Group #10590635 — 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	C₆₁	C₆₂	C₆₃	C₆₄	C₆₅	C₆₆
size	1	1	2	2	2	2	2	2	2	4	4	4	4	4	4	4	4	4	4	4	4	4	4	18	18	18	18	24	24	24	24	24	24	1	1	2	2	2	2	2	2	2	4	4	4	4	4	4	4	4	4	4	4	4	4	4	18	18	18	18	24	24	24	24	24	24
order	1	2	3	3	4	6	6	8	8	3	6	12	12	12	12	24	24	24	24	24	24	24	24	16	16	16	16	2	4	6	6	12	12	2	2	6	6	4	6	6	8	8	6	6	12	12	12	12	24	24	24	24	24	24	24	24	16	16	16	16	2	4	6	6	12	12
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	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	-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	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	1	1	1	1	1	1	1	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	-2	-2	-2	-2	-2	0	0	0	0	0	0	0	0	0	0	2	2	2	2	2	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
χ₆	2	2	2	2	-2	2	2	0	0	2	2	-2	-2	-2	-2	0	0	0	0	0	0	0	0	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	0	0	0	0	0	0	2	2	2	2	-2	2	2	0	0	2	2	-2	-2	-2	-2	0	0	0	0	0	0	0	0	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	0	0	0	0	0	0
χ₇	2	2	2	2	-2	2	2	0	0	2	2	-2	-2	-2	-2	0	0	0	0	0	0	0	0	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	0	0	0	0	0	0	2	2	2	2	-2	2	2	0	0	2	2	-2	-2	-2	-2	0	0	0	0	0	0	0	0	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	0	0	0	0	0	0
χ₈	2	2	2	-1	2	-1	2	2	2	-1	-1	-1	2	-1	-1	2	2	-1	-1	-1	-1	-1	-1	0	0	0	0	2	0	-1	-1	0	0	2	2	2	-1	2	-1	2	2	2	-1	-1	-1	2	-1	-1	2	2	-1	-1	-1	-1	-1	-1	0	0	0	0	2	0	-1	-1	0	0
χ₉	2	2	2	-1	2	-1	2	2	2	-1	-1	-1	2	-1	-1	2	2	-1	-1	-1	-1	-1	-1	0	0	0	0	-2	0	1	1	0	0	2	2	2	-1	2	-1	2	2	2	-1	-1	-1	2	-1	-1	2	2	-1	-1	-1	-1	-1	-1	0	0	0	0	-2	0	1	1	0	0
χ₁₀	2	2	2	-1	2	-1	2	-2	-2	-1	-1	-1	2	-1	-1	-2	-2	1	1	1	1	1	1	0	0	0	0	0	0	$- i \sqrt{3}$	$i \sqrt{3}$	0	0	2	2	2	-1	2	-1	2	-2	-2	-1	-1	-1	2	-1	-1	-2	-2	1	1	1	1	1	1	0	0	0	0	0	0	$- i \sqrt{3}$	$i \sqrt{3}$	0	0
χ₁₁	2	2	2	-1	2	-1	2	-2	-2	-1	-1	-1	2	-1	-1	-2	-2	1	1	1	1	1	1	0	0	0	0	0	0	$i \sqrt{3}$	$- i \sqrt{3}$	0	0	2	2	2	-1	2	-1	2	-2	-2	-1	-1	-1	2	-1	-1	-2	-2	1	1	1	1	1	1	0	0	0	0	0	0	$i \sqrt{3}$	$- i \sqrt{3}$	0	0
