Group #67111 — 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
size	1	2	2	2	2	2	2	2	3	6	6	6	6	6	6	6	8	8	8	8	8	8	8	8	8	8	8	8	8	8	8	90	90
order	1	3	5	5	15	15	15	15	2	6	10	10	30	30	30	30	9	9	9	45	45	45	45	45	45	45	45	45	45	45	45	2	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
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
χ₃	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	-1	-1	-1	-1	-1	-1	0	0
χ₄	2	2	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	2	2	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	2	2	2	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	0	0
χ₅	2	2	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	2	2	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	-1	-1	-1	ζ⁶+ζ³⁹	ζ⁶+ζ³⁹	ζ⁶+ζ³⁹	ζ²¹+ζ²⁴	ζ²¹+ζ²⁴	ζ²¹+ζ²⁴	ζ¹²+ζ³³	ζ¹²+ζ³³	ζ¹²+ζ³³	ζ³+ζ⁴²	ζ³+ζ⁴²	ζ³+ζ⁴²	0	0
χ₆	2	2	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	2	2	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	-1	-1	-1	ζ²¹+ζ²⁴	ζ²¹+ζ²⁴	ζ²¹+ζ²⁴	ζ⁶+ζ³⁹	ζ⁶+ζ³⁹	ζ⁶+ζ³⁹	ζ³+ζ⁴²	ζ³+ζ⁴²	ζ³+ζ⁴²	ζ¹²+ζ³³	ζ¹²+ζ³³	ζ¹²+ζ³³	0	0
χ₇	2	2	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	2	2	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	2	2	2	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	0	0
χ₈	2	2	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	2	2	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	-1	-1	-1	ζ¹²+ζ³³	ζ¹²+ζ³³	ζ¹²+ζ³³	ζ³+ζ⁴²	ζ³+ζ⁴²	ζ³+ζ⁴²	ζ²¹+ζ²⁴	ζ²¹+ζ²⁴	ζ²¹+ζ²⁴	ζ⁶+ζ³⁹	ζ⁶+ζ³⁹	ζ⁶+ζ³⁹	0	0
