Group #83809 — 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	C₆₇	C₆₈	C₆₉	C₇₀	C₇₁	C₇₂
size	1	1	2	2	2	2	2	2	2	2	2	2	2	2	2	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	24	24	24	24	1	1	2	2	2	2	2	2	2	2	2	2	2	2	2	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	24	24	24	24
order	1	2	2	3	4	4	6	8	8	12	12	24	24	24	24	2	4	6	6	6	8	8	8	12	12	12	24	24	24	24	24	24	4	4	8	8	2	2	2	6	4	4	6	8	8	12	12	24	24	24	24	2	4	6	6	6	8	8	8	12	12	12	24	24	24	24	24	24	4	4	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	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	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	-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	-1	-1	-1	-1	1	1
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	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	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	1	1	-1	-1	-1	-1	-1	-1	1	-1	-1	-1	1	1	1	-1	-1	-1	-1	1	1	1	1	1	-1	-1	1
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	1	1	-1	-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	2	2	2	2	-2	-2	2	0	0	-2	-2	0	0	0	0	0	0	2	0	0	0	$2 i$	$- 2 i$	-2	0	0	0	0	$2 i$	$2 i$	$- 2 i$	$- 2 i$	0	0	0	0	2	2	2	2	-2	-2	2	0	0	-2	-2	0	0	0	0	0	0	2	0	0	0	$2 i$	$- 2 i$	-2	0	0	0	0	$2 i$	$2 i$	$- 2 i$	$- 2 i$	0	0	0	0
χ₁₀	2	2	2	2	-2	-2	2	0	0	-2	-2	0	0	0	0	0	0	2	0	0	0	$- 2 i$	$2 i$	-2	0	0	0	0	$- 2 i$	$- 2 i$	$2 i$	$2 i$	0	0	0	0	2	2	2	2	-2	-2	2	0	0	-2	-2	0	0	0	0	0	0	2	0	0	0	$- 2 i$	$2 i$	-2	0	0	0	0	$- 2 i$	$- 2 i$	$2 i$	$2 i$	0	0	0	0
χ₁₁	2	2	2	-1	2	2	-1	2	2	-1	-1	-1	-1	-1	-1	2	2	-1	-1	-1	2	2	2	-1	-1	-1	-1	-1	-1	-1	-1	-1	0	0	0	0	2	2	2	-1	2	2	-1	2	2	-1	-1	-1	-1	-1	-1	2	2	-1	-1	-1	2	2	2	-1	-1	-1	-1	-1	-1	-1	-1	-1	0	0	0	0
χ₁₂	2	2	2	-1	2	2	-1	2	2	-1	-1	-1	-1	-1	-1	-2	-2	-1	1	1	2	-2	-2	-1	1	1	-1	-1	1	1	1	1	0	0	0	0	2	2	2	-1	2	2	-1	2	2	-1	-1	-1	-1	-1	-1	-2	-2	-1	1	1	2	-2	-2	-1	1	1	-1	-1	1	1	1	1	0	0	0	0
χ₁₃	2	2	2	-1	2	2	-1	-2	-2	-1	-1	1	1	1	1	2	2	-1	-1	-1	-2	-2	-2	-1	-1	-1	1	1	1	1	1	1	0	0	0	0	2	2	2	-1	2	2	-1	-2	-2	-1	-1	1	1	1	1	2	2	-1	-1	-1	-2	-2	-2	-1	-1	-1	1	1	1	1	1	1	0	0	0	0
χ₁₄	2	2	2	-1	2	2	-1	-2	-2	-1	-1	1	1	1	1	-2	-2	-1	1	1	-2	2	2	-1	1	1	1	1	-1	-1	-1	-1	0	0	0	0	2	2	2	-1	2	2	-1	-2	-2	-1	-1	1	1	1	1	-2	-2	-1	1	1	-2	2	2	-1	1	1	1	1	-1	-1	-1	-1	0	0	0	0
χ₁₅	2	2	2	-1	-2	-2	-1	0	0	1	1	$\sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$- \sqrt{3}$	0	0	-1	$- i \sqrt{3}$	$i \sqrt{3}$	0	$2 i$	$- 2 i$	1	$- i \sqrt{3}$	$i \sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$- i$	$- i$	$i$	$i$	0	0	0	0	2	2	2	-1	-2	-2	-1	0	0	1	1	$\sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$- \sqrt{3}$	0	0	-1	$- i \sqrt{3}$	$i \sqrt{3}$	0	$2 i$	$- 2 i$	1	$- i \sqrt{3}$	$i \sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$- i$	$- i$	$i$	$i$	0	0	0	0
