Group #11746777 — 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
size	1	1	2	2	2	4	4	4	4	4	4	4	4	4	4	8	8	8	8	8	8	8	8	8	8	8	8	10	10	10	10	10	10	16	16	16	16	16	16	20	20	20	40	40	40	60	60	60	60	120	120
order	1	2	3	4	6	5	8	10	12	15	15	24	24	30	30	2	6	6	20	40	40	60	60	120	120	120	120	2	4	6	6	8	8	10	10	30	30	30	30	12	24	24	2	6	6	16	16	16	16	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
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
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	1	1	1	-1	-1	-1	-1	-1	-1	$i$	$i$	$- i$	$- i$	$i$	$- i$
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	1	-1	-1	-1	-1	-1	-1	1	1	1	1	1	1	-1	-1	-1	-1	-1	-1	$- i$	$- i$	$i$	$i$	$- i$	$i$
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
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
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	1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	1	1	1	$i$	$i$	$- i$	$- i$	$- i$	$i$
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	-1	-1	-1	-1	-1	-1	-1	1	1	1	$- i$	$- i$	$i$	$i$	$i$	$- i$
χ₉	2	2	2	2	2	2	-2	2	2	2	2	-2	-2	2	2	0	0	0	2	-2	-2	2	2	-2	-2	-2	-2	2	2	2	2	-2	-2	0	0	0	0	0	0	2	-2	-2	0	0	0	0	0	0	0	0	0
χ₁₀	2	2	2	2	2	2	-2	2	2	2	2	-2	-2	2	2	0	0	0	2	-2	-2	2	2	-2	-2	-2	-2	-2	-2	-2	-2	2	2	0	0	0	0	0	0	-2	2	2	0	0	0	0	0	0	0	0	0
χ₁₁	2	2	2	-2	2	2	0	2	-2	2	2	0	0	2	2	0	0	0	-2	0	0	-2	-2	0	0	0	0	2	-2	2	2	0	0	0	0	0	0	0	0	-2	0	0	0	0	0	$- i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	0	0
χ₁₂	2	2	2	-2	2	2	0	2	-2	2	2	0	0	2	2	0	0	0	-2	0	0	-2	-2	0	0	0	0	2	-2	2	2	0	0	0	0	0	0	0	0	-2	0	0	0	0	0	$i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	0	0
χ₁₃	2	2	2	-2	2	2	0	2	-2	2	2	0	0	2	2	0	0	0	-2	0	0	-2	-2	0	0	0	0	-2	2	-2	-2	0	0	0	0	0	0	0	0	2	0	0	0	0	0	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	0	0
χ₁₄	2	2	2	-2	2	2	0	2	-2	2	2	0	0	2	2	0	0	0	-2	0	0	-2	-2	0	0	0	0	-2	2	-2	-2	0	0	0	0	0	0	0	0	2	0	0	0	0	0	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	0	0
χ₁₅	2	2	-1	2	-1	2	2	2	-1	-1	-1	-1	-1	-1	-1	2	-1	-1	2	2	2	-1	-1	-1	-1	-1	-1	2	2	-1	-1	2	2	2	2	-1	-1	-1	-1	-1	-1	-1	2	-1	-1	0	0	0	0	0	0
χ₁₆	2	2	-1	2	-1	2	2	2	-1	-1	-1	-1	-1	-1	-1	2	-1	-1	2	2	2	-1	-1	-1	-1	-1	-1	-2	-2	1	1	-2	-2	2	2	-1	-1	-1	-1	1	1	1	-2	1	1	0	0	0	0	0	0
