Group #6192 — 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	1	2	2	2	2	2	2	2	2	2	2	4	4	4	4	4	4	4	4	6	6	6	6	6	6	6	6	6	18	18	18	54
order	1	2	3	3	6	6	9	9	9	18	18	18	3	6	9	9	9	18	18	18	4	12	12	36	36	36	36	36	36	2	6	6	2
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	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
χ₅	2	2	2	2	2	2	-1	-1	-1	-1	-1	-1	2	2	-1	-1	-1	-1	-1	-1	2	2	2	-1	-1	-1	-1	-1	-1	0	0	0	0
χ₆	2	2	2	2	2	2	-1	-1	-1	-1	-1	-1	2	2	-1	-1	-1	-1	-1	-1	-2	-2	-2	1	1	1	1	1	1	0	0	0	0
χ₇	2	2	2	-1	-1	2	2	2	2	2	2	2	-1	-1	-1	-1	-1	-1	-1	-1	0	0	0	0	0	0	0	0	0	2	-1	-1	0
χ₈	2	2	2	-1	-1	2	2	2	2	2	2	2	-1	-1	-1	-1	-1	-1	-1	-1	0	0	0	0	0	0	0	0	0	-2	1	1	0
χ₉	2	2	-1	2	2	-1	ζ²²−ζ²⁶+ζ³⁴	−ζ¹⁴−ζ²²	ζ¹⁴+ζ²⁶−ζ³⁴	ζ²²−ζ²⁶+ζ³⁴	−ζ¹⁴−ζ²²	ζ¹⁴+ζ²⁶−ζ³⁴	-1	-1	ζ²²−ζ²⁶+ζ³⁴	−ζ¹⁴−ζ²²	ζ¹⁴+ζ²⁶−ζ³⁴	ζ²²−ζ²⁶+ζ³⁴	−ζ¹⁴−ζ²²	ζ¹⁴+ζ²⁶−ζ³⁴	2	-1	-1	ζ²²−ζ²⁶+ζ³⁴	ζ²²−ζ²⁶+ζ³⁴	−ζ¹⁴−ζ²²	−ζ¹⁴−ζ²²	ζ¹⁴+ζ²⁶−ζ³⁴	ζ¹⁴+ζ²⁶−ζ³⁴	0	0	0	0
χ₁₀	2	2	-1	2	2	-1	ζ²²−ζ²⁶+ζ³⁴	−ζ¹⁴−ζ²²	ζ¹⁴+ζ²⁶−ζ³⁴	ζ²²−ζ²⁶+ζ³⁴	−ζ¹⁴−ζ²²	ζ¹⁴+ζ²⁶−ζ³⁴	-1	-1	ζ²²−ζ²⁶+ζ³⁴	−ζ¹⁴−ζ²²	ζ¹⁴+ζ²⁶−ζ³⁴	ζ²²−ζ²⁶+ζ³⁴	−ζ¹⁴−ζ²²	ζ¹⁴+ζ²⁶−ζ³⁴	-2	1	1	−ζ²²+ζ²⁶−ζ³⁴	−ζ²²+ζ²⁶−ζ³⁴	ζ¹⁴+ζ²²	ζ¹⁴+ζ²²	−ζ¹⁴−ζ²⁶+ζ³⁴	−ζ¹⁴−ζ²⁶+ζ³⁴	0	0	0	0