χ₁₂	2	2	-1	2	2	2	-1	2	2	-1	-1	2	-1	-1	-1	-1	-1	2	2	-1	-1	-1	-1	0	0	0	0	0	2	0	0	-1	-1	2	2	-1	2	2	2	-1	2	2	-1	-1	2	-1	-1	-1	-1	-1	2	2	-1	-1	-1	-1	0	0	0	0	0	2	0	0	-1	-1
χ₁₃	2	2	-1	2	2	2	-1	2	2	-1	-1	2	-1	-1	-1	-1	-1	2	2	-1	-1	-1	-1	0	0	0	0	0	-2	0	0	1	1	2	2	-1	2	2	2	-1	2	2	-1	-1	2	-1	-1	-1	-1	-1	2	2	-1	-1	-1	-1	0	0	0	0	0	-2	0	0	1	1
χ₁₄	2	2	-1	2	2	2	-1	-2	-2	-1	-1	2	-1	-1	-1	1	1	-2	-2	1	1	1	1	0	0	0	0	0	0	0	0	$- i \sqrt{3}$	$i \sqrt{3}$	2	2	-1	2	2	2	-1	-2	-2	-1	-1	2	-1	-1	-1	1	1	-2	-2	1	1	1	1	0	0	0	0	0	0	0	0	$- i \sqrt{3}$	$i \sqrt{3}$
χ₁₅	2	2	-1	2	2	2	-1	-2	-2	-1	-1	2	-1	-1	-1	1	1	-2	-2	1	1	1	1	0	0	0	0	0	0	0	0	$i \sqrt{3}$	$- i \sqrt{3}$	2	2	-1	2	2	2	-1	-2	-2	-1	-1	2	-1	-1	-1	1	1	-2	-2	1	1	1	1	0	0	0	0	0	0	0	0	$i \sqrt{3}$	$- i \sqrt{3}$
χ₁₆	2	-2	2	2	0	-2	-2	$\sqrt{2}$	$- \sqrt{2}$	2	-2	0	0	0	0	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	−ζ²⁵−ζ³¹−ζ⁴¹−ζ⁴⁷	ζ²⁵+ζ³¹+ζ⁴¹+ζ⁴⁷	ζ¹¹+ζ¹³+ζ²⁹+ζ⁴³	−ζ¹¹−ζ¹³−ζ²⁹−ζ⁴³	0	0	0	0	0	0	2	-2	2	2	0	-2	-2	$\sqrt{2}$	$- \sqrt{2}$	2	-2	0	0	0	0	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	−ζ²⁵−ζ³¹−ζ⁴¹−ζ⁴⁷	ζ²⁵+ζ³¹+ζ⁴¹+ζ⁴⁷	ζ¹¹+ζ¹³+ζ²⁹+ζ⁴³	−ζ¹¹−ζ¹³−ζ²⁹−ζ⁴³	0	0	0	0	0	0
χ₁₇	2	-2	2	2	0	-2	-2	$\sqrt{2}$	$- \sqrt{2}$	2	-2	0	0	0	0	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	ζ²⁵+ζ³¹+ζ⁴¹+ζ⁴⁷	−ζ²⁵−ζ³¹−ζ⁴¹−ζ⁴⁷	−ζ¹¹−ζ¹³−ζ²⁹−ζ⁴³	ζ¹¹+ζ¹³+ζ²⁹+ζ⁴³	0	0	0	0	0	0	2	-2	2	2	0	-2	-2	$\sqrt{2}$	$- \sqrt{2}$	2	-2	0	0	0	0	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	ζ²⁵+ζ³¹+ζ⁴¹+ζ⁴⁷	−ζ²⁵−ζ³¹−ζ⁴¹−ζ⁴⁷	−ζ¹¹−ζ¹³−ζ²⁹−ζ⁴³	ζ¹¹+ζ¹³+ζ²⁹+ζ⁴³	0	0	0	0	0	0
χ₁₈	2	-2	2	2	0	-2	-2	$- \sqrt{2}$	$\sqrt{2}$	2	-2	0	0	0	0	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	ζ¹¹+ζ¹³+ζ²⁹+ζ⁴³	−ζ¹¹−ζ¹³−ζ²⁹−ζ⁴³	ζ²⁵+ζ³¹+ζ⁴¹+ζ⁴⁷	−ζ²⁵−ζ³¹−ζ⁴¹−ζ⁴⁷	0	0	0	0	0	0	2	-2	2	2	0	-2	-2	$- \sqrt{2}$	$\sqrt{2}$	2	-2	0	0	0	0	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	ζ¹¹+ζ¹³+ζ²⁹+ζ⁴³	−ζ¹¹−ζ¹³−ζ²⁹−ζ⁴³	ζ²⁵+ζ³¹+ζ⁴¹+ζ⁴⁷	−ζ²⁵−ζ³¹−ζ⁴¹−ζ⁴⁷	0	0	0	0	0	0
χ₁₉	2	-2	2	2	0	-2	-2	$- \sqrt{2}$	$\sqrt{2}$	2	-2	0	0	0	0	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	−ζ¹¹−ζ¹³−ζ²⁹−ζ⁴³	ζ¹¹+ζ¹³+ζ²⁹+ζ⁴³	−ζ²⁵−ζ³¹−ζ⁴¹−ζ⁴⁷	ζ²⁵+ζ³¹+ζ⁴¹+ζ⁴⁷	0	0	0	0	0	0	2	-2	2	2	0	-2	-2	$- \sqrt{2}$	$\sqrt{2}$	2	-2	0	0	0	0	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	−ζ¹¹−ζ¹³−ζ²⁹−ζ⁴³	ζ¹¹+ζ¹³+ζ²⁹+ζ⁴³	−ζ²⁵−ζ³¹−ζ⁴¹−ζ⁴⁷	ζ²⁵+ζ³¹+ζ⁴¹+ζ⁴⁷	0	0	0	0	0	0