χ₁₆	2	2	2	-1	-2	-2	-1	0	0	1	1	$\sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$- \sqrt{3}$	0	0	-1	$i \sqrt{3}$	$- i \sqrt{3}$	0	$- 2 i$	$2 i$	1	$i \sqrt{3}$	$- i \sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$i$	$i$	$- i$	$- i$	0	0	0	0	2	2	2	-1	-2	-2	-1	0	0	1	1	$\sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$- \sqrt{3}$	0	0	-1	$i \sqrt{3}$	$- i \sqrt{3}$	0	$- 2 i$	$2 i$	1	$i \sqrt{3}$	$- i \sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$i$	$i$	$- i$	$- i$	0	0	0	0
χ₁₇	2	2	2	-1	-2	-2	-1	0	0	1	1	$- \sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$\sqrt{3}$	0	0	-1	$- i \sqrt{3}$	$i \sqrt{3}$	0	$- 2 i$	$2 i$	1	$- i \sqrt{3}$	$i \sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$i$	$i$	$- i$	$- i$	0	0	0	0	2	2	2	-1	-2	-2	-1	0	0	1	1	$- \sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$\sqrt{3}$	0	0	-1	$- i \sqrt{3}$	$i \sqrt{3}$	0	$- 2 i$	$2 i$	1	$- i \sqrt{3}$	$i \sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$i$	$i$	$- i$	$- i$	0	0	0	0
χ₁₈	2	2	2	-1	-2	-2	-1	0	0	1	1	$- \sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$\sqrt{3}$	0	0	-1	$i \sqrt{3}$	$- i \sqrt{3}$	0	$2 i$	$- 2 i$	1	$i \sqrt{3}$	$- i \sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$- i$	$- i$	$i$	$i$	0	0	0	0	2	2	2	-1	-2	-2	-1	0	0	1	1	$- \sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$\sqrt{3}$	0	0	-1	$i \sqrt{3}$	$- i \sqrt{3}$	0	$2 i$	$- 2 i$	1	$i \sqrt{3}$	$- i \sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$- i$	$- i$	$i$	$i$	0	0	0	0
χ₁₉	2	2	-2	2	2	-2	2	2	2	2	2	2	2	2	2	0	0	-2	0	0	-2	0	0	-2	0	0	-2	-2	0	0	0	0	0	0	0	0	2	2	-2	2	2	-2	2	2	2	2	2	2	2	2	2	0	0	-2	0	0	-2	0	0	-2	0	0	-2	-2	0	0	0	0	0	0	0	0
χ₂₀	2	2	-2	2	2	-2	2	-2	-2	2	2	-2	-2	-2	-2	0	0	-2	0	0	2	0	0	-2	0	0	2	2	0	0	0	0	0	0	0	0	2	2	-2	2	2	-2	2	-2	-2	2	2	-2	-2	-2	-2	0	0	-2	0	0	2	0	0	-2	0	0	2	2	0	0	0	0	0	0	0	0
χ₂₁	2	2	-2	2	-2	2	2	0	0	-2	-2	0	0	0	0	2	-2	-2	2	2	0	0	0	2	-2	-2	0	0	0	0	0	0	0	0	0	0	2	2	-2	2	-2	2	2	0	0	-2	-2	0	0	0	0	2	-2	-2	2	2	0	0	0	2	-2	-2	0	0	0	0	0	0	0	0	0	0
χ₂₂	2	2	-2	2	-2	2	2	0	0	-2	-2	0	0	0	0	-2	2	-2	-2	-2	0	0	0	2	2	2	0	0	0	0	0	0	0	0	0	0	2	2	-2	2	-2	2	2	0	0	-2	-2	0	0	0	0	-2	2	-2	-2	-2	0	0	0	2	2	2	0	0	0	0	0	0	0	0	0	0