χ₁₇	2	2	-1	2	-1	2	2	2	-1	-1	-1	-1	-1	-1	-1	-2	1	1	2	2	2	-1	-1	-1	-1	-1	-1	2	2	-1	-1	2	2	-2	-2	1	1	1	1	-1	-1	-1	-2	1	1	0	0	0	0	0	0
χ₁₈	2	2	-1	2	-1	2	2	2	-1	-1	-1	-1	-1	-1	-1	-2	1	1	2	2	2	-1	-1	-1	-1	-1	-1	-2	-2	1	1	-2	-2	-2	-2	1	1	1	1	1	1	1	2	-1	-1	0	0	0	0	0	0
χ₁₉	2	2	-1	2	-1	2	-2	2	-1	-1	-1	1	1	-1	-1	0	$- i \sqrt{3}$	$i \sqrt{3}$	2	-2	-2	-1	-1	1	1	1	1	2	2	-1	-1	-2	-2	0	0	$- i \sqrt{3}$	$- i \sqrt{3}$	$i \sqrt{3}$	$i \sqrt{3}$	-1	1	1	0	$- i \sqrt{3}$	$i \sqrt{3}$	0	0	0	0	0	0
χ₂₀	2	2	-1	2	-1	2	-2	2	-1	-1	-1	1	1	-1	-1	0	$- i \sqrt{3}$	$i \sqrt{3}$	2	-2	-2	-1	-1	1	1	1	1	-2	-2	1	1	2	2	0	0	$- i \sqrt{3}$	$- i \sqrt{3}$	$i \sqrt{3}$	$i \sqrt{3}$	1	-1	-1	0	$i \sqrt{3}$	$- i \sqrt{3}$	0	0	0	0	0	0
χ₂₁	2	2	-1	2	-1	2	-2	2	-1	-1	-1	1	1	-1	-1	0	$i \sqrt{3}$	$- i \sqrt{3}$	2	-2	-2	-1	-1	1	1	1	1	2	2	-1	-1	-2	-2	0	0	$i \sqrt{3}$	$i \sqrt{3}$	$- i \sqrt{3}$	$- i \sqrt{3}$	-1	1	1	0	$i \sqrt{3}$	$- i \sqrt{3}$	0	0	0	0	0	0
χ₂₂	2	2	-1	2	-1	2	-2	2	-1	-1	-1	1	1	-1	-1	0	$i \sqrt{3}$	$- i \sqrt{3}$	2	-2	-2	-1	-1	1	1	1	1	-2	-2	1	1	2	2	0	0	$i \sqrt{3}$	$i \sqrt{3}$	$- i \sqrt{3}$	$- i \sqrt{3}$	1	-1	-1	0	$- i \sqrt{3}$	$i \sqrt{3}$	0	0	0	0	0	0
χ₂₃	4	4	4	4	4	-1	4	-1	4	-1	-1	4	4	-1	-1	4	4	4	-1	-1	-1	-1	-1	-1	-1	-1	-1	0	0	0	0	0	0	-1	-1	-1	-1	-1	-1	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₄	4	4	4	4	4	-1	4	-1	4	-1	-1	4	4	-1	-1	-4	-4	-4	-1	-1	-1	-1	-1	-1	-1	-1	-1	0	0	0	0	0	0	1	1	1	1	1	1	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₅	4	4	4	4	4	-1	-4	-1	4	-1	-1	-4	-4	-1	-1	0	0	0	-1	1	1	-1	-1	1	1	1	1	0	0	0	0	0	0	$- \sqrt{5}$	$\sqrt{5}$	$- \sqrt{5}$	$\sqrt{5}$	$- \sqrt{5}$	$\sqrt{5}$	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₆	4	4	4	4	4	-1	-4	-1	4	-1	-1	-4	-4	-1	-1	0	0	0	-1	1	1	-1	-1	1	1	1	1	0	0	0	0	0	0	$\sqrt{5}$	$- \sqrt{5}$	$\sqrt{5}$	$- \sqrt{5}$	$\sqrt{5}$	$- \sqrt{5}$	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₇	4	4	-2	4	-2	-1	4	-1	-2	$\frac{1 - i \sqrt{15}}{2}$	$\frac{1 + i \sqrt{15}}{2}$	-2	-2	$\frac{1 - i \sqrt{15}}{2}$	$\frac{1 + i \sqrt{15}}{2}$	4	-2	-2	-1	-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	-1	-1	$\frac{1 - i \sqrt{15}}{2}$	$\frac{1 + i \sqrt{15}}{2}$	$\frac{1 + i \sqrt{15}}{2}$	$\frac{1 - i \sqrt{15}}{2}$	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₈	