χ₁₁	2	2	-1	2	2	-1	−ζ¹⁴−ζ²²	ζ¹⁴+ζ²⁶−ζ³⁴	ζ²²−ζ²⁶+ζ³⁴	−ζ¹⁴−ζ²²	ζ¹⁴+ζ²⁶−ζ³⁴	ζ²²−ζ²⁶+ζ³⁴	-1	-1	−ζ¹⁴−ζ²²	ζ¹⁴+ζ²⁶−ζ³⁴	ζ²²−ζ²⁶+ζ³⁴	−ζ¹⁴−ζ²²	ζ¹⁴+ζ²⁶−ζ³⁴	ζ²²−ζ²⁶+ζ³⁴	2	-1	-1	−ζ¹⁴−ζ²²	−ζ¹⁴−ζ²²	ζ¹⁴+ζ²⁶−ζ³⁴	ζ¹⁴+ζ²⁶−ζ³⁴	ζ²²−ζ²⁶+ζ³⁴	ζ²²−ζ²⁶+ζ³⁴	0	0	0	0
χ₁₂	2	2	-1	2	2	-1	−ζ¹⁴−ζ²²	ζ¹⁴+ζ²⁶−ζ³⁴	ζ²²−ζ²⁶+ζ³⁴	−ζ¹⁴−ζ²²	ζ¹⁴+ζ²⁶−ζ³⁴	ζ²²−ζ²⁶+ζ³⁴	-1	-1	−ζ¹⁴−ζ²²	ζ¹⁴+ζ²⁶−ζ³⁴	ζ²²−ζ²⁶+ζ³⁴	−ζ¹⁴−ζ²²	ζ¹⁴+ζ²⁶−ζ³⁴	ζ²²−ζ²⁶+ζ³⁴	-2	1	1	ζ¹⁴+ζ²²	ζ¹⁴+ζ²²	−ζ¹⁴−ζ²⁶+ζ³⁴	−ζ¹⁴−ζ²⁶+ζ³⁴	−ζ²²+ζ²⁶−ζ³⁴	−ζ²²+ζ²⁶−ζ³⁴	0	0	0	0
χ₁₃	2	2	-1	2	2	-1	ζ¹⁴+ζ²⁶−ζ³⁴	ζ²²−ζ²⁶+ζ³⁴	−ζ¹⁴−ζ²²	ζ¹⁴+ζ²⁶−ζ³⁴	ζ²²−ζ²⁶+ζ³⁴	−ζ¹⁴−ζ²²	-1	-1	ζ¹⁴+ζ²⁶−ζ³⁴	ζ²²−ζ²⁶+ζ³⁴	−ζ¹⁴−ζ²²	ζ¹⁴+ζ²⁶−ζ³⁴	ζ²²−ζ²⁶+ζ³⁴	−ζ¹⁴−ζ²²	2	-1	-1	ζ¹⁴+ζ²⁶−ζ³⁴	ζ¹⁴+ζ²⁶−ζ³⁴	ζ²²−ζ²⁶+ζ³⁴	ζ²²−ζ²⁶+ζ³⁴	−ζ¹⁴−ζ²²	−ζ¹⁴−ζ²²	0	0	0	0
χ₁₄	2	2	-1	2	2	-1	ζ¹⁴+ζ²⁶−ζ³⁴	ζ²²−ζ²⁶+ζ³⁴	−ζ¹⁴−ζ²²	ζ¹⁴+ζ²⁶−ζ³⁴	ζ²²−ζ²⁶+ζ³⁴	−ζ¹⁴−ζ²²	-1	-1	ζ¹⁴+ζ²⁶−ζ³⁴	ζ²²−ζ²⁶+ζ³⁴	−ζ¹⁴−ζ²²	ζ¹⁴+ζ²⁶−ζ³⁴	ζ²²−ζ²⁶+ζ³⁴	−ζ¹⁴−ζ²²	-2	1	1	−ζ¹⁴−ζ²⁶+ζ³⁴	−ζ¹⁴−ζ²⁶+ζ³⁴	−ζ²²+ζ²⁶−ζ³⁴	−ζ²²+ζ²⁶−ζ³⁴	ζ¹⁴+ζ²²	ζ¹⁴+ζ²²	0	0	0	0
χ₁₅	2	-2	2	2	-2	-2	2	2	2	-2	-2	-2	2	-2	2	2	2	-2	-2	-2	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₁₆	2	-2	2	2	-2	-2	-1	-1	-1	1	1	1	2	-2	-1	-1	-1	1	1	1	0	0	0	$\sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	0	0	0	0
