Group #72224570 — 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	2	8	8	9	9	16	16	16	16	18	18	32	32	32	32	32	72	72	81	108	108	144	144	162	162	162	162	162	162	162	162	162	162	162	162	162	162	162	162	162	162	162	216	216	216	216	432	432	972	972
order	1	3	3	3	2	2	3	3	3	3	6	6	3	3	3	3	3	6	6	2	2	2	6	6	4	4	6	8	8	8	8	12	12	12	12	24	24	24	24	24	24	24	24	6	6	6	6	6	6	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	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	-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
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	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
χ₉	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	0	0	2	2	-2	-2	2	0	0	0	0	-2	-2	-2	-2	0	0	0	0	0	0	0	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	2	2	2	-2	-2	0	0	2	-2	0	0	-2	$- i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	0	0	0	0	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	0	0	0	0	0	0	0	0
χ₁₁	2	2	2	2	2	-2	2	2	2	2	2	-2	2	2	2	2	2	2	-2	-2	0	0	2	-2	0	0	-2	$i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	0	0	0	0	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	0	0	0	0	0	0	0	0
χ₁₂	2	2	2	2	-2	2	2	2	2	2	-2	2	2	2	2	2	2	-2	2	-2	0	0	-2	2	0	0	-2	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	0	0	0	0	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	0	0	0	0	0	0	0	0
χ₁₃	2	2	2	2	-2	2	2	2	2	2	-2	2	2	2	2	2	2	-2	2	-2	0	0	-2	2	0	0	-2	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	0	0	0	0	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	0	0	0	0	0	0	0	0
χ₁₄	2	2	2	2	-2	-2	2	2	2	2	-2	-2	2	2	2	2	2	-2	-2	2	0	0	-2	-2	2	-2	2	0	0	0	0	2	2	-2	-2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₁₅	2	-1	2	2	2	2	-1	-1	2	2	-1	-1	2	-1	-1	-1	-1	2	2	2	0	0	-1	-1	2	2	-1	2	2	2	2	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	0	0	0	0	0	0	0	0
χ₁₆	2	-1	2	2	2	2	-1	-1	2	2	-1	-1	2	-1	-1	-1	-1	2	2	2	0	0	-1	-1	2	2	-1	-2	-2	-2	-2	-1	-1	-1	-1	1	1	1	1	1	1	1	1	0	0	0	0	0	0	0	0
χ₁₇	2	-1	2	2	2	2	-1	-1	2	2	-1	-1	2	-1	-1	-1	-1	2	2	2	0	0	-1	-1	-2	-2	-1	0	0	0	0	1	1	1	1	$\sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	0	0	0	0	0	0	0	0
χ₁₈	2	-1	2	2	2	2	-1	-1	2	2	-1	-1	2	-1	-1	-1	-1	2	2	2	0	0	-1	-1	-2	-2	-1	0	0	0	0	1	1	1	1	$- \sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	0	0	0	0	0	0	0	0
χ₁₉	2	-1	2	2	2	-2	-1	-1	2	2	-1	1	2	-1	-1	-1	-1	2	-2	-2	0	0	-1	1	0	0	1	$- i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$\sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	ζ⁵+ζ⁷	ζ¹³+ζ²³	−ζ⁵−ζ⁷	−ζ¹³−ζ²³	ζ⁵+ζ⁷	ζ¹³+ζ²³	−ζ⁵−ζ⁷	−ζ¹³−ζ²³	0	0	0	0	0	0	0	0