χ₂₃	2	2	-2	-1	2	-2	-1	2	2	-1	-1	-1	-1	-1	-1	0	0	1	$- i \sqrt{3}$	$i \sqrt{3}$	-2	0	0	1	$i \sqrt{3}$	$- i \sqrt{3}$	1	1	$- i \sqrt{3}$	$i \sqrt{3}$	$- i \sqrt{3}$	$i \sqrt{3}$	0	0	0	0	2	2	-2	-1	2	-2	-1	2	2	-1	-1	-1	-1	-1	-1	0	0	1	$- i \sqrt{3}$	$i \sqrt{3}$	-2	0	0	1	$i \sqrt{3}$	$- i \sqrt{3}$	1	1	$- i \sqrt{3}$	$i \sqrt{3}$	$- i \sqrt{3}$	$i \sqrt{3}$	0	0	0	0
χ₂₄	2	2	-2	-1	2	-2	-1	2	2	-1	-1	-1	-1	-1	-1	0	0	1	$i \sqrt{3}$	$- i \sqrt{3}$	-2	0	0	1	$- i \sqrt{3}$	$i \sqrt{3}$	1	1	$i \sqrt{3}$	$- i \sqrt{3}$	$i \sqrt{3}$	$- i \sqrt{3}$	0	0	0	0	2	2	-2	-1	2	-2	-1	2	2	-1	-1	-1	-1	-1	-1	0	0	1	$i \sqrt{3}$	$- i \sqrt{3}$	-2	0	0	1	$- i \sqrt{3}$	$i \sqrt{3}$	1	1	$i \sqrt{3}$	$- i \sqrt{3}$	$i \sqrt{3}$	$- i \sqrt{3}$	0	0	0	0
χ₂₅	2	2	-2	-1	2	-2	-1	-2	-2	-1	-1	1	1	1	1	0	0	1	$- i \sqrt{3}$	$i \sqrt{3}$	2	0	0	1	$i \sqrt{3}$	$- i \sqrt{3}$	-1	-1	$i \sqrt{3}$	$- i \sqrt{3}$	$i \sqrt{3}$	$- i \sqrt{3}$	0	0	0	0	2	2	-2	-1	2	-2	-1	-2	-2	-1	-1	1	1	1	1	0	0	1	$- i \sqrt{3}$	$i \sqrt{3}$	2	0	0	1	$i \sqrt{3}$	$- i \sqrt{3}$	-1	-1	$i \sqrt{3}$	$- i \sqrt{3}$	$i \sqrt{3}$	$- i \sqrt{3}$	0	0	0	0
χ₂₆	2	2	-2	-1	2	-2	-1	-2	-2	-1	-1	1	1	1	1	0	0	1	$i \sqrt{3}$	$- i \sqrt{3}$	2	0	0	1	$- i \sqrt{3}$	$i \sqrt{3}$	-1	-1	$- i \sqrt{3}$	$i \sqrt{3}$	$- i \sqrt{3}$	$i \sqrt{3}$	0	0	0	0	2	2	-2	-1	2	-2	-1	-2	-2	-1	-1	1	1	1	1	0	0	1	$i \sqrt{3}$	$- i \sqrt{3}$	2	0	0	1	$- i \sqrt{3}$	$i \sqrt{3}$	-1	-1	$- i \sqrt{3}$	$i \sqrt{3}$	$- i \sqrt{3}$	$i \sqrt{3}$	0	0	0	0
χ₂₇	2	2	-2	-1	-2	2	-1	0	0	1	1	$\sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$- \sqrt{3}$	2	-2	1	-1	-1	0	0	0	-1	1	1	$- \sqrt{3}$	$\sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	0	0	0	0	2	2	-2	-1	-2	2	-1	0	0	1	1	$\sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$- \sqrt{3}$	2	-2	1	-1	-1	0	0	0	-1	1	1	$- \sqrt{3}$	$\sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	0	0	0	0
χ₂₈	2	2	-2	-1	-2	2	-1	0	0	1	1	$\sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$- \sqrt{3}$	-2	2	1	1	1	0	0	0	-1	-1	-1	$- \sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	0	0	0	0	2	2	-2	-1	-2	2	-1	0	0	1	1	$\sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$- \sqrt{3}$	-2	2	1	1	1	0	0	0	-1	-1	-1	$- \sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	0	0	0	0
χ₂₉	2	2	-2	-1	-2	2	-1	0	0	1	1	$- \sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$\sqrt{3}$	2	-2	1	-1	-1	0	0	0	-1	1	1	$\sqrt{3}$	$- \sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	0	0	0	0	2	2	-2	-1	-2	2	-1	0	0	1	1	$- \sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$\sqrt{3}$	2	-2	1	-1	-1	0	0	0	-1	1	1	$\sqrt{3}$	$- \sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	0	0	0	0
