Group #90656 — 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
size	1	2	3	3	3	3	6	6	6	6	6	6	6	6	6	6	45	45	45	45	45	50	50	50
order	1	3	5	5	5	5	5	5	15	15	15	15	15	15	15	15	2	10	10	10	10	3	3	3
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
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
χ₃	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	0	0	0	0	0	-1	-1	-1
χ₄	2	-1	2	2	2	2	2	2	-1	-1	-1	-1	-1	-1	-1	-1	0	0	0	0	0	2	-1	-1
χ₅	2	-1	2	2	2	2	2	2	-1	-1	-1	-1	-1	-1	-1	-1	0	0	0	0	0	-1	2	-1
χ₆	2	-1	2	2	2	2	2	2	-1	-1	-1	-1	-1	-1	-1	-1	0	0	0	0	0	-1	-1	2
χ₇	3	3	−2ζ−ζ⁸−2ζ¹¹−ζ¹³	−ζ−2ζ²−2ζ⁷−ζ¹¹	−ζ²−2ζ⁴−ζ⁷−2ζ¹⁴	−ζ⁴−2ζ⁸−2ζ¹³−ζ¹⁴	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	−2ζ−ζ⁸−2ζ¹¹−ζ¹³	−ζ−2ζ²−2ζ⁷−ζ¹¹	−ζ²−2ζ⁴−ζ⁷−2ζ¹⁴	−ζ⁴−2ζ⁸−2ζ¹³−ζ¹⁴	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	1	−ζ⁸−ζ¹³	−ζ−ζ¹¹	−ζ²−ζ⁷	−ζ⁴−ζ¹⁴	0	0	0
χ₈	3	3	−2ζ−ζ⁸−2ζ¹¹−ζ¹³	−ζ−2ζ²−2ζ⁷−ζ¹¹	−ζ²−2ζ⁴−ζ⁷−2ζ¹⁴	−ζ⁴−2ζ⁸−2ζ¹³−ζ¹⁴	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	−2ζ−ζ⁸−2ζ¹¹−ζ¹³	−ζ−2ζ²−2ζ⁷−ζ¹¹	−ζ²−2ζ⁴−ζ⁷−2ζ¹⁴	−ζ⁴−2ζ⁸−2ζ¹³−ζ¹⁴	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	-1	ζ⁸+ζ¹³	ζ+ζ¹¹	ζ²+ζ⁷	ζ⁴+ζ¹⁴	0	0	0
χ₉	3	3	−ζ−2ζ²−2ζ⁷−ζ¹¹	−ζ²−2ζ⁴−ζ⁷−2ζ¹⁴	−ζ⁴−2ζ⁸−2ζ¹³−ζ¹⁴	−2ζ−ζ⁸−2ζ¹¹−ζ¹³	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	−ζ−2ζ²−2ζ⁷−ζ¹¹	−ζ²−2ζ⁴−ζ⁷−2ζ¹⁴	−ζ⁴−2ζ⁸−2ζ¹³−ζ¹⁴	−2ζ−ζ⁸−2ζ¹¹−ζ¹³	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	1	−ζ−ζ¹¹	−ζ²−ζ⁷	−ζ⁴−ζ¹⁴	−ζ⁸−ζ¹³	0	0	0
χ₁₀	3	3	−ζ−2ζ²−2ζ⁷−ζ¹¹	−ζ²−2ζ⁴−ζ⁷−2ζ¹⁴	−ζ⁴−2ζ⁸−2ζ¹³−ζ¹⁴	−2ζ−ζ⁸−2ζ¹¹−ζ¹³	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	−ζ−2ζ²−2ζ⁷−ζ¹¹	−ζ²−2ζ⁴−ζ⁷−2ζ¹⁴	−ζ⁴−2ζ⁸−2ζ¹³−ζ¹⁴	−2ζ−ζ⁸−2ζ¹¹−ζ¹³	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	-1	ζ+ζ¹¹	ζ²+ζ⁷	ζ⁴+ζ¹⁴	ζ⁸+ζ¹³	0	0	0