χ₂₀	2	-1	2	2	2	-2	-1	-1	2	2	-1	1	2	-1	-1	-1	-1	2	-2	-2	0	0	-1	1	0	0	1	$- i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$- \sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	ζ¹³+ζ²³	ζ⁵+ζ⁷	−ζ¹³−ζ²³	−ζ⁵−ζ⁷	ζ¹³+ζ²³	ζ⁵+ζ⁷	−ζ¹³−ζ²³	−ζ⁵−ζ⁷	0	0	0	0	0	0	0	0
χ₂₁	2	-1	2	2	2	-2	-1	-1	2	2	-1	1	2	-1	-1	-1	-1	2	-2	-2	0	0	-1	1	0	0	1	$i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$\sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	−ζ⁵−ζ⁷	−ζ¹³−ζ²³	ζ⁵+ζ⁷	ζ¹³+ζ²³	−ζ⁵−ζ⁷	−ζ¹³−ζ²³	ζ⁵+ζ⁷	ζ¹³+ζ²³	0	0	0	0	0	0	0	0
χ₂₂	2	-1	2	2	2	-2	-1	-1	2	2	-1	1	2	-1	-1	-1	-1	2	-2	-2	0	0	-1	1	0	0	1	$i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$- \sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	−ζ¹³−ζ²³	−ζ⁵−ζ⁷	ζ¹³+ζ²³	ζ⁵+ζ⁷	−ζ¹³−ζ²³	−ζ⁵−ζ⁷	ζ¹³+ζ²³	ζ⁵+ζ⁷	0	0	0	0	0	0	0	0
χ₂₃	2	-1	2	2	-2	2	-1	-1	2	2	1	-1	2	-1	-1	-1	-1	-2	2	-2	0	0	1	-1	0	0	1	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$\sqrt{3}$	$- \sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	ζ¹³+ζ²³	ζ⁵+ζ⁷	−ζ¹³−ζ²³	−ζ⁵−ζ⁷	−ζ¹³−ζ²³	−ζ⁵−ζ⁷	ζ¹³+ζ²³	ζ⁵+ζ⁷	0	0	0	0	0	0	0	0
χ₂₄	2	-1	2	2	-2	2	-1	-1	2	2	1	-1	2	-1	-1	-1	-1	-2	2	-2	0	0	1	-1	0	0	1	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$- \sqrt{3}$	$\sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	ζ⁵+ζ⁷	ζ¹³+ζ²³	−ζ⁵−ζ⁷	−ζ¹³−ζ²³	−ζ⁵−ζ⁷	−ζ¹³−ζ²³	ζ⁵+ζ⁷	ζ¹³+ζ²³	0	0	0	0	0	0	0	0
χ₂₅	2	-1	2	2	-2	2	-1	-1	2	2	1	-1	2	-1	-1	-1	-1	-2	2	-2	0	0	1	-1	0	0	1	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$\sqrt{3}$	$- \sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	−ζ¹³−ζ²³	−ζ⁵−ζ⁷	ζ¹³+ζ²³	ζ⁵+ζ⁷	ζ¹³+ζ²³	ζ⁵+ζ⁷	−ζ¹³−ζ²³	−ζ⁵−ζ⁷	0	0	0	0	0	0	0	0
χ₂₆	2	-1	2	2	-2	2	-1	-1	2	2	1	-1	2	-1	-1	-1	-1	-2	2	-2	0	0	1	-1	0	0	1	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$- \sqrt{3}$	$\sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	−ζ⁵−ζ⁷	−ζ¹³−ζ²³	ζ⁵+ζ⁷	ζ¹³+ζ²³	ζ⁵+ζ⁷	ζ¹³+ζ²³	−ζ⁵−ζ⁷	−ζ¹³−ζ²³	0	0	0	0	0	0	0	0
χ₂₇	2	-1	2	2	-2	-2	-1	-1	2	2	1	1	2	-1	-1	-1	-1	-2	-2	2	0	0	1	1	2	-2	-1	0	0	0	0	-1	-1	1	1	$\sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	0	0	0	0	0	0	0	0
χ₂₈	2	-1	2	2	-2	-2	-1	-1	2	2	1	1	2	-1	-1	-1	-1	-2	-2	2	0	0	1	1	2	-2	-1	0	0	0	0	-1	-1	1	1	$- \sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	0	0	0	0	0	0	0	0
χ₂₉	2	-1	2	2	-2	-2	-1	-1	2	2	1	1	2	-1	-1	-1	-1	-2	-2	2	0	0	1	1	-2	2	-1	2	2	-2	-2	1	1	-1	-1	-1	-1	-1	-1	1	1	1	1	0	0	0	0	0	0	0	0
χ₃₀	2	-1	2	2	-2	-2	-1	-1	2	2	1	1	2	-1	-1	-1	-1	-2	-2	2	0	0	1	1	-2	2	-1	-2	-2	2	2	1	1	-1	-1	1	1	1	1	-1	-1	-1	-1	0	0	0	0	0	0	0	0
χ₃₁	8	8	8	-1	0	8	8	-1	-1	-1	0	8	-1	-1	-1	-1	-1	0	-1	0	2	2	0	-1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	2	-1	2	-1	-1	-1	0	0