χ₃₀	2	2	-2	-1	-2	2	-1	0	0	1	1	$- \sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$\sqrt{3}$	-2	2	1	1	1	0	0	0	-1	-1	-1	$\sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	0	0	0	0	2	2	-2	-1	-2	2	-1	0	0	1	1	$- \sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$\sqrt{3}$	-2	2	1	1	1	0	0	0	-1	-1	-1	$\sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	0	0	0	0
χ₃₁	4	-4	0	4	0	0	-4	$2 \sqrt{2}$	$- 2 \sqrt{2}$	0	0	$2 \sqrt{2}$	$- 2 \sqrt{2}$	$2 \sqrt{2}$	$- 2 \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	4	-4	0	4	0	0	-4	$2 \sqrt{2}$	$- 2 \sqrt{2}$	0	0	$2 \sqrt{2}$	$- 2 \sqrt{2}$	$2 \sqrt{2}$	$- 2 \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₂	4	-4	0	4	0	0	-4	$- 2 \sqrt{2}$	$2 \sqrt{2}$	0	0	$- 2 \sqrt{2}$	$2 \sqrt{2}$	$- 2 \sqrt{2}$	$2 \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	4	-4	0	4	0	0	-4	$- 2 \sqrt{2}$	$2 \sqrt{2}$	0	0	$- 2 \sqrt{2}$	$2 \sqrt{2}$	$- 2 \sqrt{2}$	$2 \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₃	4	-4	0	-2	0	0	2	$2 \sqrt{2}$	$- 2 \sqrt{2}$	$2 \sqrt{3}$	$- 2 \sqrt{3}$	2ζ⁵−2ζ⁷	−2ζ⁵+2ζ⁷	2ζ¹³−2ζ²³	−2ζ¹³+2ζ²³	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	4	-4	0	-2	0	0	2	$2 \sqrt{2}$	$- 2 \sqrt{2}$	$2 \sqrt{3}$	$- 2 \sqrt{3}$	2ζ⁵−2ζ⁷	−2ζ⁵+2ζ⁷	2ζ¹³−2ζ²³	−2ζ¹³+2ζ²³	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₄	4	-4	0	-2	0	0	2	$2 \sqrt{2}$	$- 2 \sqrt{2}$	$- 2 \sqrt{3}$	$2 \sqrt{3}$	2ζ¹³−2ζ²³	−2ζ¹³+2ζ²³	2ζ⁵−2ζ⁷	−2ζ⁵+2ζ⁷	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	4	-4	0	-2	0	0	2	$2 \sqrt{2}$	$- 2 \sqrt{2}$	$- 2 \sqrt{3}$	$2 \sqrt{3}$	2ζ¹³−2ζ²³	−2ζ¹³+2ζ²³	2ζ⁵−2ζ⁷	−2ζ⁵+2ζ⁷	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₅	4	-4	0	-2	0	0	2	$- 2 \sqrt{2}$	$2 \sqrt{2}$	$2 \sqrt{3}$	$- 2 \sqrt{3}$	−2ζ⁵+2ζ⁷	2ζ⁵−2ζ⁷	−2ζ¹³+2ζ²³	2ζ¹³−2ζ²³	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	4	-4	0	-2	0	0	2	$- 2 \sqrt{2}$	$2 \sqrt{2}$	$2 \sqrt{3}$	$- 2 \sqrt{3}$	−2ζ⁵+2ζ⁷	2ζ⁵−2ζ⁷	−2ζ¹³+2ζ²³	2ζ¹³−2ζ²³	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₆	4	-4	0	-2	0	0	2	$- 2 \sqrt{2}$	$2 \sqrt{2}$	$- 2 \sqrt{3}$	$2 \sqrt{3}$	−2ζ¹³+2ζ²³	2ζ¹³−2ζ²³	−2ζ⁵+2ζ⁷	2ζ⁵−2ζ⁷	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	4	-4	0	-2	0	0	2	$- 2 \sqrt{2}$	$2 \sqrt{2}$	$- 2 \sqrt{3}$	$2 \sqrt{3}$	−2ζ¹³+2ζ²³	2ζ¹³−2ζ²³	−2ζ⁵+2ζ⁷	2ζ⁵−2ζ⁷	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
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	-1	-1	-1	-1	-1	-1
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	1	1	1	1	1	1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	1	1	1	1