χ₂₀	4	4	4	-2	-4	-2	4	0	0	-2	-2	2	-4	2	2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	4	4	4	-2	-4	-2	4	0	0	-2	-2	2	-4	2	2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₁	4	4	-2	4	-4	4	-2	0	0	-2	-2	-4	2	2	2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	4	4	-2	4	-4	4	-2	0	0	-2	-2	-4	2	2	2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₂	4	4	-2	-2	4	-2	-2	4	4	1	1	-2	-2	1	1	-2	-2	-2	-2	1	1	1	1	0	0	0	0	0	0	0	0	0	0	4	4	-2	-2	4	-2	-2	4	4	1	1	-2	-2	1	1	-2	-2	-2	-2	1	1	1	1	0	0	0	0	0	0	0	0	0	0
χ₂₃	4	4	-2	-2	4	-2	-2	-4	-4	1	1	-2	-2	1	1	2	2	2	2	-1	-1	-1	-1	0	0	0	0	0	0	0	0	0	0	4	4	-2	-2	4	-2	-2	-4	-4	1	1	-2	-2	1	1	2	2	2	2	-1	-1	-1	-1	0	0	0	0	0	0	0	0	0	0
χ₂₄	4	4	-2	-2	-4	-2	-2	0	0	1	1	2	2	-1	-1	0	0	0	0	$3 i$	$- 3 i$	$3 i$	$- 3 i$	0	0	0	0	0	0	0	0	0	0	4	4	-2	-2	-4	-2	-2	0	0	1	1	2	2	-1	-1	0	0	0	0	$3 i$	$- 3 i$	$3 i$	$- 3 i$	0	0	0	0	0	0	0	0	0	0
χ₂₅	4	4	-2	-2	-4	-2	-2	0	0	1	1	2	2	-1	-1	0	0	0	0	$- 3 i$	$3 i$	$- 3 i$	$3 i$	0	0	0	0	0	0	0	0	0	0	4	4	-2	-2	-4	-2	-2	0	0	1	1	2	2	-1	-1	0	0	0	0	$- 3 i$	$3 i$	$- 3 i$	$3 i$	0	0	0	0	0	0	0	0	0	0
χ₂₆	4	-4	4	-2	0	2	-4	$2 \sqrt{2}$	$- 2 \sqrt{2}$	-2	2	0	0	0	0	$2 \sqrt{2}$	$- 2 \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	0	0	0	0	0	0	0	0	0	0	4	-4	4	-2	0	2	-4	$2 \sqrt{2}$	$- 2 \sqrt{2}$	-2	2	0	0	0	0	$2 \sqrt{2}$	$- 2 \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	0	0	0	0	0	0	0	0	0	0
χ₂₇	4	-4	4	-2	0	2	-4	$- 2 \sqrt{2}$	$2 \sqrt{2}$	-2	2	0	0	0	0	$- 2 \sqrt{2}$	$2 \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	4	-4	4	-2	0	2	-4	$- 2 \sqrt{2}$	$2 \sqrt{2}$	-2	2	0	0	0	0	$- 2 \sqrt{2}$	$2 \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	0	0	0	0	0	0	0	0	0	0
χ₂₈	4	-4	-2	4	0	-4	2	$2 \sqrt{2}$	$- 2 \sqrt{2}$	-2	2	0	0	0	0	$- \sqrt{2}$	$\sqrt{2}$	$2 \sqrt{2}$	$- 2 \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	0	0	0	0	0	0	0	0	0	0	4	-4	-2	4	0	-4	2	$2 \sqrt{2}$	$- 2 \sqrt{2}$	-2	2	0	0	0	0	$- \sqrt{2}$	$\sqrt{2}$	$2 \sqrt{2}$	$- 2 \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	0	0	0	0	0	0	0	0	0	0