χ₁₁	3	3	−ζ²−2ζ⁴−ζ⁷−2ζ¹⁴	−ζ⁴−2ζ⁸−2ζ¹³−ζ¹⁴	−2ζ−ζ⁸−2ζ¹¹−ζ¹³	−ζ−2ζ²−2ζ⁷−ζ¹¹	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	−ζ²−2ζ⁴−ζ⁷−2ζ¹⁴	−ζ⁴−2ζ⁸−2ζ¹³−ζ¹⁴	−2ζ−ζ⁸−2ζ¹¹−ζ¹³	−ζ−2ζ²−2ζ⁷−ζ¹¹	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	1	−ζ²−ζ⁷	−ζ⁴−ζ¹⁴	−ζ⁸−ζ¹³	−ζ−ζ¹¹	0	0	0
χ₁₂	3	3	−ζ²−2ζ⁴−ζ⁷−2ζ¹⁴	−ζ⁴−2ζ⁸−2ζ¹³−ζ¹⁴	−2ζ−ζ⁸−2ζ¹¹−ζ¹³	−ζ−2ζ²−2ζ⁷−ζ¹¹	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	−ζ²−2ζ⁴−ζ⁷−2ζ¹⁴	−ζ⁴−2ζ⁸−2ζ¹³−ζ¹⁴	−2ζ−ζ⁸−2ζ¹¹−ζ¹³	−ζ−2ζ²−2ζ⁷−ζ¹¹	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	-1	ζ²+ζ⁷	ζ⁴+ζ¹⁴	ζ⁸+ζ¹³	ζ+ζ¹¹	0	0	0
χ₁₃	3	3	−ζ⁴−2ζ⁸−2ζ¹³−ζ¹⁴	−2ζ−ζ⁸−2ζ¹¹−ζ¹³	−ζ−2ζ²−2ζ⁷−ζ¹¹	−ζ²−2ζ⁴−ζ⁷−2ζ¹⁴	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	−ζ⁴−2ζ⁸−2ζ¹³−ζ¹⁴	−2ζ−ζ⁸−2ζ¹¹−ζ¹³	−ζ−2ζ²−2ζ⁷−ζ¹¹	−ζ²−2ζ⁴−ζ⁷−2ζ¹⁴	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	1	−ζ⁴−ζ¹⁴	−ζ⁸−ζ¹³	−ζ−ζ¹¹	−ζ²−ζ⁷	0	0	0
χ₁₄	3	3	−ζ⁴−2ζ⁸−2ζ¹³−ζ¹⁴	−2ζ−ζ⁸−2ζ¹¹−ζ¹³	−ζ−2ζ²−2ζ⁷−ζ¹¹	−ζ²−2ζ⁴−ζ⁷−2ζ¹⁴	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	−ζ⁴−2ζ⁸−2ζ¹³−ζ¹⁴	−2ζ−ζ⁸−2ζ¹¹−ζ¹³	−ζ−2ζ²−2ζ⁷−ζ¹¹	−ζ²−2ζ⁴−ζ⁷−2ζ¹⁴	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	-1	ζ⁴+ζ¹⁴	ζ⁸+ζ¹³	ζ+ζ¹¹	ζ²+ζ⁷	0	0	0
χ₁₅	6	6	$1 - \sqrt{5}$	$1 + \sqrt{5}$	$1 - \sqrt{5}$	$1 + \sqrt{5}$	$\frac{- 3 + \sqrt{5}}{2}$	$\frac{- 3 - \sqrt{5}}{2}$	$1 - \sqrt{5}$	$1 + \sqrt{5}$	$1 - \sqrt{5}$	$1 + \sqrt{5}$	$\frac{- 3 + \sqrt{5}}{2}$	$\frac{- 3 + \sqrt{5}}{2}$	$\frac{- 3 - \sqrt{5}}{2}$	$\frac{- 3 - \sqrt{5}}{2}$	0	0	0	0	0	0	0	0
χ₁₆	6	6	$1 + \sqrt{5}$	$1 - \sqrt{5}$	$1 + \sqrt{5}$	$1 - \sqrt{5}$	$\frac{- 3 - \sqrt{5}}{2}$	$\frac{- 3 + \sqrt{5}}{2}$	$1 + \sqrt{5}$	$1 - \sqrt{5}$	$1 + \sqrt{5}$	$1 - \sqrt{5}$	$\frac{- 3 - \sqrt{5}}{2}$	$\frac{- 3 - \sqrt{5}}{2}$	$\frac{- 3 + \sqrt{5}}{2}$	$\frac{- 3 + \sqrt{5}}{2}$	0	0	0	0	0	0	0	0
χ₁₇	6	-3	−4ζ−2ζ⁸−4ζ¹¹−2ζ¹³	−2ζ−4ζ²−4ζ⁷−2ζ¹¹	−2ζ²−4ζ⁴−2ζ⁷−4ζ¹⁴	−2ζ⁴−4ζ⁸−4ζ¹³−2ζ¹⁴	$1 - \sqrt{5}$	$1 + \sqrt{5}$	2ζ+ζ⁸+2ζ¹¹+ζ¹³	ζ+2ζ²+2ζ⁷+ζ¹¹	ζ²+2ζ⁴+ζ⁷+2ζ¹⁴	ζ⁴+2ζ⁸+2ζ¹³+ζ¹⁴	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	0	0	0	0	0	0	0	0