χ₃₉	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	-1	-1	1	-1	-1	1	-1	-1	1	-1	-1	1	1	-1	-1	-1	-1	1	1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	1	1	-1	1	1	-1	1	1	-1	1	1	-1	-1	1	1	1	1	-1	-1	1	1
χ₄₀	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	-1	-1	1	-1	-1	1	-1	-1	1	-1	-1	1	1	-1	-1	-1	-1	-1	-1	1	1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	1	1	-1	1	1	-1	1	1	-1	1	1	-1	-1	1	1	1	1	1	1	-1	-1
χ₄₁	1	1	1	1	1	1	1	-1	-1	1	1	-1	-1	-1	-1	1	1	1	1	1	-1	-1	-1	1	1	1	-1	-1	-1	-1	-1	-1	1	-1	1	-1	-1	-1	-1	-1	-1	-1	-1	1	1	-1	-1	1	1	1	1	-1	-1	-1	-1	-1	1	1	1	-1	-1	-1	1	1	1	1	1	1	-1	1	-1	1
χ₄₂	1	1	1	1	1	1	1	-1	-1	1	1	-1	-1	-1	-1	1	1	1	1	1	-1	-1	-1	1	1	1	-1	-1	-1	-1	-1	-1	-1	1	-1	1	-1	-1	-1	-1	-1	-1	-1	1	1	-1	-1	1	1	1	1	-1	-1	-1	-1	-1	1	1	1	-1	-1	-1	1	1	1	1	1	1	1	-1	1	-1
χ₄₃	1	1	1	1	1	1	1	-1	-1	1	1	-1	-1	-1	-1	-1	-1	1	-1	-1	-1	1	1	1	-1	-1	-1	-1	1	1	1	1	1	-1	-1	1	-1	-1	-1	-1	-1	-1	-1	1	1	-1	-1	1	1	1	1	1	1	-1	1	1	1	-1	-1	-1	1	1	1	1	-1	-1	-1	-1	-1	1	1	-1
χ₄₄	1	1	1	1	1	1	1	-1	-1	1	1	-1	-1	-1	-1	-1	-1	1	-1	-1	-1	1	1	1	-1	-1	-1	-1	1	1	1	1	-1	1	1	-1	-1	-1	-1	-1	-1	-1	-1	1	1	-1	-1	1	1	1	1	1	1	-1	1	1	1	-1	-1	-1	1	1	1	1	-1	-1	-1	-1	1	-1	-1	1
χ₄₅	2	2	2	2	-2	-2	2	0	0	-2	-2	0	0	0	0	0	0	2	0	0	0	$2 i$	$- 2 i$	-2	0	0	0	0	$2 i$	$2 i$	$- 2 i$	$- 2 i$	0	0	0	0	-2	-2	-2	-2	2	2	-2	0	0	2	2	0	0	0	0	0	0	-2	0	0	0	$- 2 i$	$2 i$	2	0	0	0	0	$- 2 i$	$- 2 i$	$2 i$	$2 i$	0	0	0	0
χ₄₆	2	2	2	2	-2	-2	2	0	0	-2	-2	0	0	0	0	0	0	2	0	0	0	$- 2 i$	$2 i$	-2	0	0	0	0	$- 2 i$	$- 2 i$	$2 i$	$2 i$	0	0	0	0	-2	-2	-2	-2	2	2	-2	0	0	2	2	0	0	0	0	0	0	-2	0	0	0	$2 i$	$- 2 i$	2	0	0	0	0	$2 i$	$2 i$	$- 2 i$	$- 2 i$	0	0	0	0
χ₄₇	2	2	2	-1	2	2	-1	2	2	-1	-1	-1	-1	-1	-1	2	2	-1	-1	-1	2	2	2	-1	-1	-1	-1	-1	-1	-1	-1	-1	0	0	0	0	-2	-2	-2	1	-2	-2	1	-2	-2	1	1	1	1	1	1	-2	-2	1	1	1	-2	-2	-2	1	1	1	1	1	1	1	1	1	0	0	0	0
χ₄₈	2	2	2	-1	2	2	-1	2	2	-1	-1	-1	-1	-1	-1	-2	-2	-1	1	1	2	-2	-2	-1	1	1	-1	-1	1	1	1	1	0	0	0	0	-2	-2	-2	1	-2	-2	1	-2	-2	1	1	1	1	1	1	2	2	1	-1	-1	-2	2	2	1	-1	-1	1	1	-1	-1	-1	-1	0	0	0	0
χ₄₉	2	2	2	-1	2	2	-1	-2	-2	-1	-1	1	1	1	1	2	2	-1	-1	-1	-2	-2	-2	-1	-1	-1	1	1	1	1	1	1	0	0	0	0	-2	-2	-2	1	-2	-2	1	2	2	1	1	-1	-1	-1	-1	-2	-2	1	1	1	2	2	2	1	1	1	-1	-1	-1	-1	-1	-1	0	0	0	0
χ₅₀	2	2	2	-1	2	2	-1	-2	-2	-1	-1	1	1	1	1	-2	-2	-1	1	1	-2	2	2	-1	1	1	1	1	-1	-1	-1	-1	0	0	0	0	-2	-2	-2	1	-2	-2	1	2	2	1	1	-1	-1	-1	-1	2	2	1	-1	-1	2	-2	-2	1	-1	-1	-1	-1	1	1	1	1	0	0	0	0