χ₂₉	4	-4	-2	4	0	-4	2	$- 2 \sqrt{2}$	$2 \sqrt{2}$	-2	2	0	0	0	0	$\sqrt{2}$	$- \sqrt{2}$	$- 2 \sqrt{2}$	$2 \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	4	-4	-2	4	0	-4	2	$- 2 \sqrt{2}$	$2 \sqrt{2}$	-2	2	0	0	0	0	$\sqrt{2}$	$- \sqrt{2}$	$- 2 \sqrt{2}$	$2 \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	0	0	0	0	0	0	0	0	0	0
χ₃₀	4	-4	-2	-2	0	2	2	$2 \sqrt{2}$	$- 2 \sqrt{2}$	1	-1	0	0	$3 i$	$- 3 i$	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	−2ζ¹⁰−ζ¹⁴−2ζ²⁶−ζ⁴⁶	ζ¹⁰+2ζ¹⁴+ζ²⁶+2ζ⁴⁶	2ζ¹⁰+ζ¹⁴+2ζ²⁶+ζ⁴⁶	−ζ¹⁰−2ζ¹⁴−ζ²⁶−2ζ⁴⁶	0	0	0	0	0	0	0	0	0	0	4	-4	-2	-2	0	2	2	$2 \sqrt{2}$	$- 2 \sqrt{2}$	1	-1	0	0	$3 i$	$- 3 i$	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	−2ζ¹⁰−ζ¹⁴−2ζ²⁶−ζ⁴⁶	ζ¹⁰+2ζ¹⁴+ζ²⁶+2ζ⁴⁶	2ζ¹⁰+ζ¹⁴+2ζ²⁶+ζ⁴⁶	−ζ¹⁰−2ζ¹⁴−ζ²⁶−2ζ⁴⁶	0	0	0	0	0	0	0	0	0	0
χ₃₁	4	-4	-2	-2	0	2	2	$2 \sqrt{2}$	$- 2 \sqrt{2}$	1	-1	0	0	$- 3 i$	$3 i$	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	ζ¹⁰+2ζ¹⁴+ζ²⁶+2ζ⁴⁶	−2ζ¹⁰−ζ¹⁴−2ζ²⁶−ζ⁴⁶	−ζ¹⁰−2ζ¹⁴−ζ²⁶−2ζ⁴⁶	2ζ¹⁰+ζ¹⁴+2ζ²⁶+ζ⁴⁶	0	0	0	0	0	0	0	0	0	0	4	-4	-2	-2	0	2	2	$2 \sqrt{2}$	$- 2 \sqrt{2}$	1	-1	0	0	$- 3 i$	$3 i$	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	ζ¹⁰+2ζ¹⁴+ζ²⁶+2ζ⁴⁶	−2ζ¹⁰−ζ¹⁴−2ζ²⁶−ζ⁴⁶	−ζ¹⁰−2ζ¹⁴−ζ²⁶−2ζ⁴⁶	2ζ¹⁰+ζ¹⁴+2ζ²⁶+ζ⁴⁶	0	0	0	0	0	0	0	0	0	0
χ₃₂	4	-4	-2	-2	0	2	2	$- 2 \sqrt{2}$	$2 \sqrt{2}$	1	-1	0	0	$3 i$	$- 3 i$	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	2ζ¹⁰+ζ¹⁴+2ζ²⁶+ζ⁴⁶	−ζ¹⁰−2ζ¹⁴−ζ²⁶−2ζ⁴⁶	−2ζ¹⁰−ζ¹⁴−2ζ²⁶−ζ⁴⁶	ζ¹⁰+2ζ¹⁴+ζ²⁶+2ζ⁴⁶	0	0	0	0	0	0	0	0	0	0	4	-4	-2	-2	0	2	2	$- 2 \sqrt{2}$	$2 \sqrt{2}$	1	-1	0	0	$3 i$	$- 3 i$	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	2ζ¹⁰+ζ¹⁴+2ζ²⁶+ζ⁴⁶	−ζ¹⁰−2ζ¹⁴−ζ²⁶−2ζ⁴⁶	−2ζ¹⁰−ζ¹⁴−2ζ²⁶−ζ⁴⁶	ζ¹⁰+2ζ¹⁴+ζ²⁶+2ζ⁴⁶	0	0	0	0	0	0	0	0	0	0
χ₃₃	4	-4	-2	-2	0	2	2	$- 2 \sqrt{2}$	$2 \sqrt{2}$	1	-1	0	0	$- 3 i$	$3 i$	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	−ζ¹⁰−2ζ¹⁴−ζ²⁶−2ζ⁴⁶	2ζ¹⁰+ζ¹⁴+2ζ²⁶+ζ⁴⁶	ζ¹⁰+2ζ¹⁴+ζ²⁶+2ζ⁴⁶	−2ζ¹⁰−ζ¹⁴−2ζ²⁶−ζ⁴⁶	0	0	0	0	0	0	0	0	0	0	4	-4	-2	-2	0	2	2	$- 2 \sqrt{2}$	$2 \sqrt{2}$	1	-1	0	0	$- 3 i$	$3 i$	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	−ζ¹⁰−2ζ¹⁴−ζ²⁶−2ζ⁴⁶	2ζ¹⁰+ζ¹⁴+2ζ²⁶+ζ⁴⁶	ζ¹⁰+2ζ¹⁴+ζ²⁶+2ζ⁴⁶	−2ζ¹⁰−ζ¹⁴−2ζ²⁶−ζ⁴⁶	0	0	0	0	0	0	0	0	0	0