4	4	-2	4	-2	-1	4	-1	-2	$\frac{1 - i \sqrt{15}}{2}$	$\frac{1 + i \sqrt{15}}{2}$	-2	-2	$\frac{1 - i \sqrt{15}}{2}$	$\frac{1 + i \sqrt{15}}{2}$	-4	2	2	-1	-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	1	1	$\frac{- 1 + i \sqrt{15}}{2}$	$\frac{- 1 - i \sqrt{15}}{2}$	$\frac{- 1 - i \sqrt{15}}{2}$	$\frac{- 1 + i \sqrt{15}}{2}$	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₉	4	4	-2	4	-2	-1	4	-1	-2	$\frac{1 + i \sqrt{15}}{2}$	$\frac{1 - i \sqrt{15}}{2}$	-2	-2	$\frac{1 + i \sqrt{15}}{2}$	$\frac{1 - i \sqrt{15}}{2}$	4	-2	-2	-1	-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	-1	-1	$\frac{1 + i \sqrt{15}}{2}$	$\frac{1 - i \sqrt{15}}{2}$	$\frac{1 - i \sqrt{15}}{2}$	$\frac{1 + i \sqrt{15}}{2}$	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₀	4	4	-2	4	-2	-1	4	-1	-2	$\frac{1 + i \sqrt{15}}{2}$	$\frac{1 - i \sqrt{15}}{2}$	-2	-2	$\frac{1 + i \sqrt{15}}{2}$	$\frac{1 - i \sqrt{15}}{2}$	-4	2	2	-1	-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	1	1	$\frac{- 1 - i \sqrt{15}}{2}$	$\frac{- 1 + i \sqrt{15}}{2}$	$\frac{- 1 + i \sqrt{15}}{2}$	$\frac{- 1 - i \sqrt{15}}{2}$	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₁	4	4	-2	4	-2	-1	-4	-1	-2	$\frac{1 - i \sqrt{15}}{2}$	$\frac{1 + i \sqrt{15}}{2}$	2	2	$\frac{1 - i \sqrt{15}}{2}$	$\frac{1 + i \sqrt{15}}{2}$	0	$- 2 i \sqrt{3}$	$2 i \sqrt{3}$	-1	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	$\sqrt{5}$	$- \sqrt{5}$	ζ²⁸−ζ⁴⁴+ζ⁵²−ζ¹¹⁶	ζ⁴−ζ⁶⁸+ζ⁷⁶−ζ⁹²	−ζ⁴+ζ⁶⁸−ζ⁷⁶+ζ⁹²	−ζ²⁸+ζ⁴⁴−ζ⁵²+ζ¹¹⁶	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₂	4	4	-2	4	-2	-1	-4	-1	-2	$\frac{1 - i \sqrt{15}}{2}$	$\frac{1 + i \sqrt{15}}{2}$	2	2	$\frac{1 - i \sqrt{15}}{2}$	$\frac{1 + i \sqrt{15}}{2}$	0	$2 i \sqrt{3}$	$- 2 i \sqrt{3}$	-1	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	$- \sqrt{5}$	$\sqrt{5}$	−ζ²⁸+ζ⁴⁴−ζ⁵²+ζ¹¹⁶	−ζ⁴+ζ⁶⁸−ζ⁷⁶+ζ⁹²	ζ⁴−ζ⁶⁸+ζ⁷⁶−ζ⁹²	ζ²⁸−ζ⁴⁴+ζ⁵²−ζ¹¹⁶	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₃	4	4	-2	4	-2	-1	-4	-1	-2	$\frac{1 + i \sqrt{15}}{2}$	$\frac{1 - i \sqrt{15}}{2}$	2	2	$\frac{1 + i \sqrt{15}}{2}$	$\frac{1 - i \sqrt{15}}{2}$	0	$- 2 i \sqrt{3}$	$2 i \sqrt{3}$	-1	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	$- \sqrt{5}$	$\sqrt{5}$	ζ⁴−ζ⁶⁸+ζ⁷⁶−ζ⁹²	ζ²⁸−ζ⁴⁴+ζ⁵²−ζ¹¹⁶	