Group #92213 — 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
size	1	2	2	2	2	3	3	6	6	6	6	6	6	6	6	6	6	6	18	18	18	18	18	18	18	18	18	81	81	81
order	1	3	9	9	9	3	3	9	9	27	27	27	27	27	27	27	27	27	3	9	9	27	27	27	27	27	27	2	6	6
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
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
χ₃	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	-1	-1	-1	-1	-1	-1	-1	-1	-1	0	0	0
χ₄	2	2	2	2	2	2	2	2	2	-1	-1	-1	-1	-1	-1	-1	-1	-1	2	2	2	-1	-1	-1	-1	-1	-1	0	0	0
χ₅	2	2	2	2	2	2	2	2	2	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	2	2	2	-1	-1	-1	0	0	0
χ₆	2	2	2	2	2	2	2	2	2	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	2	2	2	0	0	0
χ₇	2	2	-1	-1	-1	2	2	-1	-1	ζ³+ζ²⁴	ζ³+ζ²⁴	ζ³+ζ²⁴	ζ⁶+ζ²¹	ζ⁶+ζ²¹	ζ⁶+ζ²¹	ζ¹²+ζ¹⁵	ζ¹²+ζ¹⁵	ζ¹²+ζ¹⁵	2	-1	-1	ζ³+ζ²⁴	ζ⁶+ζ²¹	ζ¹²+ζ¹⁵	ζ³+ζ²⁴	ζ⁶+ζ²¹	ζ¹²+ζ¹⁵	0	0	0
χ₈	2	2	-1	-1	-1	2	2	-1	-1	ζ³+ζ²⁴	ζ³+ζ²⁴	ζ³+ζ²⁴	ζ⁶+ζ²¹	ζ⁶+ζ²¹	ζ⁶+ζ²¹	ζ¹²+ζ¹⁵	ζ¹²+ζ¹⁵	ζ¹²+ζ¹⁵	-1	2	-1	ζ⁶+ζ²¹	ζ¹²+ζ¹⁵	ζ³+ζ²⁴	ζ¹²+ζ¹⁵	ζ³+ζ²⁴	ζ⁶+ζ²¹	0	0	0
χ₉	2	2	-1	-1	-1	2	2	-1	-1	ζ³+ζ²⁴	ζ³+ζ²⁴	ζ³+ζ²⁴	ζ⁶+ζ²¹	ζ⁶+ζ²¹	ζ⁶+ζ²¹	ζ¹²+ζ¹⁵	ζ¹²+ζ¹⁵	ζ¹²+ζ¹⁵	-1	-1	2	ζ¹²+ζ¹⁵	ζ³+ζ²⁴	ζ⁶+ζ²¹	ζ⁶+ζ²¹	ζ¹²+ζ¹⁵	ζ³+ζ²⁴	0	0	0
χ₁₀	2	2	-1	-1	-1	2	2	-1	-1	ζ⁶+ζ²¹	ζ⁶+ζ²¹	ζ⁶+ζ²¹	ζ¹²+ζ¹⁵	ζ¹²+ζ¹⁵	ζ¹²+ζ¹⁵	ζ³+ζ²⁴	ζ³+ζ²⁴	ζ³+ζ²⁴	2	-1	-1	ζ⁶+ζ²¹	ζ¹²+ζ¹⁵	ζ³+ζ²⁴	ζ⁶+ζ²¹	ζ¹²+ζ¹⁵	ζ³+ζ²⁴	0	0	0
χ₁₁	2	2	-1	-1	-1	2	2	-1	-1	ζ⁶+ζ²¹	ζ⁶+ζ²¹	ζ⁶+ζ²¹	ζ¹²+ζ¹⁵	ζ¹²+ζ¹⁵	ζ¹²+ζ¹⁵	ζ³+ζ²⁴	ζ³+ζ²⁴	ζ³+ζ²⁴	-1	2	-1	ζ¹²+ζ¹⁵	ζ³+ζ²⁴	ζ⁶+ζ²¹	ζ³+ζ²⁴	ζ⁶+ζ²¹	ζ¹²+ζ¹⁵	0	0	0
