{3}$	$2 \sqrt{3}$	1	-1	$\frac{- 1 + i \sqrt{15}}{2}$	$\frac{- 1 - i \sqrt{15}}{2}$	$- i \sqrt{5}$	$i \sqrt{5}$	$\frac{1 - i \sqrt{15}}{2}$	$\frac{1 + i \sqrt{15}}{2}$	−ζ⁷+ζ¹¹−ζ⁴³+ζ⁵⁹	−ζ¹⁹+ζ²³−ζ³¹+ζ⁴⁷	ζ⁷−ζ¹¹+ζ⁴³−ζ⁵⁹	ζ¹⁹−ζ²³+ζ³¹−ζ⁴⁷	0	0	0	0	0	0	0	0	0	0	0
χ₅₈	4	-4	-2	0	2	$2 \sqrt{3}$	$- 2 \sqrt{3}$	-1	1	$\frac{1 + i \sqrt{15}}{2}$	$\frac{1 - i \sqrt{15}}{2}$	$- i \sqrt{5}$	$i \sqrt{5}$	$\frac{- 1 - i \sqrt{15}}{2}$	$\frac{- 1 + i \sqrt{15}}{2}$	ζ¹⁹−ζ²³+ζ³¹−ζ⁴⁷	ζ⁷−ζ¹¹+ζ⁴³−ζ⁵⁹	−ζ¹⁹+ζ²³−ζ³¹+ζ⁴⁷	−ζ⁷+ζ¹¹−ζ⁴³+ζ⁵⁹	0	0	0	0	0	0	0	0	0	0	0	-4	4	2	0	-2	$- 2 \sqrt{3}$	$2 \sqrt{3}$	1	-1	$\frac{- 1 - i \sqrt{15}}{2}$	$\frac{- 1 + i \sqrt{15}}{2}$	$i \sqrt{5}$	$- i \sqrt{5}$	$\frac{1 + i \sqrt{15}}{2}$	$\frac{1 - i \sqrt{15}}{2}$	−ζ¹⁹+ζ²³−ζ³¹+ζ⁴⁷	−ζ⁷+ζ¹¹−ζ⁴³+ζ⁵⁹	ζ¹⁹−ζ²³+ζ³¹−ζ⁴⁷	ζ⁷−ζ¹¹+ζ⁴³−ζ⁵⁹	0	0	0	0	0	0	0	0	0	0	0
χ₅₉	4	-4	-2	0	2	$- 2 \sqrt{3}$	$2 \sqrt{3}$	-1	1	$\frac{1 - i \sqrt{15}}{2}$	$\frac{1 + i \sqrt{15}}{2}$	$- i \sqrt{5}$	$i \sqrt{5}$	$\frac{- 1 + i \sqrt{15}}{2}$	$\frac{- 1 - i \sqrt{15}}{2}$	−ζ⁷+ζ¹¹−ζ⁴³+ζ⁵⁹	−ζ¹⁹+ζ²³−ζ³¹+ζ⁴⁷	ζ⁷−ζ¹¹+ζ⁴³−ζ⁵⁹	ζ¹⁹−ζ²³+ζ³¹−ζ⁴⁷	0	0	0	0	0	0	0	0	0	0	0	-4	4	2	0	-2	$2 \sqrt{3}$	$- 2 \sqrt{3}$	1	-1	$\frac{- 1 + i \sqrt{15}}{2}$	$\frac{- 1 - i \sqrt{15}}{2}$	$i \sqrt{5}$	$- i \sqrt{5}$	$\frac{1 - i \sqrt{15}}{2}$	$\frac{1 + i \sqrt{15}}{2}$	ζ⁷−ζ¹¹+ζ⁴³−ζ⁵⁹	ζ¹⁹−ζ²³+ζ³¹−ζ⁴⁷	−ζ⁷+ζ¹¹−ζ⁴³+ζ⁵⁹	−ζ¹⁹+ζ²³−ζ³¹+ζ⁴⁷	0	0	0	0	0	0	0	0	0	0	0
χ₆₀	4	-4	-2	0	2	$- 2 \sqrt{3}$	$2 \sqrt{3}$	-1	1	$\frac{1 + i \sqrt{15}}{2}$	$\frac{1 - i \sqrt{15}}{2}$	$i \sqrt{5}$	$- i \sqrt{5}$	$\frac{- 1 - i \sqrt{15}}{2}$	$\frac{- 1 + i \sqrt{15}}{2}$	−ζ¹⁹+ζ²³−ζ³¹+ζ⁴⁷	−ζ⁷+ζ¹¹−ζ⁴³+ζ⁵⁹	ζ¹⁹−ζ²³+ζ³¹−ζ⁴⁷	ζ⁷−ζ¹¹+ζ⁴³−ζ⁵⁹	0	0	0	0	0	0	0	0	0	0	0	-4	4	2	0	-2	$2 \sqrt{3}$	$- 2 \sqrt{3}$	1	-1	$\frac{- 1 - i \sqrt{15}}{2}$	$\frac{- 1 + i \sqrt{15}}{2}$	$- i \sqrt{5}$	$i \sqrt{5}$	$\frac{1 + i \sqrt{15}}{2}$	$\frac{1 - i \sqrt{15}}{2}$	ζ¹⁹−ζ²³+ζ³¹−ζ⁴⁷	ζ⁷−ζ¹¹+ζ⁴³−ζ⁵⁹	−ζ¹⁹+ζ²³−ζ³¹+ζ⁴⁷	−ζ⁷+ζ¹¹−ζ⁴³+ζ⁵⁹	0	0	0	0	0	0	0	0	0	0	0

Character table — Group #91985