−ζ²⁸+ζ⁴⁴−ζ⁵²+ζ¹¹⁶	−ζ⁴+ζ⁶⁸−ζ⁷⁶+ζ⁹²	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₄	4	4	-2	4	-2	-1	-4	-1	-2	$\frac{1 + i \sqrt{15}}{2}$	$\frac{1 - i \sqrt{15}}{2}$	2	2	$\frac{1 + i \sqrt{15}}{2}$	$\frac{1 - i \sqrt{15}}{2}$	0	$2 i \sqrt{3}$	$- 2 i \sqrt{3}$	-1	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	$\sqrt{5}$	$- \sqrt{5}$	−ζ⁴+ζ⁶⁸−ζ⁷⁶+ζ⁹²	−ζ²⁸+ζ⁴⁴−ζ⁵²+ζ¹¹⁶	ζ²⁸−ζ⁴⁴+ζ⁵²−ζ¹¹⁶	ζ⁴−ζ⁶⁸+ζ⁷⁶−ζ⁹²	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₅	4	4	-2	-4	-2	4	0	4	2	-2	-2	0	0	-2	-2	0	0	0	-4	0	0	2	2	0	0	0	0	4	-4	-2	-2	0	0	0	0	0	0	0	0	2	0	0	0	0	0	0	0	0	0	0	0
χ₃₆	4	4	-2	-4	-2	4	0	4	2	-2	-2	0	0	-2	-2	0	0	0	-4	0	0	2	2	0	0	0	0	-4	4	2	2	0	0	0	0	0	0	0	0	-2	0	0	0	0	0	0	0	0	0	0	0
χ₃₇	4	-4	4	0	-4	4	0	-4	0	4	4	0	0	-4	-4	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	$2 \sqrt{2}$	$- 2 \sqrt{2}$	0	0	0	0	0	0	0	$2 \sqrt{2}$	$- 2 \sqrt{2}$	0	0	0	0	0	0	0	0	0
χ₃₈	4	-4	4	0	-4	4	0	-4	0	4	4	0	0	-4	-4	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	$- 2 \sqrt{2}$	$2 \sqrt{2}$	0	0	0	0	0	0	0	$- 2 \sqrt{2}$	$2 \sqrt{2}$	0	0	0	0	0	0	0	0	0
χ₃₉	4	-4	-2	0	2	4	0	-4	0	-2	-2	$- i \sqrt{6}$	$i \sqrt{6}$	2	2	0	0	0	0	0	0	0	0	$- i \sqrt{6}$	$i \sqrt{6}$	$- i \sqrt{6}$	$i \sqrt{6}$	0	0	$- 2 i \sqrt{3}$	$2 i \sqrt{3}$	$2 \sqrt{2}$	$- 2 \sqrt{2}$	0	0	0	0	0	0	0	$- \sqrt{2}$	$\sqrt{2}$	0	0	0	0	0	0	0	0	0
χ₄₀	4	-4	-2	0	2	4	0	-4	0	-2	-2	$- i \sqrt{6}$	$i \sqrt{6}$	2	2	0	0	0	0	0	0	0	0	$- i \sqrt{6}$	$i \sqrt{6}$	$- i \sqrt{6}$	$i \sqrt{6}$	0	0	$2 i \sqrt{3}$	$- 2 i \sqrt{3}$	$- 2 \sqrt{2}$	$2 \sqrt{2}$	0	0	0	0	0	0	0	$\sqrt{2}$	$- \sqrt{2}$	0	0	0	0	0	0	0	0	0
χ₄₁	4	-4	-2	0	2	4	0	-4	0	-2	-2	$i \sqrt{6}$	$- i \sqrt{6}$	2	2	0	0	0	0	0	0	0	0	$i \sqrt{6}$	$- i \sqrt{6}$	$i \sqrt{6}$	$- i \sqrt{6}$	0	0	$- 2 i \sqrt{3}$	$2 i \sqrt{3}$	$- 2 \sqrt{2}$	$2 \sqrt{2}$	0	0	0	0	0	0	0	$\sqrt{2}$	$- \sqrt{2}$	0	0	0	0	0	0	0	0	0
χ₄₂	4	-4	-2	0	2	4	0	-4	0	-2	-2	$i \sqrt{6}$	$- i \sqrt{6}$	2	2	0	0	0	0	0	0	0	0	$i \sqrt{6}$	$- i \sqrt{6}$	$i \sqrt{6}$	$- i \sqrt{6}$	0	0	$2 i \sqrt{3}$	$- 2 i \sqrt{3}$	$2 \sqrt{2}$	$- 2 \sqrt{2}$	0	0	0	0	0	0	0	$- \sqrt{2}$	$\sqrt{2}$	0	0	0	0	0	0	0	0	0