χ₁₇	2	-2	2	2	-2	-2	-1	-1	-1	1	1	1	2	-2	-1	-1	-1	1	1	1	0	0	0	$- \sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	0	0	0	0
χ₁₈	2	-2	2	-1	1	-2	2	2	2	-2	-2	-2	-1	1	-1	-1	-1	1	1	1	0	0	0	0	0	0	0	0	0	0	$- i \sqrt{3}$	$i \sqrt{3}$	0
χ₁₉	2	-2	2	-1	1	-2	2	2	2	-2	-2	-2	-1	1	-1	-1	-1	1	1	1	0	0	0	0	0	0	0	0	0	0	$i \sqrt{3}$	$- i \sqrt{3}$	0
χ₂₀	2	-2	-1	2	-2	1	ζ²²−ζ²⁶+ζ³⁴	−ζ¹⁴−ζ²²	ζ¹⁴+ζ²⁶−ζ³⁴	−ζ²²+ζ²⁶−ζ³⁴	ζ¹⁴+ζ²²	−ζ¹⁴−ζ²⁶+ζ³⁴	-1	1	ζ²²−ζ²⁶+ζ³⁴	−ζ¹⁴−ζ²²	ζ¹⁴+ζ²⁶−ζ³⁴	−ζ²²+ζ²⁶−ζ³⁴	ζ¹⁴+ζ²²	−ζ¹⁴−ζ²⁶+ζ³⁴	0	$\sqrt{3}$	$- \sqrt{3}$	ζ⁷+ζ³¹+ζ³⁵	−ζ⁷−ζ³¹−ζ³⁵	ζ²³−ζ³¹	−ζ²³+ζ³¹	−ζ⁷−ζ²³−ζ³⁵	ζ⁷+ζ²³+ζ³⁵	0	0	0	0
χ₂₁	2	-2	-1	2	-2	1	ζ²²−ζ²⁶+ζ³⁴	−ζ¹⁴−ζ²²	ζ¹⁴+ζ²⁶−ζ³⁴	−ζ²²+ζ²⁶−ζ³⁴	ζ¹⁴+ζ²²	−ζ¹⁴−ζ²⁶+ζ³⁴	-1	1	ζ²²−ζ²⁶+ζ³⁴	−ζ¹⁴−ζ²²	ζ¹⁴+ζ²⁶−ζ³⁴	−ζ²²+ζ²⁶−ζ³⁴	ζ¹⁴+ζ²²	−ζ¹⁴−ζ²⁶+ζ³⁴	0	$- \sqrt{3}$	$\sqrt{3}$	−ζ⁷−ζ³¹−ζ³⁵	ζ⁷+ζ³¹+ζ³⁵	−ζ²³+ζ³¹	ζ²³−ζ³¹	ζ⁷+ζ²³+ζ³⁵	−ζ⁷−ζ²³−ζ³⁵	0	0	0	0
χ₂₂	2	-2	-1	2	-2	1	−ζ¹⁴−ζ²²	ζ¹⁴+ζ²⁶−ζ³⁴	ζ²²−ζ²⁶+ζ³⁴	ζ¹⁴+ζ²²	−ζ¹⁴−ζ²⁶+ζ³⁴	−ζ²²+ζ²⁶−ζ³⁴	-1	1	−ζ¹⁴−ζ²²	ζ¹⁴+ζ²⁶−ζ³⁴	ζ²²−ζ²⁶+ζ³⁴	ζ¹⁴+ζ²²	−ζ¹⁴−ζ²⁶+ζ³⁴	−ζ²²+ζ²⁶−ζ³⁴	0	$\sqrt{3}$	$- \sqrt{3}$	ζ²³−ζ³¹	−ζ²³+ζ³¹	−ζ⁷−ζ²³−ζ³⁵	ζ⁷+ζ²³+ζ³⁵	ζ⁷+ζ³¹+ζ³⁵	−ζ⁷−ζ³¹−ζ³⁵	0	0	0	0
