Group #72224532 — 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
size	1	2	8	8	16	16	16	16	16	16	16	16	16	16	16	16	16	16	27	27	81	81	81	81	81	81	81	162	162	162	162	162	162	162	216	216	243	243	243	243	243	243
order	1	3	3	3	3	3	3	3	3	3	3	3	3	3	3	3	3	3	2	2	2	4	4	8	8	8	8	6	12	12	24	24	24	24	6	6	4	4	8	8	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
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
χ₃	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	-1	-1	$i$	$i$	$- i$	$- i$	1	-1	-1	$i$	$i$	$- i$	$- i$	1	1	-1	-1	$i$	$i$	$- i$	$- i$
χ₄	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	-1	-1	$- i$	$- i$	$i$	$i$	1	-1	-1	$- i$	$- i$	$i$	$i$	1	1	-1	-1	$- i$	$- i$	$i$	$i$
χ₅	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	-1	-1	$i$	$- i$	ζ⁷+ζ²³	−ζ⁷−ζ²³	−ζ⁵−ζ¹³	ζ⁵+ζ¹³	-1	$i$	$- i$	ζ⁷+ζ²³	−ζ⁷−ζ²³	−ζ⁵−ζ¹³	ζ⁵+ζ¹³	1	-1	$i$	$- i$	ζ⁷+ζ²³	−ζ⁷−ζ²³	−ζ⁵−ζ¹³	ζ⁵+ζ¹³
χ₆	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	-1	-1	$i$	$- i$	−ζ⁷−ζ²³	ζ⁷+ζ²³	ζ⁵+ζ¹³	−ζ⁵−ζ¹³	-1	$i$	$- i$	−ζ⁷−ζ²³	ζ⁷+ζ²³	ζ⁵+ζ¹³	−ζ⁵−ζ¹³	1	-1	$i$	$- i$	−ζ⁷−ζ²³	ζ⁷+ζ²³	ζ⁵+ζ¹³	−ζ⁵−ζ¹³
χ₇	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	-1	-1	$- i$	$i$	−ζ⁵−ζ¹³	ζ⁵+ζ¹³	ζ⁷+ζ²³	−ζ⁷−ζ²³	-1	$- i$	$i$	−ζ⁵−ζ¹³	ζ⁵+ζ¹³	ζ⁷+ζ²³	−ζ⁷−ζ²³	1	-1	$- i$	$i$	−ζ⁵−ζ¹³	ζ⁵+ζ¹³	ζ⁷+ζ²³	−ζ⁷−ζ²³
χ₈	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	-1	-1	$- i$	$i$	ζ⁵+ζ¹³	−ζ⁵−ζ¹³	−ζ⁷−ζ²³	ζ⁷+ζ²³	-1	$- i$	$i$	ζ⁵+ζ¹³	−ζ⁵−ζ¹³	−ζ⁷−ζ²³	ζ⁷+ζ²³	1	-1	$- i$	$i$	ζ⁵+ζ¹³	−ζ⁵−ζ¹³	−ζ⁷−ζ²³	ζ⁷+ζ²³
χ₉	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	-1	1	-1	$i$	$- i$	ζ⁷+ζ²³	−ζ⁷−ζ²³	−ζ⁵−ζ¹³	ζ⁵+ζ¹³	-1	$i$	$- i$	ζ⁷+ζ²³	−ζ⁷−ζ²³	−ζ⁵−ζ¹³	ζ⁵+ζ¹³	-1	1	$- i$	$i$	−ζ⁷−ζ²³	ζ⁷+ζ²³	ζ⁵+ζ¹³	−ζ⁵−ζ¹³
χ₁₀	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	-1	1	-1	$i$	$- i$	−ζ⁷−ζ²³	ζ⁷+ζ²³	ζ⁵+ζ¹³	−ζ⁵−ζ¹³	-1	$i$	$- i$	−ζ⁷−ζ²³	ζ⁷+ζ²³	ζ⁵+ζ¹³	−ζ⁵−ζ¹³	-1	1	$- i$	$i$	ζ⁷+ζ²³	−ζ⁷−ζ²³	−ζ⁵−ζ¹³	ζ⁵+ζ¹³
χ₁₁	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	-1	1	-1	$- i$	$i$	−ζ⁵−ζ¹³	ζ⁵+ζ¹³	ζ⁷+ζ²³	−ζ⁷−ζ²³	-1	$- i$	$i$	−ζ⁵−ζ¹³	ζ⁵+ζ¹³	ζ⁷+ζ²³	−ζ⁷−ζ²³	-1	1	$i$	$- i$	ζ⁵+ζ¹³	−ζ⁵−ζ¹³	−ζ⁷−ζ²³	ζ⁷+ζ²³
χ₁₂	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	-1	1	-1	$- i$	$i$	ζ⁵+ζ¹³	−ζ⁵−ζ¹³	−ζ⁷−ζ²³	ζ⁷+ζ²³	-1	$- i$	$i$	ζ⁵+ζ¹³	−ζ⁵−ζ¹³	−ζ⁷−ζ²³	ζ⁷+ζ²³	-1	1	$i$	$- i$	−ζ⁵−ζ¹³	ζ⁵+ζ¹³	ζ⁷+ζ²³	−ζ⁷−ζ²³
χ₁₃	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	-1	-1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	-1	-1	-1	-1	-1	-1	-1	-1