χ₉	2	2	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	2	2	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	-1	-1	-1	ζ³+ζ⁴²	ζ³+ζ⁴²	ζ³+ζ⁴²	ζ¹²+ζ³³	ζ¹²+ζ³³	ζ¹²+ζ³³	ζ⁶+ζ³⁹	ζ⁶+ζ³⁹	ζ⁶+ζ³⁹	ζ²¹+ζ²⁴	ζ²¹+ζ²⁴	ζ²¹+ζ²⁴	0	0
χ₁₀	2	-1	2	2	-1	-1	-1	-1	2	-1	2	2	-1	-1	-1	-1	ζ⁴+ζ⁷−ζ⁸+ζ¹³+ζ¹⁶−ζ¹⁷+ζ²²−ζ²⁶+ζ³¹+ζ³⁴+ζ⁴³−ζ⁴⁴	−ζ⁴−ζ¹³−ζ¹⁴−ζ²²−ζ²³−ζ³¹−ζ³²−ζ⁴¹	−ζ⁷+ζ⁸+ζ¹⁴−ζ¹⁶+ζ¹⁷+ζ²³+ζ²⁶+ζ³²−ζ³⁴+ζ⁴¹−ζ⁴³+ζ⁴⁴	ζ⁴+ζ⁷−ζ⁸+ζ¹³+ζ¹⁶−ζ¹⁷+ζ²²−ζ²⁶+ζ³¹+ζ³⁴+ζ⁴³−ζ⁴⁴	−ζ⁴−ζ¹³−ζ¹⁴−ζ²²−ζ²³−ζ³¹−ζ³²−ζ⁴¹	−ζ⁷+ζ⁸+ζ¹⁴−ζ¹⁶+ζ¹⁷+ζ²³+ζ²⁶+ζ³²−ζ³⁴+ζ⁴¹−ζ⁴³+ζ⁴⁴	ζ⁴+ζ⁷−ζ⁸+ζ¹³+ζ¹⁶−ζ¹⁷+ζ²²−ζ²⁶+ζ³¹+ζ³⁴+ζ⁴³−ζ⁴⁴	−ζ⁴−ζ¹³−ζ¹⁴−ζ²²−ζ²³−ζ³¹−ζ³²−ζ⁴¹	−ζ⁷+ζ⁸+ζ¹⁴−ζ¹⁶+ζ¹⁷+ζ²³+ζ²⁶+ζ³²−ζ³⁴+ζ⁴¹−ζ⁴³+ζ⁴⁴	ζ⁴+ζ⁷−ζ⁸+ζ¹³+ζ¹⁶−ζ¹⁷+ζ²²−ζ²⁶+ζ³¹+ζ³⁴+ζ⁴³−ζ⁴⁴	−ζ⁴−ζ¹³−ζ¹⁴−ζ²²−ζ²³−ζ³¹−ζ³²−ζ⁴¹	−ζ⁷+ζ⁸+ζ¹⁴−ζ¹⁶+ζ¹⁷+ζ²³+ζ²⁶+ζ³²−ζ³⁴+ζ⁴¹−ζ⁴³+ζ⁴⁴	ζ⁴+ζ⁷−ζ⁸+ζ¹³+ζ¹⁶−ζ¹⁷+ζ²²−ζ²⁶+ζ³¹+ζ³⁴+ζ⁴³−ζ⁴⁴	−ζ⁴−ζ¹³−ζ¹⁴−ζ²²−ζ²³−ζ³¹−ζ³²−ζ⁴¹	−ζ⁷+ζ⁸+ζ¹⁴−ζ¹⁶+ζ¹⁷+ζ²³+ζ²⁶+ζ³²−ζ³⁴+ζ⁴¹−ζ⁴³+ζ⁴⁴	0	0
χ₁₁	2	-1	2	2	-1	-1	-1	-1	2	-1	2	2	-1	-1	-1	-1	−ζ⁴−ζ¹³−ζ¹⁴−ζ²²−ζ²³−ζ³¹−ζ³²−ζ⁴¹	−ζ⁷+ζ⁸+ζ¹⁴−ζ¹⁶+ζ¹⁷+ζ²³+ζ²⁶+ζ³²−ζ³⁴+ζ⁴¹−ζ⁴³+ζ⁴⁴	ζ⁴+ζ⁷−ζ⁸+ζ¹³+ζ¹⁶−ζ¹⁷+ζ²²−ζ²⁶+ζ³¹+ζ³⁴+ζ⁴³−ζ⁴⁴	−ζ⁴−ζ¹³−ζ¹⁴−ζ²²−ζ²³−ζ³¹−ζ³²−ζ⁴¹	−ζ⁷+ζ⁸+ζ¹⁴−ζ¹⁶+ζ¹⁷+ζ²³+ζ²⁶+ζ³²−ζ³⁴+ζ⁴¹−ζ⁴³+ζ⁴⁴	ζ⁴+ζ⁷−ζ⁸+ζ¹³+ζ¹⁶−ζ¹⁷+ζ²²−ζ²⁶+ζ³¹+ζ³⁴+ζ⁴³−ζ⁴⁴	−ζ⁴−ζ¹³−ζ¹⁴−ζ²²−ζ²³−ζ³¹−ζ³²−ζ⁴¹	