χ₂₃	2	-2	-1	2	-2	1	−ζ¹⁴−ζ²²	ζ¹⁴+ζ²⁶−ζ³⁴	ζ²²−ζ²⁶+ζ³⁴	ζ¹⁴+ζ²²	−ζ¹⁴−ζ²⁶+ζ³⁴	−ζ²²+ζ²⁶−ζ³⁴	-1	1	−ζ¹⁴−ζ²²	ζ¹⁴+ζ²⁶−ζ³⁴	ζ²²−ζ²⁶+ζ³⁴	ζ¹⁴+ζ²²	−ζ¹⁴−ζ²⁶+ζ³⁴	−ζ²²+ζ²⁶−ζ³⁴	0	$- \sqrt{3}$	$\sqrt{3}$	−ζ²³+ζ³¹	ζ²³−ζ³¹	ζ⁷+ζ²³+ζ³⁵	−ζ⁷−ζ²³−ζ³⁵	−ζ⁷−ζ³¹−ζ³⁵	ζ⁷+ζ³¹+ζ³⁵	0	0	0	0
χ₂₄	2	-2	-1	2	-2	1	ζ¹⁴+ζ²⁶−ζ³⁴	ζ²²−ζ²⁶+ζ³⁴	−ζ¹⁴−ζ²²	−ζ¹⁴−ζ²⁶+ζ³⁴	−ζ²²+ζ²⁶−ζ³⁴	ζ¹⁴+ζ²²	-1	1	ζ¹⁴+ζ²⁶−ζ³⁴	ζ²²−ζ²⁶+ζ³⁴	−ζ¹⁴−ζ²²	−ζ¹⁴−ζ²⁶+ζ³⁴	−ζ²²+ζ²⁶−ζ³⁴	ζ¹⁴+ζ²²	0	$\sqrt{3}$	$- \sqrt{3}$	−ζ⁷−ζ²³−ζ³⁵	ζ⁷+ζ²³+ζ³⁵	ζ⁷+ζ³¹+ζ³⁵	−ζ⁷−ζ³¹−ζ³⁵	ζ²³−ζ³¹	−ζ²³+ζ³¹	0	0	0	0
χ₂₅	2	-2	-1	2	-2	1	ζ¹⁴+ζ²⁶−ζ³⁴	ζ²²−ζ²⁶+ζ³⁴	−ζ¹⁴−ζ²²	−ζ¹⁴−ζ²⁶+ζ³⁴	−ζ²²+ζ²⁶−ζ³⁴	ζ¹⁴+ζ²²	-1	1	ζ¹⁴+ζ²⁶−ζ³⁴	ζ²²−ζ²⁶+ζ³⁴	−ζ¹⁴−ζ²²	−ζ¹⁴−ζ²⁶+ζ³⁴	−ζ²²+ζ²⁶−ζ³⁴	ζ¹⁴+ζ²²	0	$- \sqrt{3}$	$\sqrt{3}$	ζ⁷+ζ²³+ζ³⁵	−ζ⁷−ζ²³−ζ³⁵	−ζ⁷−ζ³¹−ζ³⁵	ζ⁷+ζ³¹+ζ³⁵	−ζ²³+ζ³¹	ζ²³−ζ³¹	0	0	0	0
χ₂₆	4	4	4	-2	-2	4	-2	-2	-2	-2	-2	-2	-2	-2	1	1	1	1	1	1	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₇	4	4	-2	-2	-2	-2	2ζ²²−2ζ²⁶+2ζ³⁴	−2ζ¹⁴−2ζ²²	2ζ¹⁴+2ζ²⁶−2ζ³⁴	2ζ²²−2ζ²⁶+2ζ³⁴	−2ζ¹⁴−2ζ²²	2ζ¹⁴+2ζ²⁶−2ζ³⁴	1	1	−ζ²²+ζ²⁶−ζ³⁴	ζ¹⁴+ζ²²	−ζ¹⁴−ζ²⁶+ζ³⁴	−ζ²²+ζ²⁶−ζ³⁴	ζ¹⁴+ζ²²	−ζ¹⁴−ζ²⁶+ζ³⁴	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₈	4	4	-2	-2	-2	-2	−2ζ¹⁴−2ζ²²	2ζ¹⁴+2ζ²⁶−2ζ³⁴	2ζ²²−2ζ²⁶+2ζ³⁴	−2ζ¹⁴−2ζ²²	2ζ¹⁴+2ζ²⁶−2ζ³⁴	