χ₁₂	2	2	-1	-1	-1	2	2	-1	-1	ζ⁶+ζ²¹	ζ⁶+ζ²¹	ζ⁶+ζ²¹	ζ¹²+ζ¹⁵	ζ¹²+ζ¹⁵	ζ¹²+ζ¹⁵	ζ³+ζ²⁴	ζ³+ζ²⁴	ζ³+ζ²⁴	-1	-1	2	ζ³+ζ²⁴	ζ⁶+ζ²¹	ζ¹²+ζ¹⁵	ζ¹²+ζ¹⁵	ζ³+ζ²⁴	ζ⁶+ζ²¹	0	0	0
χ₁₃	2	2	-1	-1	-1	2	2	-1	-1	ζ¹²+ζ¹⁵	ζ¹²+ζ¹⁵	ζ¹²+ζ¹⁵	ζ³+ζ²⁴	ζ³+ζ²⁴	ζ³+ζ²⁴	ζ⁶+ζ²¹	ζ⁶+ζ²¹	ζ⁶+ζ²¹	2	-1	-1	ζ¹²+ζ¹⁵	ζ³+ζ²⁴	ζ⁶+ζ²¹	ζ¹²+ζ¹⁵	ζ³+ζ²⁴	ζ⁶+ζ²¹	0	0	0
χ₁₄	2	2	-1	-1	-1	2	2	-1	-1	ζ¹²+ζ¹⁵	ζ¹²+ζ¹⁵	ζ¹²+ζ¹⁵	ζ³+ζ²⁴	ζ³+ζ²⁴	ζ³+ζ²⁴	ζ⁶+ζ²¹	ζ⁶+ζ²¹	ζ⁶+ζ²¹	-1	2	-1	ζ³+ζ²⁴	ζ⁶+ζ²¹	ζ¹²+ζ¹⁵	ζ⁶+ζ²¹	ζ¹²+ζ¹⁵	ζ³+ζ²⁴	0	0	0
χ₁₅	2	2	-1	-1	-1	2	2	-1	-1	ζ¹²+ζ¹⁵	ζ¹²+ζ¹⁵	ζ¹²+ζ¹⁵	ζ³+ζ²⁴	ζ³+ζ²⁴	ζ³+ζ²⁴	ζ⁶+ζ²¹	ζ⁶+ζ²¹	ζ⁶+ζ²¹	-1	-1	2	ζ⁶+ζ²¹	ζ¹²+ζ¹⁵	ζ³+ζ²⁴	ζ³+ζ²⁴	ζ⁶+ζ²¹	ζ¹²+ζ¹⁵	0	0	0
χ₁₆	3	3	3	3	3	$\frac{- 3 + 3 i \sqrt{3}}{2}$	$\frac{- 3 - 3 i \sqrt{3}}{2}$	$\frac{- 3 + 3 i \sqrt{3}}{2}$	$\frac{- 3 - 3 i \sqrt{3}}{2}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	$\frac{- 1 + i \sqrt{3}}{2}$	$\frac{- 1 - i \sqrt{3}}{2}$
χ₁₇	3	3	3	3	3	$\frac{- 3 + 3 i \sqrt{3}}{2}$	$\frac{- 3 - 3 i \sqrt{3}}{2}$	$\frac{- 3 + 3 i \sqrt{3}}{2}$	$\frac{- 3 - 3 i \sqrt{3}}{2}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	-1	$\frac{1 - i \sqrt{3}}{2}$	$\frac{1 + i \sqrt{3}}{2}$
χ₁₈	3	3	3	3	3	$\frac{- 3 - 3 i \sqrt{3}}{2}$	$\frac{- 3 + 3 i \sqrt{3}}{2}$	$\frac{- 3 - 3 i \sqrt{3}}{2}$	$\frac{- 3 + 3 i \sqrt{3}}{2}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	$\frac{- 1 - i \sqrt{3}}{2}$	$\frac{- 1 + i \sqrt{3}}{2}$