−ζ⁷+ζ⁸+ζ¹⁴−ζ¹⁶+ζ¹⁷+ζ²³+ζ²⁶+ζ³²−ζ³⁴+ζ⁴¹−ζ⁴³+ζ⁴⁴	ζ⁴+ζ⁷−ζ⁸+ζ¹³+ζ¹⁶−ζ¹⁷+ζ²²−ζ²⁶+ζ³¹+ζ³⁴+ζ⁴³−ζ⁴⁴	−ζ⁴−ζ¹³−ζ¹⁴−ζ²²−ζ²³−ζ³¹−ζ³²−ζ⁴¹	−ζ⁷+ζ⁸+ζ¹⁴−ζ¹⁶+ζ¹⁷+ζ²³+ζ²⁶+ζ³²−ζ³⁴+ζ⁴¹−ζ⁴³+ζ⁴⁴	ζ⁴+ζ⁷−ζ⁸+ζ¹³+ζ¹⁶−ζ¹⁷+ζ²²−ζ²⁶+ζ³¹+ζ³⁴+ζ⁴³−ζ⁴⁴	−ζ⁴−ζ¹³−ζ¹⁴−ζ²²−ζ²³−ζ³¹−ζ³²−ζ⁴¹	−ζ⁷+ζ⁸+ζ¹⁴−ζ¹⁶+ζ¹⁷+ζ²³+ζ²⁶+ζ³²−ζ³⁴+ζ⁴¹−ζ⁴³+ζ⁴⁴	ζ⁴+ζ⁷−ζ⁸+ζ¹³+ζ¹⁶−ζ¹⁷+ζ²²−ζ²⁶+ζ³¹+ζ³⁴+ζ⁴³−ζ⁴⁴	0	0
χ₁₂	2	-1	2	2	-1	-1	-1	-1	2	-1	2	2	-1	-1	-1	-1	−ζ⁷+ζ⁸+ζ¹⁴−ζ¹⁶+ζ¹⁷+ζ²³+ζ²⁶+ζ³²−ζ³⁴+ζ⁴¹−ζ⁴³+ζ⁴⁴	ζ⁴+ζ⁷−ζ⁸+ζ¹³+ζ¹⁶−ζ¹⁷+ζ²²−ζ²⁶+ζ³¹+ζ³⁴+ζ⁴³−ζ⁴⁴	−ζ⁴−ζ¹³−ζ¹⁴−ζ²²−ζ²³−ζ³¹−ζ³²−ζ⁴¹	−ζ⁷+ζ⁸+ζ¹⁴−ζ¹⁶+ζ¹⁷+ζ²³+ζ²⁶+ζ³²−ζ³⁴+ζ⁴¹−ζ⁴³+ζ⁴⁴	ζ⁴+ζ⁷−ζ⁸+ζ¹³+ζ¹⁶−ζ¹⁷+ζ²²−ζ²⁶+ζ³¹+ζ³⁴+ζ⁴³−ζ⁴⁴	−ζ⁴−ζ¹³−ζ¹⁴−ζ²²−ζ²³−ζ³¹−ζ³²−ζ⁴¹	−ζ⁷+ζ⁸+ζ¹⁴−ζ¹⁶+ζ¹⁷+ζ²³+ζ²⁶+ζ³²−ζ³⁴+ζ⁴¹−ζ⁴³+ζ⁴⁴	ζ⁴+ζ⁷−ζ⁸+ζ¹³+ζ¹⁶−ζ¹⁷+ζ²²−ζ²⁶+ζ³¹+ζ³⁴+ζ⁴³−ζ⁴⁴	−ζ⁴−ζ¹³−ζ¹⁴−ζ²²−ζ²³−ζ³¹−ζ³²−ζ⁴¹	−ζ⁷+ζ⁸+ζ¹⁴−ζ¹⁶+ζ¹⁷+ζ²³+ζ²⁶+ζ³²−ζ³⁴+ζ⁴¹−ζ⁴³+ζ⁴⁴	ζ⁴+ζ⁷−ζ⁸+ζ¹³+ζ¹⁶−ζ¹⁷+ζ²²−ζ²⁶+ζ³¹+ζ³⁴+ζ⁴³−ζ⁴⁴	−ζ⁴−ζ¹³−ζ¹⁴−ζ²²−ζ²³−ζ³¹−ζ³²−ζ⁴¹	−ζ⁷+ζ⁸+ζ¹⁴−ζ¹⁶+ζ¹⁷+ζ²³+ζ²⁶+ζ³²−ζ³⁴+ζ⁴¹−ζ⁴³+ζ⁴⁴	ζ⁴+ζ⁷−ζ⁸+ζ¹³+ζ¹⁶−ζ¹⁷+ζ²²−ζ²⁶+ζ³¹+ζ³⁴+ζ⁴³−ζ⁴⁴	−ζ⁴−ζ¹³−ζ¹⁴−ζ²²−ζ²³−ζ³¹−ζ³²−ζ⁴¹	0	0
χ₁₃	2	-1	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	ζ⁶+ζ³⁹	ζ²¹+ζ²⁴	ζ¹²+ζ³³	ζ³+ζ⁴²	2	-1	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	ζ⁶+ζ³⁹	ζ²¹+ζ²⁴	ζ¹²+ζ³³	ζ³+ζ⁴²	ζ⁴+ζ⁷−ζ⁸+ζ¹³+ζ¹⁶−ζ¹⁷+ζ²²−ζ²⁶+ζ³¹+ζ³⁴+ζ⁴³−ζ⁴⁴	−ζ⁴−ζ¹³−ζ¹⁴−ζ²²−ζ²³−ζ³¹−ζ³²−ζ⁴¹	−ζ⁷+ζ⁸+ζ¹⁴−ζ¹⁶+ζ¹⁷+ζ²³+ζ²⁶+ζ³²−ζ³⁴+ζ⁴¹−ζ⁴³+ζ⁴⁴	−ζ¹⁶−ζ³¹+ζ⁴⁴	ζ¹⁴+ζ³¹	−ζ¹⁴+ζ¹⁶−ζ⁴⁴	−ζ⁴+ζ²⁶−ζ³⁴	ζ⁴+ζ⁴¹	−ζ²⁶+ζ³⁴−ζ⁴¹	−ζ¹³+ζ¹⁷−ζ⁴³	ζ¹³+ζ³²	−ζ¹⁷−ζ³²+ζ⁴³	−ζ⁷+ζ⁸−ζ²²	ζ²²+ζ²³	ζ⁷−ζ⁸−ζ²³	0	0