2ζ²²−2ζ²⁶+2ζ³⁴	1	1	ζ¹⁴+ζ²²	−ζ¹⁴−ζ²⁶+ζ³⁴	−ζ²²+ζ²⁶−ζ³⁴	ζ¹⁴+ζ²²	−ζ¹⁴−ζ²⁶+ζ³⁴	−ζ²²+ζ²⁶−ζ³⁴	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₉	4	4	-2	-2	-2	-2	2ζ¹⁴+2ζ²⁶−2ζ³⁴	2ζ²²−2ζ²⁶+2ζ³⁴	−2ζ¹⁴−2ζ²²	2ζ¹⁴+2ζ²⁶−2ζ³⁴	2ζ²²−2ζ²⁶+2ζ³⁴	−2ζ¹⁴−2ζ²²	1	1	−ζ¹⁴−ζ²⁶+ζ³⁴	−ζ²²+ζ²⁶−ζ³⁴	ζ¹⁴+ζ²²	−ζ¹⁴−ζ²⁶+ζ³⁴	−ζ²²+ζ²⁶−ζ³⁴	ζ¹⁴+ζ²²	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₀	4	-4	4	-2	2	-4	-2	-2	-2	2	2	2	-2	2	1	1	1	-1	-1	-1	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₁	4	-4	-2	-2	2	2	2ζ²²−2ζ²⁶+2ζ³⁴	−2ζ¹⁴−2ζ²²	2ζ¹⁴+2ζ²⁶−2ζ³⁴	−2ζ²²+2ζ²⁶−2ζ³⁴	2ζ¹⁴+2ζ²²	−2ζ¹⁴−2ζ²⁶+2ζ³⁴	1	-1	−ζ²²+ζ²⁶−ζ³⁴	ζ¹⁴+ζ²²	−ζ¹⁴−ζ²⁶+ζ³⁴	ζ²²−ζ²⁶+ζ³⁴	−ζ¹⁴−ζ²²	ζ¹⁴+ζ²⁶−ζ³⁴	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₂	4	-4	-2	-2	2	2	−2ζ¹⁴−2ζ²²	2ζ¹⁴+2ζ²⁶−2ζ³⁴	2ζ²²−2ζ²⁶+2ζ³⁴	2ζ¹⁴+2ζ²²	−2ζ¹⁴−2ζ²⁶+2ζ³⁴	−2ζ²²+2ζ²⁶−2ζ³⁴	1	-1	ζ¹⁴+ζ²²	−ζ¹⁴−ζ²⁶+ζ³⁴	−ζ²²+ζ²⁶−ζ³⁴	−ζ¹⁴−ζ²²	ζ¹⁴+ζ²⁶−ζ³⁴	ζ²²−ζ²⁶+ζ³⁴	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₃	4	-4	-2	-2	2	2	2ζ¹⁴+2ζ²⁶−2ζ³⁴	2ζ²²−2ζ²⁶+2ζ³⁴	−2ζ¹⁴−2ζ²²	−2ζ¹⁴−2ζ²⁶+2ζ³⁴	−2ζ²²+2ζ²⁶−2ζ³⁴	2ζ¹⁴+2ζ²²	1	-1	−ζ¹⁴−ζ²⁶+ζ³⁴	−ζ²²+ζ²⁶−ζ³⁴	ζ¹⁴+ζ²²	ζ¹⁴+ζ²⁶−ζ³⁴	ζ²²−ζ²⁶+ζ³⁴	−ζ¹⁴−ζ²²	0	0	0	0	0	0	0	0	0	0	0	0	0

Character table — Group #6192