Group #72224523 — 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
size	1	2	8	8	8	8	16	16	16	16	16	16	16	16	16	16	16	16	16	81	108	162	162	162	162	162	162	162	162	162	162	216	216	216	216	972
order	1	3	3	3	3	3	3	3	3	3	3	3	3	3	3	3	3	3	3	2	2	4	6	8	8	12	12	24	24	24	24	6	6	6	6	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
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
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
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
χ₅	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	0	-2	2	0	0	-2	-2	0	0	0	0	0	0	0	0	0
χ₆	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	-2	0	0	-2	$- i \sqrt{2}$	$i \sqrt{2}$	0	0	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	0	0	0	0	0
χ₇	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	-2	0	0	-2	$i \sqrt{2}$	$- i \sqrt{2}$	0	0	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	0	0	0	0	0
χ₈	2	-1	2	2	2	2	2	2	2	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	2	0	2	-1	2	2	-1	-1	-1	-1	-1	-1	0	0	0	0	0
χ₉	2	-1	2	2	2	2	2	2	2	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	2	0	2	-1	-2	-2	-1	-1	1	1	1	1	0	0	0	0	0
χ₁₀	2	-1	2	2	2	2	2	2	2	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	2	0	-2	-1	0	0	1	1	$\sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	0	0	0	0	0
χ₁₁	2	-1	2	2	2	2	2	2	2	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	2	0	-2	-1	0	0	1	1	$- \sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	0	0	0	0	0
χ₁₂	2	-1	2	2	2	2	2	2	2	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-2	0	0	1	$- i \sqrt{2}$	$i \sqrt{2}$	$\sqrt{3}$	$- \sqrt{3}$	ζ⁵+ζ⁷	ζ¹³+ζ²³	−ζ⁵−ζ⁷	−ζ¹³−ζ²³	0	0	0	0	0
χ₁₃	2	-1	2	2	2	2	2	2	2	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-2	0	0	1	$- i \sqrt{2}$	$i \sqrt{2}$	$- \sqrt{3}$	$\sqrt{3}$	ζ¹³+ζ²³	ζ⁵+ζ⁷	−ζ¹³−ζ²³	−ζ⁵−ζ⁷	0	0	0	0	0
χ₁₄	2	-1	2	2	2	2	2	2	2	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-2	0	0	1	$i \sqrt{2}$	$- i \sqrt{2}$	$\sqrt{3}$	$- \sqrt{3}$	−ζ⁵−ζ⁷	−ζ¹³−ζ²³	ζ⁵+ζ⁷	ζ¹³+ζ²³	0	0	0	0	0
χ₁₅	2	-1	2	2	2	2	2	2	2	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-2	0	0	1	$i \sqrt{2}$	$- i \sqrt{2}$	$- \sqrt{3}$	$\sqrt{3}$	−ζ¹³−ζ²³	−ζ⁵−ζ⁷	ζ¹³+ζ²³	ζ⁵+ζ⁷	0	0	0	0	0
χ₁₆	8	8	2	5	-1	-1	2	-4	-1	2	2	2	5	-4	-4	-1	-1	-1	-1	0	2	0	0	0	0	0	0	0	0	0	0	2	-1	-1	-1	0
χ₁₇	8	8	2	5	-1	-1	2	-4	-1	2	2	2	5	-4	-4	-1	-1	-1	-1	0	-2	0	0	0	0	0	0	0	0	0	0	-2	1	1	1	0
χ₁₈	8	8	5	2	-1	-1	-4	2	-1	5	-4	-4	2	2	2	-1	-1	-1	-1	0	2	0	0	0	0	0	0	0	0	0	0	-1	2	-1	-1	0
χ₁₉	8	8	5	2	-1	-1	-4	2	-1	5	-4	-4	2	2	2	-1	-1	-1	-1	0	-2	0	0	0	0	0	0	0	0	0	0	1	-2	1	1	0