χ₁₄	2	-1	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	ζ⁶+ζ³⁹	ζ²¹+ζ²⁴	ζ¹²+ζ³³	ζ³+ζ⁴²	2	-1	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	ζ⁶+ζ³⁹	ζ²¹+ζ²⁴	ζ¹²+ζ³³	ζ³+ζ⁴²	−ζ⁴−ζ¹³−ζ¹⁴−ζ²²−ζ²³−ζ³¹−ζ³²−ζ⁴¹	−ζ⁷+ζ⁸+ζ¹⁴−ζ¹⁶+ζ¹⁷+ζ²³+ζ²⁶+ζ³²−ζ³⁴+ζ⁴¹−ζ⁴³+ζ⁴⁴	ζ⁴+ζ⁷−ζ⁸+ζ¹³+ζ¹⁶−ζ¹⁷+ζ²²−ζ²⁶+ζ³¹+ζ³⁴+ζ⁴³−ζ⁴⁴	ζ¹⁴+ζ³¹	−ζ¹⁴+ζ¹⁶−ζ⁴⁴	−ζ¹⁶−ζ³¹+ζ⁴⁴	ζ⁴+ζ⁴¹	−ζ²⁶+ζ³⁴−ζ⁴¹	−ζ⁴+ζ²⁶−ζ³⁴	ζ¹³+ζ³²	−ζ¹⁷−ζ³²+ζ⁴³	−ζ¹³+ζ¹⁷−ζ⁴³	ζ²²+ζ²³	ζ⁷−ζ⁸−ζ²³	−ζ⁷+ζ⁸−ζ²²	0	0
χ₁₅	2	-1	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	ζ⁶+ζ³⁹	ζ²¹+ζ²⁴	ζ¹²+ζ³³	ζ³+ζ⁴²	2	-1	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	ζ⁶+ζ³⁹	ζ²¹+ζ²⁴	ζ¹²+ζ³³	ζ³+ζ⁴²	−ζ⁷+ζ⁸+ζ¹⁴−ζ¹⁶+ζ¹⁷+ζ²³+ζ²⁶+ζ³²−ζ³⁴+ζ⁴¹−ζ⁴³+ζ⁴⁴	ζ⁴+ζ⁷−ζ⁸+ζ¹³+ζ¹⁶−ζ¹⁷+ζ²²−ζ²⁶+ζ³¹+ζ³⁴+ζ⁴³−ζ⁴⁴	−ζ⁴−ζ¹³−ζ¹⁴−ζ²²−ζ²³−ζ³¹−ζ³²−ζ⁴¹	−ζ¹⁴+ζ¹⁶−ζ⁴⁴	−ζ¹⁶−ζ³¹+ζ⁴⁴	ζ¹⁴+ζ³¹	−ζ²⁶+ζ³⁴−ζ⁴¹	−ζ⁴+ζ²⁶−ζ³⁴	ζ⁴+ζ⁴¹	−ζ¹⁷−ζ³²+ζ⁴³	−ζ¹³+ζ¹⁷−ζ⁴³	ζ¹³+ζ³²	ζ⁷−ζ⁸−ζ²³	−ζ⁷+ζ⁸−ζ²²	ζ²²+ζ²³	0	0
χ₁₆	2	-1	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	ζ²¹+ζ²⁴	ζ⁶+ζ³⁹	ζ³+ζ⁴²	ζ¹²+ζ³³	2	-1	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	ζ²¹+ζ²⁴	ζ⁶+ζ³⁹	ζ³+ζ⁴²	ζ¹²+ζ³³	ζ⁴+ζ⁷−ζ⁸+ζ¹³+ζ¹⁶−ζ¹⁷+ζ²²−ζ²⁶+ζ³¹+ζ³⁴+ζ⁴³−ζ⁴⁴	−ζ⁴−ζ¹³−ζ¹⁴−ζ²²−ζ²³−ζ³¹−ζ³²−ζ⁴¹	−ζ⁷+ζ⁸+ζ¹⁴−ζ¹⁶+ζ¹⁷+ζ²³+ζ²⁶+ζ³²−ζ³⁴+ζ⁴¹−ζ⁴³+ζ⁴⁴	−ζ⁴+ζ²⁶−ζ³⁴	ζ⁴+ζ⁴¹	−ζ²⁶+ζ³⁴−ζ⁴¹	−ζ¹⁶−ζ³¹+ζ⁴⁴	ζ¹⁴+ζ³¹	−ζ¹⁴+ζ¹⁶−ζ⁴⁴	−ζ⁷+ζ⁸−ζ²²	ζ²²+ζ²³	ζ⁷−ζ⁸−ζ²³	−ζ¹³+ζ¹⁷−ζ⁴³	ζ¹³+ζ³²	−ζ¹⁷−ζ³²+ζ⁴³	0	0