χ₃₂	8	8	8	-1	0	8	8	-1	-1	-1	0	8	-1	-1	-1	-1	-1	0	-1	0	-2	-2	0	-1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	-2	1	-2	1	1	1	0	0
χ₃₃	8	8	8	-1	0	-8	8	-1	-1	-1	0	-8	-1	-1	-1	-1	-1	0	1	0	2	-2	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	2	-1	-2	1	-1	1	0	0
χ₃₄	8	8	8	-1	0	-8	8	-1	-1	-1	0	-8	-1	-1	-1	-1	-1	0	1	0	-2	2	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	-2	1	2	-1	1	-1	0	0
χ₃₅	8	8	-1	8	8	0	-1	8	-1	-1	8	0	-1	-1	-1	-1	-1	-1	0	0	2	2	-1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	-1	2	-1	2	-1	-1	0	0
χ₃₆	8	8	-1	8	8	0	-1	8	-1	-1	8	0	-1	-1	-1	-1	-1	-1	0	0	-2	-2	-1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	-2	1	-2	1	1	0	0
χ₃₇	8	8	-1	8	-8	0	-1	8	-1	-1	-8	0	-1	-1	-1	-1	-1	1	0	0	2	-2	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	-1	2	1	-2	-1	1	0	0
χ₃₈	8	8	-1	8	-8	0	-1	8	-1	-1	-8	0	-1	-1	-1	-1	-1	1	0	0	-2	2	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	-2	-1	2	1	-1	0	0
χ₃₉	16	16	-2	-2	0	0	-2	-2	7	-2	0	0	-2	7	-2	-2	-2	0	0	0	0	4	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	-2	-2	0	1	0	0
χ₄₀	16	16	-2	-2	0	0	-2	-2	7	-2	0	0	-2	7	-2	-2	-2	0	0	0	0	-4	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	2	2	0	-1	0	0
χ₄₁	16	16	-2	-2	0	0	-2	-2	-2	7	0	0	-2	-2	7	-2	-2	0	0	0	4	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	-2	-2	0	0	1	0	0	0
χ₄₂	16	16	-2	-2	0	0	-2	-2	-2	7	0	0	-2	-2	7	-2	-2	0	0	0	-4	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	2	2	0	0	-1	0	0	0
χ₄₃	16	-8	16	-2	0	16	-8	1	-2	-2	0	-8	-2	1	1	1	1	0	-2	0	0	0	0	1	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	16	-8	16	-2	0	-16	-8	1	-2	-2	0	8	-2	1	1	1	1	0	2	0	0	0	0	-1	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	16	-8	-2	16	16	0	1	-8	-2	-2	-8	0	-2	1	1	1	1	-2	0	0	0	0	1	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	16	-8	-2	16	-16	0	1	-8	-2	-2	8	0	-2	1	1	1	1	2	0	0	0	0	-1	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
χ₄₇	32	32	-4	-4	0	0	-4	-4	-4	-4	0	0	5	-4	-4	5	5	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	0	0	0	0	0	0
χ₄₈	32	-16	-4	-4	0	0	2	2	14	-4	0	0	-4	-7	2	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	0	0	0	0	0	0
χ₄₉	32	-16	-4	-4	0	0	2	2	-4	14	0	0	-4	2	-7	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	0	0	0	0	0	0
χ₅₀	32	-16	-4	-4	0	0	2	2	-4	-4	0	0	5	2	2	$\frac{- 5 - 9 i \sqrt{3}}{2}$	$\frac{- 5 + 9 i \sqrt{3}}{2}$	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	0	0	0	0	0	0
χ₅₁	32	-16	-4	-4	0	0	2	2	-4	-4	0	0	5	2	2	$\frac{- 5 + 9 i \sqrt{3}}{2}$	$\frac{- 5 - 9 i \sqrt{3}}{2}$	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	0	0	0	0	0	0

Character table — Group #72224570