χ₁₄	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	-1	-1	1	1	1	-1	-1	-1	-1	1	1	1	-1	-1	-1	-1	-1	-1	-1	-1	1	1	1	1
χ₁₅	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	-1	-1	1	-1	-1	$i$	$i$	$- i$	$- i$	1	-1	-1	$i$	$i$	$- i$	$- i$	-1	-1	1	1	$- i$	$- i$	$i$	$i$
χ₁₆	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	-1	-1	1	-1	-1	$- i$	$- i$	$i$	$i$	1	-1	-1	$- i$	$- i$	$i$	$i$	-1	-1	1	1	$i$	$i$	$- i$	$- i$
χ₁₇	2	-1	2	2	2	2	2	2	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	0	0	2	2	2	2	2	2	2	-1	-1	-1	-1	-1	-1	-1	0	0	0	0	0	0	0	0
χ₁₈	2	-1	2	2	2	2	2	2	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	0	0	2	2	2	-2	-2	-2	-2	-1	-1	-1	1	1	1	1	0	0	0	0	0	0	0	0
χ₁₉	2	-1	2	2	2	2	2	2	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	0	0	2	-2	-2	$2 i$	$2 i$	$- 2 i$	$- 2 i$	-1	1	1	$- i$	$- i$	$i$	$i$	0	0	0	0	0	0	0	0
χ₂₀	2	-1	2	2	2	2	2	2	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	0	0	2	-2	-2	$- 2 i$	$- 2 i$	$2 i$	$2 i$	-1	1	1	$i$	$i$	$- i$	$- i$	0	0	0	0	0	0	0	0
χ₂₁	2	-1	2	2	2	2	2	2	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	0	0	-2	$2 i$	$- 2 i$	2ζ⁷+2ζ²³	−2ζ⁷−2ζ²³	−2ζ⁵−2ζ¹³	2ζ⁵+2ζ¹³	1	$- i$	$i$	−ζ⁷−ζ²³	ζ⁷+ζ²³	ζ⁵+ζ¹³	−ζ⁵−ζ¹³	0	0	0	0	0	0	0	0
χ₂₂	2	-1	2	2	2	2	2	2	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	0	0	-2	$2 i$	$- 2 i$	−2ζ⁷−2ζ²³	2ζ⁷+2ζ²³	2ζ⁵+2ζ¹³	−2ζ⁵−2ζ¹³	1	$- i$	$i$	ζ⁷+ζ²³	−ζ⁷−ζ²³	−ζ⁵−ζ¹³	ζ⁵+ζ¹³	0	0	0	0	0	0	0	0
χ₂₃	2	-1	2	2	2	2	2	2	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	0	0	-2	$- 2 i$	$2 i$	−2ζ⁵−2ζ¹³	2ζ⁵+2ζ¹³	2ζ⁷+2ζ²³	−2ζ⁷−2ζ²³	1	$i$	$- i$	ζ⁵+ζ¹³	−ζ⁵−ζ¹³	−ζ⁷−ζ²³	ζ⁷+ζ²³	0	0	0	0	0	0	0	0
χ₂₄	2	-1	2	2	2	2	2	2	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	0	0	-2	$- 2 i$	$2 i$	2ζ⁵+2ζ¹³	−2ζ⁵−2ζ¹³	−2ζ⁷−2ζ²³	2ζ⁷+2ζ²³	1	$i$	$- i$	−ζ⁵−ζ¹³	ζ⁵+ζ¹³	ζ⁷+ζ²³	−ζ⁷−ζ²³	0	0	0	0	0	0	0	0
χ₂₅	8	8	8	-1	-1	-1	-1	-1	8	-1	-1	-1	-1	-1	-1	-1	-1	-1	0	8	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	-1	0	0	0	0	0	0
χ₂₆	8	8	8	-1	-1	-1	-1	-1	8	-1	-1	-1	-1	-1	-1	-1	-1	-1	0	-8	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0
χ₂₇	8	8	-1	8	-1	-1	-1	-1	-1	8	-1	-1	-1	-1	-1	-1	-1	-1	8	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	-1	0	0	0	0	0	0	0
χ₂₈	8	8	-1	8	-1	-1	-1	-1	-1	8	-1	-1	-1	-1	-1	-1	-1	-1	-8	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