χ₁₇	2	-1	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	ζ²¹+ζ²⁴	ζ⁶+ζ³⁹	ζ³+ζ⁴²	ζ¹²+ζ³³	2	-1	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	ζ²¹+ζ²⁴	ζ⁶+ζ³⁹	ζ³+ζ⁴²	ζ¹²+ζ³³	−ζ⁴−ζ¹³−ζ¹⁴−ζ²²−ζ²³−ζ³¹−ζ³²−ζ⁴¹	−ζ⁷+ζ⁸+ζ¹⁴−ζ¹⁶+ζ¹⁷+ζ²³+ζ²⁶+ζ³²−ζ³⁴+ζ⁴¹−ζ⁴³+ζ⁴⁴	ζ⁴+ζ⁷−ζ⁸+ζ¹³+ζ¹⁶−ζ¹⁷+ζ²²−ζ²⁶+ζ³¹+ζ³⁴+ζ⁴³−ζ⁴⁴	ζ⁴+ζ⁴¹	−ζ²⁶+ζ³⁴−ζ⁴¹	−ζ⁴+ζ²⁶−ζ³⁴	ζ¹⁴+ζ³¹	−ζ¹⁴+ζ¹⁶−ζ⁴⁴	−ζ¹⁶−ζ³¹+ζ⁴⁴	ζ²²+ζ²³	ζ⁷−ζ⁸−ζ²³	−ζ⁷+ζ⁸−ζ²²	ζ¹³+ζ³²	−ζ¹⁷−ζ³²+ζ⁴³	−ζ¹³+ζ¹⁷−ζ⁴³	0	0
χ₁₈	2	-1	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	ζ²¹+ζ²⁴	ζ⁶+ζ³⁹	ζ³+ζ⁴²	ζ¹²+ζ³³	2	-1	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	ζ²¹+ζ²⁴	ζ⁶+ζ³⁹	ζ³+ζ⁴²	ζ¹²+ζ³³	−ζ⁷+ζ⁸+ζ¹⁴−ζ¹⁶+ζ¹⁷+ζ²³+ζ²⁶+ζ³²−ζ³⁴+ζ⁴¹−ζ⁴³+ζ⁴⁴	ζ⁴+ζ⁷−ζ⁸+ζ¹³+ζ¹⁶−ζ¹⁷+ζ²²−ζ²⁶+ζ³¹+ζ³⁴+ζ⁴³−ζ⁴⁴	−ζ⁴−ζ¹³−ζ¹⁴−ζ²²−ζ²³−ζ³¹−ζ³²−ζ⁴¹	−ζ²⁶+ζ³⁴−ζ⁴¹	−ζ⁴+ζ²⁶−ζ³⁴	ζ⁴+ζ⁴¹	−ζ¹⁴+ζ¹⁶−ζ⁴⁴	−ζ¹⁶−ζ³¹+ζ⁴⁴	ζ¹⁴+ζ³¹	ζ⁷−ζ⁸−ζ²³	−ζ⁷+ζ⁸−ζ²²	ζ²²+ζ²³	−ζ¹⁷−ζ³²+ζ⁴³	−ζ¹³+ζ¹⁷−ζ⁴³	ζ¹³+ζ³²	0	0
χ₁₉	2	-1	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	ζ¹²+ζ³³	ζ³+ζ⁴²	ζ²¹+ζ²⁴	ζ⁶+ζ³⁹	2	-1	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	ζ¹²+ζ³³	ζ³+ζ⁴²	ζ²¹+ζ²⁴	ζ⁶+ζ³⁹	ζ⁴+ζ⁷−ζ⁸+ζ¹³+ζ¹⁶−ζ¹⁷+ζ²²−ζ²⁶+ζ³¹+ζ³⁴+ζ⁴³−ζ⁴⁴	−ζ⁴−ζ¹³−ζ¹⁴−ζ²²−ζ²³−ζ³¹−ζ³²−ζ⁴¹	−ζ⁷+ζ⁸+ζ¹⁴−ζ¹⁶+ζ¹⁷+ζ²³+ζ²⁶+ζ³²−ζ³⁴+ζ⁴¹−ζ⁴³+ζ⁴⁴	−ζ¹³+ζ¹⁷−ζ⁴³	ζ¹³+ζ³²	−ζ¹⁷−ζ³²+ζ⁴³	−ζ⁷+ζ⁸−ζ²²	ζ²²+ζ²³	ζ⁷−ζ⁸−ζ²³	−ζ⁴+ζ²⁶−ζ³⁴	ζ⁴+ζ⁴¹	−ζ²⁶+ζ³⁴−ζ⁴¹	−ζ¹⁶−ζ³¹+ζ⁴⁴	ζ¹⁴+ζ³¹	−ζ¹⁴+ζ¹⁶−ζ⁴⁴	0	0