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	1	1	1	1	1	1	1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1
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	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	-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	-1	-1	1	-1	-1	1	1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	1	1	1	1	1	-1	1	1	-1	-1
χ₃₈	2	2	2	2	2	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	-2	-2	-2	-2	-2	-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
χ₃₉	2	2	2	2	-2	2	2	0	0	2	2	-2	-2	-2	-2	0	0	0	0	0	0	0	0	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	0	0	0	0	0	0	-2	-2	-2	-2	2	-2	-2	0	0	-2	-2	2	2	2	2	0	0	0	0	0	0	0	0	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	0	0	0	0	0	0
χ₄₀	2	2	2	2	-2	2	2	0	0	2	2	-2	-2	-2	-2	0	0	0	0	0	0	0	0	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	0	0	0	0	0	0	-2	-2	-2	-2	2	-2	-2	0	0	-2	-2	2	2	2	2	0	0	0	0	0	0	0	0	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	0	0	0	0	0	0
χ₄₁	2	2	2	-1	2	-1	2	2	2	-1	-1	-1	2	-1	-1	2	2	-1	-1	-1	-1	-1	-1	0	0	0	0	2	0	-1	-1	0	0	-2	-2	-2	1	-2	1	-2	-2	-2	1	1	1	-2	1	1	-2	-2	1	1	1	1	1	1	0	0	0	0	-2	0	1	1	0	0
χ₄₂	2	2	2	-1	2	-1	2	2	2	-1	-1	-1	2	-1	-1	2	2	-1	-1	-1	-1	-1	-1	0	0	0	0	-2	0	1	1	0	0	-2	-2	-2	1	-2	1	-2	-2	-2	1	1	1	-2	1	1	-2	-2	1	1	1	1	1	1	0	0	0	0	2	0	-1	-1	0	0
χ₄₃	2	2	2	-1	2	-1	2	-2	-2	-1	-1	-1	2	-1	-1	-2	-2	1	1	1	1	1	1	0	0	0	0	0	0	$- i \sqrt{3}$	$i \sqrt{3}$	0	0	-2	-2	-2	1	-2	1	-2	2	2	1	1	1	-2	1	1	2	2	-1	-1	-1	-1	-1	-1	0	0	0	0	0	0	$i \sqrt{3}$	$- i \sqrt{3}$	0	0
χ₄₄	2	2	2	-1	2	-1	2	-2	-2	-1	-1	-1	2	-1	-1	-2	-2	1	1	1	1	1	1	0	0	0	0	0	0	$i \sqrt{3}$	$- i \sqrt{3}$	0	0	-2	-2	-2	1	-2	1	-2	2	2	1	1	1	-2	1	1	2	2	-1	-1	-1	-1	-1	-1	0	0	0	0	0	0	$- i \sqrt{3}$	$i \sqrt{3}$	0	0
χ₄₅	2	2	-1	2	2	2	-1	2	2	-1	-1	2	-1	-1	-1	-1	-1	2	2	-1	-1	-1	-1	0	0	0	0	0	2	0	0	-1	-1	-2	-2	1	-2	-2	-2	1	-2	-2	1	1	-2	1	1	1	1	1	-2	-2	1	1	1	1	0	0	0	0	0	-2	0	0	1	1