χ₅₁	2	2	2	-1	-2	-2	-1	0	0	1	1	$\sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$- \sqrt{3}$	0	0	-1	$- i \sqrt{3}$	$i \sqrt{3}$	0	$2 i$	$- 2 i$	1	$- i \sqrt{3}$	$i \sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$- i$	$- i$	$i$	$i$	0	0	0	0	-2	-2	-2	1	2	2	1	0	0	-1	-1	$- \sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$\sqrt{3}$	0	0	1	$i \sqrt{3}$	$- i \sqrt{3}$	0	$- 2 i$	$2 i$	-1	$i \sqrt{3}$	$- i \sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$i$	$i$	$- i$	$- i$	0	0	0	0
χ₅₂	2	2	2	-1	-2	-2	-1	0	0	1	1	$\sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$- \sqrt{3}$	0	0	-1	$i \sqrt{3}$	$- i \sqrt{3}$	0	$- 2 i$	$2 i$	1	$i \sqrt{3}$	$- i \sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$i$	$i$	$- i$	$- i$	0	0	0	0	-2	-2	-2	1	2	2	1	0	0	-1	-1	$- \sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$\sqrt{3}$	0	0	1	$- i \sqrt{3}$	$i \sqrt{3}$	0	$2 i$	$- 2 i$	-1	$- i \sqrt{3}$	$i \sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$- i$	$- i$	$i$	$i$	0	0	0	0
χ₅₃	2	2	2	-1	-2	-2	-1	0	0	1	1	$- \sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$\sqrt{3}$	0	0	-1	$- i \sqrt{3}$	$i \sqrt{3}$	0	$- 2 i$	$2 i$	1	$- i \sqrt{3}$	$i \sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$i$	$i$	$- i$	$- i$	0	0	0	0	-2	-2	-2	1	2	2	1	0	0	-1	-1	$\sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$- \sqrt{3}$	0	0	1	$i \sqrt{3}$	$- i \sqrt{3}$	0	$2 i$	$- 2 i$	-1	$i \sqrt{3}$	$- i \sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$- i$	$- i$	$i$	$i$	0	0	0	0
χ₅₄	2	2	2	-1	-2	-2	-1	0	0	1	1	$- \sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$\sqrt{3}$	0	0	-1	$i \sqrt{3}$	$- i \sqrt{3}$	0	$2 i$	$- 2 i$	1	$i \sqrt{3}$	$- i \sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$- i$	$- i$	$i$	$i$	0	0	0	0	-2	-2	-2	1	2	2	1	0	0	-1	-1	$\sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$- \sqrt{3}$	0	0	1	$- i \sqrt{3}$	$i \sqrt{3}$	0	$- 2 i$	$2 i$	-1	$- i \sqrt{3}$	$i \sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$i$	$i$	$- i$	$- i$	0	0	0	0
χ₅₅	2	2	-2	2	2	-2	2	2	2	2	2	2	2	2	2	0	0	-2	0	0	-2	0	0	-2	0	0	-2	-2	0	0	0	0	0	0	0	0	-2	-2	2	-2	-2	2	-2	-2	-2	-2	-2	-2	-2	-2	-2	0	0	2	0	0	2	0	0	2	0	0	2	2	0	0	0	0	0	0	0	0
χ₅₆	2	2	-2	2	2	-2	2	-2	-2	2	2	-2	-2	-2	-2	0	0	-2	0	0	2	0	0	-2	0	0	2	2	0	0	0	0	0	0	0	0	-2	-2	2	-2	-2	2	-2	2	2	-2	-2	2	2	2	2	0	0	2	0	0	-2	0	0	2	0	0	-2	-2	0	0	0	0	0	0	0	0
χ₅₇	2	2	-2	2	-2	2	2	0	0	-2	-2	0	0	0	0	2	-2	-2	2	2	0	0	0	2	-2	-2	0	0	0	0	0	0	0	0	0	0	-2	-2	2	-2	2	-2	-2	0	0	2	2	0	0	0	0	-2	2	2	-2	-2	0	0	0	-2	2	2	0	0	0	0	0	0	0	0	0	0
χ₅₈	2	2	-2	2	-2	2	2	0	0	-2	-2	0	0	0	0	-2	2	-2	-2	-2	0	0	0	2	2	2	0	0	0	0	0	0	0	0	0	0	-2	-2	2	-2	2	-2	-2	0	0	2	2	0	0	0	0	2	-2	2	2	2	0	0	0	-2	-2	-2	0	0	0	0	0	0	0	0	0	0