χ₁₈	6	-3	$1 - \sqrt{5}$	$1 + \sqrt{5}$	$1 - \sqrt{5}$	$1 + \sqrt{5}$	$\frac{- 3 + \sqrt{5}}{2}$	$\frac{- 3 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	2ζ²+ζ⁴+ζ¹¹+2ζ¹³	ζ+2ζ⁷+2ζ⁸+ζ¹⁴	2ζ⁴+ζ⁷+ζ⁸+2ζ¹¹	2ζ+ζ²+ζ¹³+2ζ¹⁴	0	0	0	0	0	0	0	0
χ₁₉	6	-3	$1 - \sqrt{5}$	$1 + \sqrt{5}$	$1 - \sqrt{5}$	$1 + \sqrt{5}$	$\frac{- 3 + \sqrt{5}}{2}$	$\frac{- 3 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	ζ+2ζ⁷+2ζ⁸+ζ¹⁴	2ζ²+ζ⁴+ζ¹¹+2ζ¹³	2ζ+ζ²+ζ¹³+2ζ¹⁴	2ζ⁴+ζ⁷+ζ⁸+2ζ¹¹	0	0	0	0	0	0	0	0
χ₂₀	6	-3	−2ζ−4ζ²−4ζ⁷−2ζ¹¹	−2ζ²−4ζ⁴−2ζ⁷−4ζ¹⁴	−2ζ⁴−4ζ⁸−4ζ¹³−2ζ¹⁴	−4ζ−2ζ⁸−4ζ¹¹−2ζ¹³	$1 + \sqrt{5}$	$1 - \sqrt{5}$	ζ+2ζ²+2ζ⁷+ζ¹¹	ζ²+2ζ⁴+ζ⁷+2ζ¹⁴	ζ⁴+2ζ⁸+2ζ¹³+ζ¹⁴	2ζ+ζ⁸+2ζ¹¹+ζ¹³	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	0	0	0	0	0	0	0	0
χ₂₁	6	-3	$1 + \sqrt{5}$	$1 - \sqrt{5}$	$1 + \sqrt{5}$	$1 - \sqrt{5}$	$\frac{- 3 - \sqrt{5}}{2}$	$\frac{- 3 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	2ζ⁴+ζ⁷+ζ⁸+2ζ¹¹	2ζ+ζ²+ζ¹³+2ζ¹⁴	ζ+2ζ⁷+2ζ⁸+ζ¹⁴	2ζ²+ζ⁴+ζ¹¹+2ζ¹³	0	0	0	0	0	0	0	0
χ₂₂	6	-3	$1 + \sqrt{5}$	$1 - \sqrt{5}$	$1 + \sqrt{5}$	$1 - \sqrt{5}$	$\frac{- 3 - \sqrt{5}}{2}$	$\frac{- 3 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	2ζ+ζ²+ζ¹³+2ζ¹⁴	2ζ⁴+ζ⁷+ζ⁸+2ζ¹¹	2ζ²+ζ⁴+ζ¹¹+2ζ¹³	ζ+2ζ⁷+2ζ⁸+ζ¹⁴	0	0	0	0	0	0	0	0
χ₂₃	6	-3	−2ζ²−4ζ⁴−2ζ⁷−4ζ¹⁴	−2ζ⁴−4ζ⁸−4ζ¹³−2ζ¹⁴	−4ζ−2ζ⁸−4ζ¹¹−2ζ¹³	−2ζ−4ζ²−4ζ⁷−2ζ¹¹	$1 - \sqrt{5}$	$1 + \sqrt{5}$	ζ²+2ζ⁴+ζ⁷+2ζ¹⁴	ζ⁴+2ζ⁸+2ζ¹³+ζ¹⁴	2ζ+ζ⁸+2ζ¹¹+ζ¹³	ζ+2ζ²+2ζ⁷+ζ¹¹	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	0	0	0	0	0	0	0	0
χ₂₄	6	-3	−2ζ⁴−4ζ⁸−4ζ¹³−2ζ¹⁴	−4ζ−2ζ⁸−4ζ¹¹−2ζ¹³	−2ζ−4ζ²−4ζ⁷−2ζ¹¹	−2ζ²−4ζ⁴−2ζ⁷−4ζ¹⁴	$1 + \sqrt{5}$	$1 - \sqrt{5}$	ζ⁴+2ζ⁸+2ζ¹³+ζ¹⁴	2ζ+ζ⁸+2ζ¹¹+ζ¹³	ζ+2ζ²+2ζ⁷+ζ¹¹	ζ²+2ζ⁴+ζ⁷+2ζ¹⁴	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	0	0	0	0	0	0	0	0

Character table — Group #90656