χ₄₆	2	2	-1	2	2	2	-1	2	2	-1	-1	2	-1	-1	-1	-1	-1	2	2	-1	-1	-1	-1	0	0	0	0	0	-2	0	0	1	1	-2	-2	1	-2	-2	-2	1	-2	-2	1	1	-2	1	1	1	1	1	-2	-2	1	1	1	1	0	0	0	0	0	2	0	0	-1	-1
χ₄₇	2	2	-1	2	2	2	-1	-2	-2	-1	-1	2	-1	-1	-1	1	1	-2	-2	1	1	1	1	0	0	0	0	0	0	0	0	$- i \sqrt{3}$	$i \sqrt{3}$	-2	-2	1	-2	-2	-2	1	2	2	1	1	-2	1	1	1	-1	-1	2	2	-1	-1	-1	-1	0	0	0	0	0	0	0	0	$i \sqrt{3}$	$- i \sqrt{3}$
χ₄₈	2	2	-1	2	2	2	-1	-2	-2	-1	-1	2	-1	-1	-1	1	1	-2	-2	1	1	1	1	0	0	0	0	0	0	0	0	$i \sqrt{3}$	$- i \sqrt{3}$	-2	-2	1	-2	-2	-2	1	2	2	1	1	-2	1	1	1	-1	-1	2	2	-1	-1	-1	-1	0	0	0	0	0	0	0	0	$- i \sqrt{3}$	$i \sqrt{3}$
χ₄₉	2	-2	2	2	0	-2	-2	$\sqrt{2}$	$- \sqrt{2}$	2	-2	0	0	0	0	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	−ζ²⁵−ζ³¹−ζ⁴¹−ζ⁴⁷	ζ²⁵+ζ³¹+ζ⁴¹+ζ⁴⁷	ζ¹¹+ζ¹³+ζ²⁹+ζ⁴³	−ζ¹¹−ζ¹³−ζ²⁹−ζ⁴³	0	0	0	0	0	0	-2	2	-2	-2	0	2	2	$- \sqrt{2}$	$\sqrt{2}$	-2	2	0	0	0	0	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	ζ²⁵+ζ³¹+ζ⁴¹+ζ⁴⁷	−ζ²⁵−ζ³¹−ζ⁴¹−ζ⁴⁷	−ζ¹¹−ζ¹³−ζ²⁹−ζ⁴³	ζ¹¹+ζ¹³+ζ²⁹+ζ⁴³	0	0	0	0	0	0
χ₅₀	2	-2	2	2	0	-2	-2	$\sqrt{2}$	$- \sqrt{2}$	2	-2	0	0	0	0	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	ζ²⁵+ζ³¹+ζ⁴¹+ζ⁴⁷	−ζ²⁵−ζ³¹−ζ⁴¹−ζ⁴⁷	−ζ¹¹−ζ¹³−ζ²⁹−ζ⁴³	ζ¹¹+ζ¹³+ζ²⁹+ζ⁴³	0	0	0	0	0	0	-2	2	-2	-2	0	2	2	$- \sqrt{2}$	$\sqrt{2}$	-2	2	0	0	0	0	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	−ζ²⁵−ζ³¹−ζ⁴¹−ζ⁴⁷	ζ²⁵+ζ³¹+ζ⁴¹+ζ⁴⁷	ζ¹¹+ζ¹³+ζ²⁹+ζ⁴³	−ζ¹¹−ζ¹³−ζ²⁹−ζ⁴³	0	0	0	0	0	0
χ₅₁	2	-2	2	2	0	-2	-2	$- \sqrt{2}$	$\sqrt{2}$	2	-2	0	0	0	0	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	ζ¹¹+ζ¹³+ζ²⁹+ζ⁴³	−ζ¹¹−ζ¹³−ζ²⁹−ζ⁴³	ζ²⁵+ζ³¹+ζ⁴¹+ζ⁴⁷	−ζ²⁵−ζ³¹−ζ⁴¹−ζ⁴⁷	0	0	0	0	0	0	-2	2	-2	-2	0	2	2	$\sqrt{2}$	$- \sqrt{2}$	-2	2	0	0	0	0	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	−ζ¹¹−ζ¹³−ζ²⁹−ζ⁴³	ζ¹¹+ζ¹³+ζ²⁹+ζ⁴³	−ζ²⁵−ζ³¹−ζ⁴¹−ζ⁴⁷	ζ²⁵+ζ³¹+ζ⁴¹+ζ⁴⁷	0	0	0	0	0	0
χ₅₂	2	-2	2	2	0	-2	-2	$- \sqrt{2}$	$\sqrt{2}$	2	-2	0	0	0	0	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	−ζ¹¹−ζ¹³−ζ²⁹−ζ⁴³	ζ¹¹+ζ¹³+ζ²⁹+ζ⁴³	−ζ²⁵−ζ³¹−ζ⁴¹−ζ⁴⁷	ζ²⁵+ζ³¹+ζ⁴¹+ζ⁴⁷	0	0	0	0	0	0	-2	2	-2	-2	0	2	2	$\sqrt{2}$	$- \sqrt{2}$	-2	2	0	0	0	0	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	ζ¹¹+ζ¹³+ζ²⁹+ζ⁴³	−ζ¹¹−ζ¹³−ζ²⁹−ζ⁴³	ζ²⁵+ζ³¹+ζ⁴¹+ζ⁴⁷	−ζ²⁵−ζ³¹−ζ⁴¹−ζ⁴⁷	0	0	0	0	0	0