χ₄₃	8	8	8	-8	8	-2	0	-2	-8	-2	-2	0	0	-2	-2	0	0	0	2	0	0	2	2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₄	8	8	-4	-8	-4	-2	0	-2	4	$1 - i \sqrt{15}$	$1 + i \sqrt{15}$	0	0	$1 - i \sqrt{15}$	$1 + i \sqrt{15}$	0	0	0	2	0	0	$- 1 + i \sqrt{15}$	$- 1 - i \sqrt{15}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₅	8	8	-4	-8	-4	-2	0	-2	4	$1 + i \sqrt{15}$	$1 - i \sqrt{15}$	0	0	$1 + i \sqrt{15}$	$1 - i \sqrt{15}$	0	0	0	2	0	0	$- 1 - i \sqrt{15}$	$- 1 + i \sqrt{15}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₆	8	-8	8	0	-8	-2	0	2	0	-2	-2	0	0	2	2	0	0	0	0	$\sqrt{10}$	$- \sqrt{10}$	0	0	$\sqrt{10}$	$- \sqrt{10}$	$- \sqrt{10}$	$\sqrt{10}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₇	8	-8	8	0	-8	-2	0	2	0	-2	-2	0	0	2	2	0	0	0	0	$- \sqrt{10}$	$\sqrt{10}$	0	0	$- \sqrt{10}$	$\sqrt{10}$	$\sqrt{10}$	$- \sqrt{10}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₈	8	-8	-4	0	4	-2	0	2	0	$1 - i \sqrt{15}$	$1 + i \sqrt{15}$	$- 2 i \sqrt{6}$	$2 i \sqrt{6}$	$- 1 + i \sqrt{15}$	$- 1 - i \sqrt{15}$	0	0	0	0	$\sqrt{10}$	$- \sqrt{10}$	0	0	−ζ⁷+ζ¹³−ζ²⁹+ζ³⁷+ζ⁷¹−ζ¹⁰¹−ζ¹⁰³+ζ¹¹⁹	ζ⁷−ζ¹³+ζ²⁹−ζ³⁷−ζ⁷¹+ζ¹⁰¹+ζ¹⁰³−ζ¹¹⁹	ζ²³−ζ³¹+ζ⁴⁷−ζ⁵³+ζ⁶¹−ζ⁷⁷−ζ⁷⁹+ζ¹⁰⁹	−ζ²³+ζ³¹−ζ⁴⁷+ζ⁵³−ζ⁶¹+ζ⁷⁷+ζ⁷⁹−ζ¹⁰⁹	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₉	8	-8	-4	0	4	-2	0	2	0	$1 - i \sqrt{15}$	$1 + i \sqrt{15}$	$2 i \sqrt{6}$	$- 2 i \sqrt{6}$	$- 1 + i \sqrt{15}$	$- 1 - i \sqrt{15}$	0	0	0	0	$- \sqrt{10}$	$\sqrt{10}$	0	0	ζ⁷−ζ¹³+ζ²⁹−ζ³⁷−ζ⁷¹+ζ¹⁰¹+ζ¹⁰³−ζ¹¹⁹	−ζ⁷+ζ¹³−ζ²⁹+ζ³⁷+ζ⁷¹−ζ¹⁰¹−ζ¹⁰³+ζ¹¹⁹	−ζ²³+ζ³¹−ζ⁴⁷+ζ⁵³−ζ⁶¹+ζ⁷⁷+ζ⁷⁹−ζ¹⁰⁹	ζ²³−ζ³¹+ζ⁴⁷−ζ⁵³+ζ⁶¹−ζ⁷⁷−ζ⁷⁹+ζ¹⁰⁹	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₅₀	8	-8	-4	0	4	-2	0	2	0	$1 + i \sqrt{15}$	$1 - i \sqrt{15}$	$- 2 i \sqrt{6}$	$2 i \sqrt{6}$	$- 1 - i \sqrt{15}$	$- 1 + i \sqrt{15}$	0	0	0	0	$- \sqrt{10}$	$\sqrt{10}$	0	0	ζ²³−ζ³¹+ζ⁴⁷−ζ⁵³+ζ⁶¹−ζ⁷⁷−ζ⁷⁹+ζ¹⁰⁹	−ζ²³+ζ³¹−ζ⁴⁷+ζ⁵³−ζ⁶¹+ζ⁷⁷+ζ⁷⁹−ζ¹⁰⁹	−ζ⁷+ζ¹³−ζ²⁹+ζ³⁷+ζ⁷¹−ζ¹⁰¹−ζ¹⁰³+ζ¹¹⁹	ζ⁷−ζ¹³+ζ²⁹−ζ³⁷−ζ⁷¹+ζ¹⁰¹+ζ¹⁰³−ζ¹¹⁹	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₅₁	8	-8	-4	0	4	-2	0	2	0	$1 + i \sqrt{15}$	$1 - i \sqrt{15}$	$2 i \sqrt{6}$	$- 2 i \sqrt{6}$	$- 1 - i \sqrt{15}$	$- 1 + i \sqrt{15}$	0	0	0	0	$\sqrt{10}$	$- \sqrt{10}$	0	0	−ζ²³+ζ³¹−ζ⁴⁷+ζ⁵³−ζ⁶¹+ζ⁷⁷+ζ⁷⁹−ζ¹⁰⁹	ζ²³−ζ³¹+ζ⁴⁷−ζ⁵³+ζ⁶¹−ζ⁷⁷−ζ⁷⁹+ζ¹⁰⁹	ζ⁷−ζ¹³+ζ²⁹−ζ³⁷−ζ⁷¹+ζ¹⁰¹+ζ¹⁰³−ζ¹¹⁹	−ζ⁷+ζ¹³−ζ²⁹+ζ³⁷+ζ⁷¹−ζ¹⁰¹−ζ¹⁰³+ζ¹¹⁹	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0

Character table — Group #11746777