χ₂₀	8	8	-1	-1	8	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	8	-1	-1	-1	0	2	0	0	0	0	0	0	0	0	0	0	-1	-1	2	-1	0
χ₂₁	8	8	-1	-1	8	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	8	-1	-1	-1	0	-2	0	0	0	0	0	0	0	0	0	0	1	1	-2	1	0
χ₂₂	8	8	-1	-1	-1	8	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	8	-1	-1	0	2	0	0	0	0	0	0	0	0	0	0	-1	-1	-1	2	0
χ₂₃	8	8	-1	-1	-1	8	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	8	-1	-1	0	-2	0	0	0	0	0	0	0	0	0	0	1	1	1	-2	0
χ₂₄	16	16	4	-8	-2	-2	4	1	-2	4	4	4	-8	1	1	-2	-2	-2	-2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₅	16	16	-8	4	-2	-2	1	4	-2	-8	1	1	4	4	4	-2	-2	-2	-2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₆	16	16	-2	-2	-2	-2	-2	-2	7	-2	-2	-2	-2	-2	-2	-2	-2	7	7	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₇	16	-8	4	10	-2	-2	4	-8	-2	-2	-2	-2	-5	4	4	1	1	1	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₈	16	-8	4	-8	-2	-2	4	1	-2	-2	$- 2 - 3 i \sqrt{3}$	$- 2 + 3 i \sqrt{3}$	4	$\frac{- 1 - 3 i \sqrt{3}}{2}$	$\frac{- 1 + 3 i \sqrt{3}}{2}$	1	1	$1 - 3 i \sqrt{3}$	$1 + 3 i \sqrt{3}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₉	16	-8	4	-8	-2	-2	4	1	-2	-2	$- 2 + 3 i \sqrt{3}$	$- 2 - 3 i \sqrt{3}$	4	$\frac{- 1 + 3 i \sqrt{3}}{2}$	$\frac{- 1 - 3 i \sqrt{3}}{2}$	1	1	$1 + 3 i \sqrt{3}$	$1 - 3 i \sqrt{3}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₀	16	-8	10	4	-2	-2	-8	4	-2	-5	4	4	-2	-2	-2	1	1	1	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₁	16	-8	-8	4	-2	-2	1	4	-2	4	$\frac{- 1 - 3 i \sqrt{3}}{2}$	$\frac{- 1 + 3 i \sqrt{3}}{2}$	-2	$- 2 - 3 i \sqrt{3}$	$- 2 + 3 i \sqrt{3}$	1	1	$1 + 3 i \sqrt{3}$	$1 - 3 i \sqrt{3}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₂	16	-8	-8	4	-2	-2	1	4	-2	4	$\frac{- 1 + 3 i \sqrt{3}}{2}$	$\frac{- 1 - 3 i \sqrt{3}}{2}$	-2	$- 2 + 3 i \sqrt{3}$	$- 2 - 3 i \sqrt{3}$	1	1	$1 - 3 i \sqrt{3}$	$1 + 3 i \sqrt{3}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₃	16	-8	-2	-2	16	-2	-2	-2	-2	1	1	1	1	1	1	-8	1	1	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₄	16	-8	-2	-2	-2	16	-2	-2	-2	1	1	1	1	1	1	1	-8	1	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₅	16	-8	-2	-2	-2	-2	-2	-2	7	1	$1 - 3 i \sqrt{3}$	$1 + 3 i \sqrt{3}$	1	$1 + 3 i \sqrt{3}$	$1 - 3 i \sqrt{3}$	1	1	$\frac{- 7 + 3 i \sqrt{3}}{2}$	$\frac{- 7 - 3 i \sqrt{3}}{2}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₆	16	-8	-2	-2	-2	-2	-2	-2	7	1	$1 + 3 i \sqrt{3}$	$1 - 3 i \sqrt{3}$	1	$1 - 3 i \sqrt{3}$	$1 + 3 i \sqrt{3}$	1	1	$\frac{- 7 - 3 i \sqrt{3}}{2}$	$\frac{- 7 + 3 i \sqrt{3}}{2}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0

Character table — Group #72224523