χ₅₃	4	4	4	-2	-4	-2	4	0	0	-2	-2	2	-4	2	2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	-4	-4	-4	2	4	2	-4	0	0	2	2	-2	4	-2	-2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₅₄	4	4	-2	4	-4	4	-2	0	0	-2	-2	-4	2	2	2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	-4	-4	2	-4	4	-4	2	0	0	2	2	4	-2	-2	-2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₅₅	4	4	-2	-2	4	-2	-2	4	4	1	1	-2	-2	1	1	-2	-2	-2	-2	1	1	1	1	0	0	0	0	0	0	0	0	0	0	-4	-4	2	2	-4	2	2	-4	-4	-1	-1	2	2	-1	-1	2	2	2	2	-1	-1	-1	-1	0	0	0	0	0	0	0	0	0	0
χ₅₆	4	4	-2	-2	4	-2	-2	-4	-4	1	1	-2	-2	1	1	2	2	2	2	-1	-1	-1	-1	0	0	0	0	0	0	0	0	0	0	-4	-4	2	2	-4	2	2	4	4	-1	-1	2	2	-1	-1	-2	-2	-2	-2	1	1	1	1	0	0	0	0	0	0	0	0	0	0
χ₅₇	4	4	-2	-2	-4	-2	-2	0	0	1	1	2	2	-1	-1	0	0	0	0	$3 i$	$- 3 i$	$3 i$	$- 3 i$	0	0	0	0	0	0	0	0	0	0	-4	-4	2	2	4	2	2	0	0	-1	-1	-2	-2	1	1	0	0	0	0	$- 3 i$	$3 i$	$- 3 i$	$3 i$	0	0	0	0	0	0	0	0	0	0
χ₅₈	4	4	-2	-2	-4	-2	-2	0	0	1	1	2	2	-1	-1	0	0	0	0	$- 3 i$	$3 i$	$- 3 i$	$3 i$	0	0	0	0	0	0	0	0	0	0	-4	-4	2	2	4	2	2	0	0	-1	-1	-2	-2	1	1	0	0	0	0	$3 i$	$- 3 i$	$3 i$	$- 3 i$	0	0	0	0	0	0	0	0	0	0
χ₅₉	4	-4	4	-2	0	2	-4	$2 \sqrt{2}$	$- 2 \sqrt{2}$	-2	2	0	0	0	0	$2 \sqrt{2}$	$- 2 \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	0	0	0	0	0	0	0	0	0	0	-4	4	-4	2	0	-2	4	$- 2 \sqrt{2}$	$2 \sqrt{2}$	2	-2	0	0	0	0	$- 2 \sqrt{2}$	$2 \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	0	0	0	0	0	0	0	0	0	0
χ₆₀	4	-4	4	-2	0	2	-4	$- 2 \sqrt{2}$	$2 \sqrt{2}$	-2	2	0	0	0	0	$- 2 \sqrt{2}$	$2 \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	-4	4	-4	2	0	-2	4	$2 \sqrt{2}$	$- 2 \sqrt{2}$	2	-2	0	0	0	0	$2 \sqrt{2}$	$- 2 \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	0	0	0	0	0	0	0	0	0	0
χ₆₁	4	-4	-2	4	0	-4	2	$2 \sqrt{2}$	$- 2 \sqrt{2}$	-2	2	0	0	0	0	$- \sqrt{2}$	$\sqrt{2}$	$2 \sqrt{2}$	$- 2 \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	0	0	0	0	0	0	0	0	0	0	-4	4	2	-4	0	4	-2	$- 2 \sqrt{2}$	$2 \sqrt{2}$	2	-2	0	0	0	0	$\sqrt{2}$	$- \sqrt{2}$	$- 2 \sqrt{2}$	$2 \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	0	0	0	0	0	0	0	0	0	0