χ₂₀	2	-1	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	ζ¹²+ζ³³	ζ³+ζ⁴²	ζ²¹+ζ²⁴	ζ⁶+ζ³⁹	2	-1	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	ζ¹²+ζ³³	ζ³+ζ⁴²	ζ²¹+ζ²⁴	ζ⁶+ζ³⁹	−ζ⁴−ζ¹³−ζ¹⁴−ζ²²−ζ²³−ζ³¹−ζ³²−ζ⁴¹	−ζ⁷+ζ⁸+ζ¹⁴−ζ¹⁶+ζ¹⁷+ζ²³+ζ²⁶+ζ³²−ζ³⁴+ζ⁴¹−ζ⁴³+ζ⁴⁴	ζ⁴+ζ⁷−ζ⁸+ζ¹³+ζ¹⁶−ζ¹⁷+ζ²²−ζ²⁶+ζ³¹+ζ³⁴+ζ⁴³−ζ⁴⁴	ζ¹³+ζ³²	−ζ¹⁷−ζ³²+ζ⁴³	−ζ¹³+ζ¹⁷−ζ⁴³	ζ²²+ζ²³	ζ⁷−ζ⁸−ζ²³	−ζ⁷+ζ⁸−ζ²²	ζ⁴+ζ⁴¹	−ζ²⁶+ζ³⁴−ζ⁴¹	−ζ⁴+ζ²⁶−ζ³⁴	ζ¹⁴+ζ³¹	−ζ¹⁴+ζ¹⁶−ζ⁴⁴	−ζ¹⁶−ζ³¹+ζ⁴⁴	0	0
χ₂₁	2	-1	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	ζ¹²+ζ³³	ζ³+ζ⁴²	ζ²¹+ζ²⁴	ζ⁶+ζ³⁹	2	-1	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	ζ¹²+ζ³³	ζ³+ζ⁴²	ζ²¹+ζ²⁴	ζ⁶+ζ³⁹	−ζ⁷+ζ⁸+ζ¹⁴−ζ¹⁶+ζ¹⁷+ζ²³+ζ²⁶+ζ³²−ζ³⁴+ζ⁴¹−ζ⁴³+ζ⁴⁴	ζ⁴+ζ⁷−ζ⁸+ζ¹³+ζ¹⁶−ζ¹⁷+ζ²²−ζ²⁶+ζ³¹+ζ³⁴+ζ⁴³−ζ⁴⁴	−ζ⁴−ζ¹³−ζ¹⁴−ζ²²−ζ²³−ζ³¹−ζ³²−ζ⁴¹	−ζ¹⁷−ζ³²+ζ⁴³	−ζ¹³+ζ¹⁷−ζ⁴³	ζ¹³+ζ³²	ζ⁷−ζ⁸−ζ²³	−ζ⁷+ζ⁸−ζ²²	ζ²²+ζ²³	−ζ²⁶+ζ³⁴−ζ⁴¹	−ζ⁴+ζ²⁶−ζ³⁴	ζ⁴+ζ⁴¹	−ζ¹⁴+ζ¹⁶−ζ⁴⁴	−ζ¹⁶−ζ³¹+ζ⁴⁴	ζ¹⁴+ζ³¹	0	0
χ₂₂	2	-1	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	ζ³+ζ⁴²	ζ¹²+ζ³³	ζ⁶+ζ³⁹	ζ²¹+ζ²⁴	2	-1	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	ζ³+ζ⁴²	ζ¹²+ζ³³	ζ⁶+ζ³⁹	ζ²¹+ζ²⁴	ζ⁴+ζ⁷−ζ⁸+ζ¹³+ζ¹⁶−ζ¹⁷+ζ²²−ζ²⁶+ζ³¹+ζ³⁴+ζ⁴³−ζ⁴⁴	−ζ⁴−ζ¹³−ζ¹⁴−ζ²²−ζ²³−ζ³¹−ζ³²−ζ⁴¹	−ζ⁷+ζ⁸+ζ¹⁴−ζ¹⁶+ζ¹⁷+ζ²³+ζ²⁶+ζ³²−ζ³⁴+ζ⁴¹−ζ⁴³+ζ⁴⁴	−ζ⁷+ζ⁸−ζ²²	ζ²²+ζ²³	ζ⁷−ζ⁸−ζ²³	−ζ¹³+ζ¹⁷−ζ⁴³	ζ¹³+ζ³²	−ζ¹⁷−ζ³²+ζ⁴³	−ζ¹⁶−ζ³¹+ζ⁴⁴	ζ¹⁴+ζ³¹	−ζ¹⁴+ζ¹⁶−ζ⁴⁴	−ζ⁴+ζ²⁶−ζ³⁴	ζ⁴+ζ⁴¹	−ζ²⁶+ζ³⁴−ζ⁴¹	0	0