χ₁₉	3	3	3	3	3	$\frac{- 3 - 3 i \sqrt{3}}{2}$	$\frac{- 3 + 3 i \sqrt{3}}{2}$	$\frac{- 3 - 3 i \sqrt{3}}{2}$	$\frac{- 3 + 3 i \sqrt{3}}{2}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	-1	$\frac{1 + i \sqrt{3}}{2}$	$\frac{1 - i \sqrt{3}}{2}$
χ₂₀	6	6	-3	-3	-3	$- 3 + 3 i \sqrt{3}$	$- 3 - 3 i \sqrt{3}$	$\frac{3 - 3 i \sqrt{3}}{2}$	$\frac{3 + 3 i \sqrt{3}}{2}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₁	6	6	-3	-3	-3	$- 3 - 3 i \sqrt{3}$	$- 3 + 3 i \sqrt{3}$	$\frac{3 + 3 i \sqrt{3}}{2}$	$\frac{3 - 3 i \sqrt{3}}{2}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₂	6	-3	3ζ³+3ζ²⁴	3ζ⁶+3ζ²¹	3ζ¹²+3ζ¹⁵	0	0	0	0	ζ−ζ⁸+2ζ¹⁰+ζ¹⁷	ζ−ζ⁸−ζ¹⁰−2ζ¹⁷	−2ζ+2ζ⁸−ζ¹⁰+ζ¹⁷	2ζ²−2ζ⁷+ζ¹¹−ζ¹⁶	−ζ²+ζ⁷+ζ¹¹+2ζ¹⁶	−ζ²+ζ⁷−2ζ¹¹−ζ¹⁶	ζ⁴−ζ⁵+2ζ¹³+ζ¹⁴	ζ⁴−ζ⁵−ζ¹³−2ζ¹⁴	−2ζ⁴+2ζ⁵−ζ¹³+ζ¹⁴	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₃	6	-3	3ζ³+3ζ²⁴	3ζ⁶+3ζ²¹	3ζ¹²+3ζ¹⁵	0	0	0	0	ζ−ζ⁸−ζ¹⁰−2ζ¹⁷	−2ζ+2ζ⁸−ζ¹⁰+ζ¹⁷	ζ−ζ⁸+2ζ¹⁰+ζ¹⁷	−ζ²+ζ⁷+ζ¹¹+2ζ¹⁶	−ζ²+ζ⁷−2ζ¹¹−ζ¹⁶	2ζ²−2ζ⁷+ζ¹¹−ζ¹⁶	ζ⁴−ζ⁵−ζ¹³−2ζ¹⁴	−2ζ⁴+2ζ⁵−ζ¹³+ζ¹⁴	ζ⁴−ζ⁵+2ζ¹³+ζ¹⁴	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₄	6	-3	3ζ³+3ζ²⁴	3ζ⁶+3ζ²¹	3ζ¹²+3ζ¹⁵	0	0	0	0	−2ζ+2ζ⁸−ζ¹⁰+ζ¹⁷	ζ−ζ⁸+2ζ¹⁰+ζ¹⁷	ζ−ζ⁸−ζ¹⁰−2ζ¹⁷	−ζ²+ζ⁷−2ζ¹¹−ζ¹⁶	2ζ²−2ζ⁷+ζ¹¹−ζ¹⁶	−ζ²+ζ⁷+ζ¹¹+2ζ¹⁶	−2ζ⁴+2ζ⁵−ζ¹³+ζ¹⁴	ζ⁴−ζ⁵+2ζ¹³+ζ¹⁴	ζ⁴−ζ⁵−ζ¹³−2ζ¹⁴	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₅	6	-3	3ζ⁶+3ζ²¹	3ζ¹²+3ζ¹⁵	3ζ³+3ζ²⁴	0	0	0	