χ₅₉	2	2	-2	-1	2	-2	-1	2	2	-1	-1	-1	-1	-1	-1	0	0	1	$- i \sqrt{3}$	$i \sqrt{3}$	-2	0	0	1	$i \sqrt{3}$	$- i \sqrt{3}$	1	1	$- i \sqrt{3}$	$i \sqrt{3}$	$- i \sqrt{3}$	$i \sqrt{3}$	0	0	0	0	-2	-2	2	1	-2	2	1	-2	-2	1	1	1	1	1	1	0	0	-1	$i \sqrt{3}$	$- i \sqrt{3}$	2	0	0	-1	$- i \sqrt{3}$	$i \sqrt{3}$	-1	-1	$i \sqrt{3}$	$- i \sqrt{3}$	$i \sqrt{3}$	$- i \sqrt{3}$	0	0	0	0
χ₆₀	2	2	-2	-1	2	-2	-1	2	2	-1	-1	-1	-1	-1	-1	0	0	1	$i \sqrt{3}$	$- i \sqrt{3}$	-2	0	0	1	$- i \sqrt{3}$	$i \sqrt{3}$	1	1	$i \sqrt{3}$	$- i \sqrt{3}$	$i \sqrt{3}$	$- i \sqrt{3}$	0	0	0	0	-2	-2	2	1	-2	2	1	-2	-2	1	1	1	1	1	1	0	0	-1	$- i \sqrt{3}$	$i \sqrt{3}$	2	0	0	-1	$i \sqrt{3}$	$- i \sqrt{3}$	-1	-1	$- i \sqrt{3}$	$i \sqrt{3}$	$- i \sqrt{3}$	$i \sqrt{3}$	0	0	0	0
χ₆₁	2	2	-2	-1	2	-2	-1	-2	-2	-1	-1	1	1	1	1	0	0	1	$- i \sqrt{3}$	$i \sqrt{3}$	2	0	0	1	$i \sqrt{3}$	$- i \sqrt{3}$	-1	-1	$i \sqrt{3}$	$- i \sqrt{3}$	$i \sqrt{3}$	$- i \sqrt{3}$	0	0	0	0	-2	-2	2	1	-2	2	1	2	2	1	1	-1	-1	-1	-1	0	0	-1	$i \sqrt{3}$	$- i \sqrt{3}$	-2	0	0	-1	$- i \sqrt{3}$	$i \sqrt{3}$	1	1	$- i \sqrt{3}$	$i \sqrt{3}$	$- i \sqrt{3}$	$i \sqrt{3}$	0	0	0	0
χ₆₂	2	2	-2	-1	2	-2	-1	-2	-2	-1	-1	1	1	1	1	0	0	1	$i \sqrt{3}$	$- i \sqrt{3}$	2	0	0	1	$- i \sqrt{3}$	$i \sqrt{3}$	-1	-1	$- i \sqrt{3}$	$i \sqrt{3}$	$- i \sqrt{3}$	$i \sqrt{3}$	0	0	0	0	-2	-2	2	1	-2	2	1	2	2	1	1	-1	-1	-1	-1	0	0	-1	$- i \sqrt{3}$	$i \sqrt{3}$	-2	0	0	-1	$i \sqrt{3}$	$- i \sqrt{3}$	1	1	$i \sqrt{3}$	$- i \sqrt{3}$	$i \sqrt{3}$	$- i \sqrt{3}$	0	0	0	0
χ₆₃	2	2	-2	-1	-2	2	-1	0	0	1	1	$\sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$- \sqrt{3}$	2	-2	1	-1	-1	0	0	0	-1	1	1	$- \sqrt{3}$	$\sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	0	0	0	0	-2	-2	2	1	2	-2	1	0	0	-1	-1	$- \sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$\sqrt{3}$	-2	2	-1	1	1	0	0	0	1	-1	-1	$\sqrt{3}$	$- \sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	0	0	0	0
χ₆₄	2	2	-2	-1	-2	2	-1	0	0	1	1	$\sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$- \sqrt{3}$	-2	2	1	1	1	0	0	0	-1	-1	-1	$- \sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	0	0	0	0	-2	-2	2	1	2	-2	1	0	0	-1	-1	$- \sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$\sqrt{3}$	2	-2	-1	-1	-1	0	0	0	1	1	1	$\sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	0	0	0	0
χ₆₅	2	2	-2	-1	-2	2	-1	0	0	1	1	$- \sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$\sqrt{3}$	2	-2	1	-1	-1	0	0	0	-1	1	1	$\sqrt{3}$	$- \sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	0	0	0	0	-2	-2	2	1	2	-2	1	0	0	-1	-1	$\sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$- \sqrt{3}$	-2	2	-1	1	1	0	0	0	1	-1	-1	$- \sqrt{3}$	$\sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	0	0	0	0