χ₆₂	4	-4	-2	4	0	-4	2	$- 2 \sqrt{2}$	$2 \sqrt{2}$	-2	2	0	0	0	0	$\sqrt{2}$	$- \sqrt{2}$	$- 2 \sqrt{2}$	$2 \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	-4	4	2	-4	0	4	-2	$2 \sqrt{2}$	$- 2 \sqrt{2}$	2	-2	0	0	0	0	$- \sqrt{2}$	$\sqrt{2}$	$2 \sqrt{2}$	$- 2 \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	0	0	0	0	0	0	0	0	0	0
χ₆₃	4	-4	-2	-2	0	2	2	$2 \sqrt{2}$	$- 2 \sqrt{2}$	1	-1	0	0	$3 i$	$- 3 i$	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	−2ζ¹⁰−ζ¹⁴−2ζ²⁶−ζ⁴⁶	ζ¹⁰+2ζ¹⁴+ζ²⁶+2ζ⁴⁶	2ζ¹⁰+ζ¹⁴+2ζ²⁶+ζ⁴⁶	−ζ¹⁰−2ζ¹⁴−ζ²⁶−2ζ⁴⁶	0	0	0	0	0	0	0	0	0	0	-4	4	2	2	0	-2	-2	$- 2 \sqrt{2}$	$2 \sqrt{2}$	-1	1	0	0	$- 3 i$	$3 i$	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	2ζ¹⁰+ζ¹⁴+2ζ²⁶+ζ⁴⁶	−ζ¹⁰−2ζ¹⁴−ζ²⁶−2ζ⁴⁶	−2ζ¹⁰−ζ¹⁴−2ζ²⁶−ζ⁴⁶	ζ¹⁰+2ζ¹⁴+ζ²⁶+2ζ⁴⁶	0	0	0	0	0	0	0	0	0	0
χ₆₄	4	-4	-2	-2	0	2	2	$2 \sqrt{2}$	$- 2 \sqrt{2}$	1	-1	0	0	$- 3 i$	$3 i$	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	ζ¹⁰+2ζ¹⁴+ζ²⁶+2ζ⁴⁶	−2ζ¹⁰−ζ¹⁴−2ζ²⁶−ζ⁴⁶	−ζ¹⁰−2ζ¹⁴−ζ²⁶−2ζ⁴⁶	2ζ¹⁰+ζ¹⁴+2ζ²⁶+ζ⁴⁶	0	0	0	0	0	0	0	0	0	0	-4	4	2	2	0	-2	-2	$- 2 \sqrt{2}$	$2 \sqrt{2}$	-1	1	0	0	$3 i$	$- 3 i$	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	−ζ¹⁰−2ζ¹⁴−ζ²⁶−2ζ⁴⁶	2ζ¹⁰+ζ¹⁴+2ζ²⁶+ζ⁴⁶	ζ¹⁰+2ζ¹⁴+ζ²⁶+2ζ⁴⁶	−2ζ¹⁰−ζ¹⁴−2ζ²⁶−ζ⁴⁶	0	0	0	0	0	0	0	0	0	0
χ₆₅	4	-4	-2	-2	0	2	2	$- 2 \sqrt{2}$	$2 \sqrt{2}$	1	-1	0	0	$3 i$	$- 3 i$	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	2ζ¹⁰+ζ¹⁴+2ζ²⁶+ζ⁴⁶	−ζ¹⁰−2ζ¹⁴−ζ²⁶−2ζ⁴⁶	−2ζ¹⁰−ζ¹⁴−2ζ²⁶−ζ⁴⁶	ζ¹⁰+2ζ¹⁴+ζ²⁶+2ζ⁴⁶	0	0	0	0	0	0	0	0	0	0	-4	4	2	2	0	-2	-2	$2 \sqrt{2}$	$- 2 \sqrt{2}$	-1	1	0	0	$- 3 i$	$3 i$	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	−2ζ¹⁰−ζ¹⁴−2ζ²⁶−ζ⁴⁶	ζ¹⁰+2ζ¹⁴+ζ²⁶+2ζ⁴⁶	2ζ¹⁰+ζ¹⁴+2ζ²⁶+ζ⁴⁶	−ζ¹⁰−2ζ¹⁴−ζ²⁶−2ζ⁴⁶	0	0	0	0	0	0	0	0	0	0
χ₆₆	4	-4	-2	-2	0	2	2	$- 2 \sqrt{2}$	$2 \sqrt{2}$	1	-1	0	0	$- 3 i$	$3 i$	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	−ζ¹⁰−2ζ¹⁴−ζ²⁶−2ζ⁴⁶	2ζ¹⁰+ζ¹⁴+2ζ²⁶+ζ⁴⁶	ζ¹⁰+2ζ¹⁴+ζ²⁶+2ζ⁴⁶	−2ζ¹⁰−ζ¹⁴−2ζ²⁶−ζ⁴⁶	0	0	0	0	0	0	0	0	0	0	-4	4	2	2	0	-2	-2	$2 \sqrt{2}$	$- 2 \sqrt{2}$	-1	1	0	0	$3 i$	$- 3 i$	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	ζ¹⁰+2ζ¹⁴+ζ²⁶+2ζ⁴⁶	−2ζ¹⁰−ζ¹⁴−2ζ²⁶−ζ⁴⁶	−ζ¹⁰−2ζ¹⁴−ζ²⁶−2ζ⁴⁶	2ζ¹⁰+ζ¹⁴+2ζ²⁶+ζ⁴⁶	0	0	0	0	0	0	0	0	0	0

Character table — Group #10590635