0	2ζ²−2ζ⁷+ζ¹¹−ζ¹⁶	−ζ²+ζ⁷+ζ¹¹+2ζ¹⁶	−ζ²+ζ⁷−2ζ¹¹−ζ¹⁶	−2ζ⁴+2ζ⁵−ζ¹³+ζ¹⁴	ζ⁴−ζ⁵+2ζ¹³+ζ¹⁴	ζ⁴−ζ⁵−ζ¹³−2ζ¹⁴	−2ζ+2ζ⁸−ζ¹⁰+ζ¹⁷	ζ−ζ⁸+2ζ¹⁰+ζ¹⁷	ζ−ζ⁸−ζ¹⁰−2ζ¹⁷	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₆	6	-3	3ζ⁶+3ζ²¹	3ζ¹²+3ζ¹⁵	3ζ³+3ζ²⁴	0	0	0	0	−ζ²+ζ⁷+ζ¹¹+2ζ¹⁶	−ζ²+ζ⁷−2ζ¹¹−ζ¹⁶	2ζ²−2ζ⁷+ζ¹¹−ζ¹⁶	ζ⁴−ζ⁵+2ζ¹³+ζ¹⁴	ζ⁴−ζ⁵−ζ¹³−2ζ¹⁴	−2ζ⁴+2ζ⁵−ζ¹³+ζ¹⁴	ζ−ζ⁸+2ζ¹⁰+ζ¹⁷	ζ−ζ⁸−ζ¹⁰−2ζ¹⁷	−2ζ+2ζ⁸−ζ¹⁰+ζ¹⁷	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₇	6	-3	3ζ⁶+3ζ²¹	3ζ¹²+3ζ¹⁵	3ζ³+3ζ²⁴	0	0	0	0	−ζ²+ζ⁷−2ζ¹¹−ζ¹⁶	2ζ²−2ζ⁷+ζ¹¹−ζ¹⁶	−ζ²+ζ⁷+ζ¹¹+2ζ¹⁶	ζ⁴−ζ⁵−ζ¹³−2ζ¹⁴	−2ζ⁴+2ζ⁵−ζ¹³+ζ¹⁴	ζ⁴−ζ⁵+2ζ¹³+ζ¹⁴	ζ−ζ⁸−ζ¹⁰−2ζ¹⁷	−2ζ+2ζ⁸−ζ¹⁰+ζ¹⁷	ζ−ζ⁸+2ζ¹⁰+ζ¹⁷	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₈	6	-3	3ζ¹²+3ζ¹⁵	3ζ³+3ζ²⁴	3ζ⁶+3ζ²¹	0	0	0	0	ζ⁴−ζ⁵+2ζ¹³+ζ¹⁴	ζ⁴−ζ⁵−ζ¹³−2ζ¹⁴	−2ζ⁴+2ζ⁵−ζ¹³+ζ¹⁴	−2ζ+2ζ⁸−ζ¹⁰+ζ¹⁷	ζ−ζ⁸+2ζ¹⁰+ζ¹⁷	ζ−ζ⁸−ζ¹⁰−2ζ¹⁷	2ζ²−2ζ⁷+ζ¹¹−ζ¹⁶	−ζ²+ζ⁷+ζ¹¹+2ζ¹⁶	−ζ²+ζ⁷−2ζ¹¹−ζ¹⁶	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₉	6	-3	3ζ¹²+3ζ¹⁵	3ζ³+3ζ²⁴	3ζ⁶+3ζ²¹	0	0	0	0	ζ⁴−ζ⁵−ζ¹³−2ζ¹⁴	−2ζ⁴+2ζ⁵−ζ¹³+ζ¹⁴	ζ⁴−ζ⁵+2ζ¹³+ζ¹⁴	ζ−ζ⁸+2ζ¹⁰+ζ¹⁷	ζ−ζ⁸−ζ¹⁰−2ζ¹⁷	−2ζ+2ζ⁸−ζ¹⁰+ζ¹⁷	−ζ²+ζ⁷+ζ¹¹+2ζ¹⁶	−ζ²+ζ⁷−2ζ¹¹−ζ¹⁶	2ζ²−2ζ⁷+ζ¹¹−ζ¹⁶	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₀	6	-3	3ζ¹²+3ζ¹⁵	3ζ³+3ζ²⁴	3ζ⁶+3ζ²¹	0	0	0	0	−2ζ⁴+2ζ⁵−ζ¹³+ζ¹⁴	ζ⁴−ζ⁵+2ζ¹³+ζ¹⁴	ζ⁴−ζ⁵−ζ¹³−2ζ¹⁴	ζ−ζ⁸−ζ¹⁰−2ζ¹⁷	−2ζ+2ζ⁸−ζ¹⁰+ζ¹⁷	ζ−ζ⁸+2ζ¹⁰+ζ¹⁷	−ζ²+ζ⁷−2ζ¹¹−ζ¹⁶	2ζ²−2ζ⁷+ζ¹¹−ζ¹⁶	−ζ²+ζ⁷+ζ¹¹+2ζ¹⁶	0	0	0	0	0	0	0	0	0	0	0	0

Character table — Group #92213