χ₆₆	2	2	-2	-1	-2	2	-1	0	0	1	1	$- \sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$\sqrt{3}$	-2	2	1	1	1	0	0	0	-1	-1	-1	$\sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	0	0	0	0	-2	-2	2	1	2	-2	1	0	0	-1	-1	$\sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$- \sqrt{3}$	2	-2	-1	-1	-1	0	0	0	1	1	1	$- \sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	0	0	0	0
χ₆₇	4	-4	0	4	0	0	-4	$2 \sqrt{2}$	$- 2 \sqrt{2}$	0	0	$2 \sqrt{2}$	$- 2 \sqrt{2}$	$2 \sqrt{2}$	$- 2 \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	-4	4	0	-4	0	0	4	$- 2 \sqrt{2}$	$2 \sqrt{2}$	0	0	$- 2 \sqrt{2}$	$2 \sqrt{2}$	$- 2 \sqrt{2}$	$2 \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₆₈	4	-4	0	4	0	0	-4	$- 2 \sqrt{2}$	$2 \sqrt{2}$	0	0	$- 2 \sqrt{2}$	$2 \sqrt{2}$	$- 2 \sqrt{2}$	$2 \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	-4	4	0	-4	0	0	4	$2 \sqrt{2}$	$- 2 \sqrt{2}$	0	0	$2 \sqrt{2}$	$- 2 \sqrt{2}$	$2 \sqrt{2}$	$- 2 \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₆₉	4	-4	0	-2	0	0	2	$2 \sqrt{2}$	$- 2 \sqrt{2}$	$2 \sqrt{3}$	$- 2 \sqrt{3}$	2ζ⁵−2ζ⁷	−2ζ⁵+2ζ⁷	2ζ¹³−2ζ²³	−2ζ¹³+2ζ²³	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	-4	4	0	2	0	0	-2	$- 2 \sqrt{2}$	$2 \sqrt{2}$	$- 2 \sqrt{3}$	$2 \sqrt{3}$	−2ζ⁵+2ζ⁷	2ζ⁵−2ζ⁷	−2ζ¹³+2ζ²³	2ζ¹³−2ζ²³	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₇₀	4	-4	0	-2	0	0	2	$2 \sqrt{2}$	$- 2 \sqrt{2}$	$- 2 \sqrt{3}$	$2 \sqrt{3}$	2ζ¹³−2ζ²³	−2ζ¹³+2ζ²³	2ζ⁵−2ζ⁷	−2ζ⁵+2ζ⁷	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	-4	4	0	2	0	0	-2	$- 2 \sqrt{2}$	$2 \sqrt{2}$	$2 \sqrt{3}$	$- 2 \sqrt{3}$	−2ζ¹³+2ζ²³	2ζ¹³−2ζ²³	−2ζ⁵+2ζ⁷	2ζ⁵−2ζ⁷	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₇₁	4	-4	0	-2	0	0	2	$- 2 \sqrt{2}$	$2 \sqrt{2}$	$2 \sqrt{3}$	$- 2 \sqrt{3}$	−2ζ⁵+2ζ⁷	2ζ⁵−2ζ⁷	−2ζ¹³+2ζ²³	2ζ¹³−2ζ²³	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	-4	4	0	2	0	0	-2	$2 \sqrt{2}$	$- 2 \sqrt{2}$	$- 2 \sqrt{3}$	$2 \sqrt{3}$	2ζ⁵−2ζ⁷	−2ζ⁵+2ζ⁷	2ζ¹³−2ζ²³	−2ζ¹³+2ζ²³	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₇₂	4	-4	0	-2	0	0	2	$- 2 \sqrt{2}$	$2 \sqrt{2}$	$- 2 \sqrt{3}$	$2 \sqrt{3}$	−2ζ¹³+2ζ²³	2ζ¹³−2ζ²³	−2ζ⁵+2ζ⁷	2ζ⁵−2ζ⁷	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	-4	4	0	2	0	0	-2	$2 \sqrt{2}$	$- 2 \sqrt{2}$	$2 \sqrt{3}$	$- 2 \sqrt{3}$	2ζ¹³−2ζ²³	−2ζ¹³+2ζ²³	2ζ⁵−2ζ⁷	−2ζ⁵+2ζ⁷	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0

Character table — Group #83809