χ₂₉	16	16	-2	-2	7	-2	-2	-2	-2	-2	7	7	-2	-2	-2	-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
χ₃₀	16	16	-2	-2	-2	7	-2	-2	-2	-2	-2	-2	7	7	-2	-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
χ₃₁	16	16	-2	-2	-2	-2	7	-2	-2	-2	-2	-2	-2	-2	7	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
χ₃₂	16	16	-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	0	0	0	0	0	0	0
χ₃₃	16	-8	16	-2	-2	-2	-2	-2	-8	1	1	1	1	1	1	1	1	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
χ₃₄	16	-8	-2	16	-2	-2	-2	-2	1	-8	1	1	1	1	1	1	1	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
χ₃₅	16	-8	-2	-2	7	-2	-2	-2	1	1	$\frac{- 7 + 3 i \sqrt{3}}{2}$	$\frac{- 7 - 3 i \sqrt{3}}{2}$	1	1	$1 - 3 i \sqrt{3}$	$1 + 3 i \sqrt{3}$	$1 - 3 i \sqrt{3}$	$1 + 3 i \sqrt{3}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₆	16	-8	-2	-2	7	-2	-2	-2	1	1	$\frac{- 7 - 3 i \sqrt{3}}{2}$	$\frac{- 7 + 3 i \sqrt{3}}{2}$	1	1	$1 + 3 i \sqrt{3}$	$1 - 3 i \sqrt{3}$	$1 + 3 i \sqrt{3}$	$1 - 3 i \sqrt{3}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₇	16	-8	-2	-2	-2	7	-2	-2	1	1	1	1	$\frac{- 7 + 3 i \sqrt{3}}{2}$	$\frac{- 7 - 3 i \sqrt{3}}{2}$	$1 - 3 i \sqrt{3}$	$1 + 3 i \sqrt{3}$	$1 + 3 i \sqrt{3}$	$1 - 3 i \sqrt{3}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₈	16	-8	-2	-2	-2	7	-2	-2	1	1	1	1	$\frac{- 7 - 3 i \sqrt{3}}{2}$	$\frac{- 7 + 3 i \sqrt{3}}{2}$	$1 + 3 i \sqrt{3}$	$1 - 3 i \sqrt{3}$	$1 - 3 i \sqrt{3}$	$1 + 3 i \sqrt{3}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₉	16	-8	-2	-2	-2	-2	7	-2	1	1	$1 - 3 i \sqrt{3}$	$1 + 3 i \sqrt{3}$	$1 - 3 i \sqrt{3}$	$1 + 3 i \sqrt{3}$	$\frac{- 7 - 3 i \sqrt{3}}{2}$	$\frac{- 7 + 3 i \sqrt{3}}{2}$	1	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
χ₄₀	16	-8	-2	-2	-2	-2	7	-2	1	1	$1 + 3 i \sqrt{3}$	$1 - 3 i \sqrt{3}$	$1 + 3 i \sqrt{3}$	$1 - 3 i \sqrt{3}$	$\frac{- 7 + 3 i \sqrt{3}}{2}$	$\frac{- 7 - 3 i \sqrt{3}}{2}$	1	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
χ₄₁	16	-8	-2	-2	-2	-2	-2	7	1	1	$1 - 3 i \sqrt{3}$	$1 + 3 i \sqrt{3}$	$1 + 3 i \sqrt{3}$	$1 - 3 i \sqrt{3}$	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	0	0	0	0	0	0	0
χ₄₂	16	-8	-2	-2	-2	-2	-2	7	1	1	$1 + 3 i \sqrt{3}$	$1 - 3 i \sqrt{3}$	$1 - 3 i \sqrt{3}$	$1 + 3 i \sqrt{3}$	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	0	0	0	0	0	0	0

Character table — Group #72224532