χ₂₃	2	-1	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	ζ³+ζ⁴²	ζ¹²+ζ³³	ζ⁶+ζ³⁹	ζ²¹+ζ²⁴	2	-1	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	ζ³+ζ⁴²	ζ¹²+ζ³³	ζ⁶+ζ³⁹	ζ²¹+ζ²⁴	−ζ⁴−ζ¹³−ζ¹⁴−ζ²²−ζ²³−ζ³¹−ζ³²−ζ⁴¹	−ζ⁷+ζ⁸+ζ¹⁴−ζ¹⁶+ζ¹⁷+ζ²³+ζ²⁶+ζ³²−ζ³⁴+ζ⁴¹−ζ⁴³+ζ⁴⁴	ζ⁴+ζ⁷−ζ⁸+ζ¹³+ζ¹⁶−ζ¹⁷+ζ²²−ζ²⁶+ζ³¹+ζ³⁴+ζ⁴³−ζ⁴⁴	ζ²²+ζ²³	ζ⁷−ζ⁸−ζ²³	−ζ⁷+ζ⁸−ζ²²	ζ¹³+ζ³²	−ζ¹⁷−ζ³²+ζ⁴³	−ζ¹³+ζ¹⁷−ζ⁴³	ζ¹⁴+ζ³¹	−ζ¹⁴+ζ¹⁶−ζ⁴⁴	−ζ¹⁶−ζ³¹+ζ⁴⁴	ζ⁴+ζ⁴¹	−ζ²⁶+ζ³⁴−ζ⁴¹	−ζ⁴+ζ²⁶−ζ³⁴	0	0
χ₂₄	2	-1	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	ζ³+ζ⁴²	ζ¹²+ζ³³	ζ⁶+ζ³⁹	ζ²¹+ζ²⁴	2	-1	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	ζ³+ζ⁴²	ζ¹²+ζ³³	ζ⁶+ζ³⁹	ζ²¹+ζ²⁴	−ζ⁷+ζ⁸+ζ¹⁴−ζ¹⁶+ζ¹⁷+ζ²³+ζ²⁶+ζ³²−ζ³⁴+ζ⁴¹−ζ⁴³+ζ⁴⁴	ζ⁴+ζ⁷−ζ⁸+ζ¹³+ζ¹⁶−ζ¹⁷+ζ²²−ζ²⁶+ζ³¹+ζ³⁴+ζ⁴³−ζ⁴⁴	−ζ⁴−ζ¹³−ζ¹⁴−ζ²²−ζ²³−ζ³¹−ζ³²−ζ⁴¹	ζ⁷−ζ⁸−ζ²³	−ζ⁷+ζ⁸−ζ²²	ζ²²+ζ²³	−ζ¹⁷−ζ³²+ζ⁴³	−ζ¹³+ζ¹⁷−ζ⁴³	ζ¹³+ζ³²	−ζ¹⁴+ζ¹⁶−ζ⁴⁴	−ζ¹⁶−ζ³¹+ζ⁴⁴	ζ¹⁴+ζ³¹	−ζ²⁶+ζ³⁴−ζ⁴¹	−ζ⁴+ζ²⁶−ζ³⁴	ζ⁴+ζ⁴¹	0	0
χ₂₅	3	3	3	3	3	3	3	3	-1	-1	-1	-1	-1	-1	-1	-1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	-1
χ₂₆	3	3	3	3	3	3	3	3	-1	-1	-1	-1	-1	-1	-1	-1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	-1	1
χ₂₇	6	6	$\frac{- 3 + 3 \sqrt{5}}{2}$	$\frac{- 3 - 3 \sqrt{5}}{2}$	$\frac{- 3 + 3 \sqrt{5}}{2}$	$\frac{- 3 + 3 \sqrt{5}}{2}$	$\frac{- 3 - 3 \sqrt{5}}{2}$	$\frac{- 3 - 3 \sqrt{5}}{2}$	-2	-2	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₈	6	6	$\frac{- 3 - 3 \sqrt{5}}{2}$	$\frac{- 3 + 3 \sqrt{5}}{2}$	$\frac{- 3 - 3 \sqrt{5}}{2}$	$\frac{- 3 - 3 \sqrt{5}}{2}$	$\frac{- 3 + 3 \sqrt{5}}{2}$	$\frac{- 3 + 3 \sqrt{5}}{2}$	-2	-2	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₉	6	-3	6	6	-3	-3	-3	-3	-2	1	-2	-2	1	1	1	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₀	6	-3	$\frac{- 3 + 3 \sqrt{5}}{2}$	$\frac{- 3 - 3 \sqrt{5}}{2}$	3ζ⁶+3ζ³⁹	3ζ²¹+3ζ²⁴	3ζ¹²+3ζ³³	3ζ³+3ζ⁴²	-2	1	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	−ζ⁶−ζ³⁹	−ζ²¹−ζ²⁴	−ζ¹²−ζ³³	−ζ³−ζ⁴²	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₁	6	-3	$\frac{- 3 + 3 \sqrt{5}}{2}$	$\frac{- 3 - 3 \sqrt{5}}{2}$	3ζ²¹+3ζ²⁴	3ζ⁶+3ζ³⁹	3ζ³+3ζ⁴²	3ζ¹²+3ζ³³	-2	1	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	−ζ²¹−ζ²⁴	−ζ⁶−ζ³⁹	−ζ³−ζ⁴²	−ζ¹²−ζ³³	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₂	6	-3	$\frac{- 3 - 3 \sqrt{5}}{2}$	$\frac{- 3 + 3 \sqrt{5}}{2}$	3ζ¹²+3ζ³³	3ζ³+3ζ⁴²	3ζ²¹+3ζ²⁴	3ζ⁶+3ζ³⁹	-2	1	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	−ζ¹²−ζ³³	−ζ³−ζ⁴²	−ζ²¹−ζ²⁴	−ζ⁶−ζ³⁹	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₃	6	-3	$\frac{- 3 - 3 \sqrt{5}}{2}$	$\frac{- 3 + 3 \sqrt{5}}{2}$	3ζ³+3ζ⁴²	3ζ¹²+3ζ³³	3ζ⁶+3ζ³⁹	3ζ²¹+3ζ²⁴	-2	1	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	−ζ³−ζ⁴²	−ζ¹²−ζ³³	−ζ⁶−ζ³⁹	−ζ²¹−ζ²⁴	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0

Character table — Group #67111