Group #88421 — 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	C₄₃	C₄₄	C₄₅	C₄₆	C₄₇	C₄₈
size	1	1	2	2	2	2	2	2	2	2	2	2	2	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	12	12	12	12	12	12	12	12	12	36	36	36	54	54
order	1	2	3	3	4	6	6	9	9	9	18	18	18	3	6	9	9	9	12	12	12	12	18	18	18	36	36	36	36	36	36	36	36	36	2	6	6	18	18	18	18	18	18	2	6	6	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	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	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	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	1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	1	1
χ₅	2	2	2	2	2	2	2	-1	-1	-1	-1	-1	-1	2	2	-1	-1	-1	2	2	2	2	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	2	2	2	-1	-1	-1	-1	-1	-1	0	0	0	0	0
χ₆	2	2	2	2	2	2	2	-1	-1	-1	-1	-1	-1	2	2	-1	-1	-1	2	2	2	2	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-2	-2	-2	1	1	1	1	1	1	0	0	0	0	0
χ₇	2	2	2	2	-2	2	2	2	2	2	2	2	2	2	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	0
χ₈	2	2	2	2	-2	2	2	-1	-1	-1	-1	-1	-1	2	2	-1	-1	-1	-2	-2	-2	-2	-1	-1	-1	1	1	1	1	1	1	1	1	1	0	0	0	$- i \sqrt{3}$	$- i \sqrt{3}$	$- i \sqrt{3}$	$i \sqrt{3}$	$i \sqrt{3}$	$i \sqrt{3}$	0	0	0	0	0
χ₉	2	2	2	2	-2	2	2	-1	-1	-1	-1	-1	-1	2	2	-1	-1	-1	-2	-2	-2	-2	-1	-1	-1	1	1	1	1	1	1	1	1	1	0	0	0	$i \sqrt{3}$	$i \sqrt{3}$	$i \sqrt{3}$	$- i \sqrt{3}$	$- i \sqrt{3}$	$- i \sqrt{3}$	0	0	0	0	0
χ₁₀	2	2	2	-1	2	2	-1	2	2	2	2	2	2	-1	-1	-1	-1	-1	2	-1	-1	-1	-1	-1	-1	2	2	2	-1	-1	-1	-1	-1	-1	0	0	0	0	0	0	0	0	0	2	-1	-1	0	0
χ₁₁	2	2	2	-1	2	2	-1	2	2	2	2	2	2	-1	-1	-1	-1	-1	2	-1	-1	-1	-1	-1	-1	2	2	2	-1	-1	-1	-1	-1	-1	0	0	0	0	0	0	0	0	0	-2	1	1	0	0
χ₁₂	2	2	2	-1	-2	2	-1	2	2	2	2	2	2	-1	-1	-1	-1	-1	-2	1	1	1	-1	-1	-1	-2	-2	-2	1	1	1	1	1	1	0	0	0	0	0	0	0	0	0	0	$- i \sqrt{3}$	$i \sqrt{3}$	0	0
χ₁₃	2	2	2	-1	-2	2	-1	2	2	2	2	2	2	-1	-1	-1	-1	-1	-2	1	1	1	-1	-1	-1	-2	-2	-2	1	1	1	1	1	1	0	0	0	0	0	0	0	0	0	0	$i \sqrt{3}$	$- i \sqrt{3}$	0	0
χ₁₄	2	2	-1	2	2	-1	2	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	-1	-1	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	-1	2	-1	-1	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	−ζ⁴−ζ⁶⁸	2	-1	-1	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	0	0	0	0	0
χ₁₅	2	2	-1	2	2	-1	2	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	-1	-1	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	-1	2	-1	-1	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	−ζ⁴−ζ⁶⁸	-2	1	1	−ζ⁴⁴+ζ⁵²−ζ⁶⁸	−ζ⁴+ζ⁴⁴−ζ⁵²	ζ⁴+ζ⁶⁸	−ζ⁴⁴+ζ⁵²−ζ⁶⁸	−ζ⁴+ζ⁴⁴−ζ⁵²	ζ⁴+ζ⁶⁸	0	0	0	0	0
χ₁₆	2	2	-1	2	2	-1	2	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	-1	-1	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	-1	2	-1	-1	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	2	-1	-1	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	0	0	0	0	0
χ₁₇	2	2	-1	2	2	-1	2	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	-1	-1	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	-1	2	-1	-1	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	-2	1	1	−ζ⁴+ζ⁴⁴−ζ⁵²	ζ⁴+ζ⁶⁸	−ζ⁴⁴+ζ⁵²−ζ⁶⁸	−ζ⁴+ζ⁴⁴−ζ⁵²	ζ⁴+ζ⁶⁸	−ζ⁴⁴+ζ⁵²−ζ⁶⁸	0	0	0	0	0
χ₁₈	2	2	-1	2	2	-1	2	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	-1	-1	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	-1	2	-1	-1	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	ζ⁴−ζ⁴⁴+ζ⁵²	2	-1	-1	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	0	0	0	0	0
χ₁₉	2	2	-1	2	2	-1	2	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	-1	-1	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	-1	2	-1	-1	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	ζ⁴−ζ⁴⁴+ζ⁵²	-2	1	1	ζ⁴+ζ⁶⁸	−ζ⁴⁴+ζ⁵²−ζ⁶⁸	−ζ⁴+ζ⁴⁴−ζ⁵²	ζ⁴+ζ⁶⁸	−ζ⁴⁴+ζ⁵²−ζ⁶⁸	−ζ⁴+ζ⁴⁴−ζ⁵²	0	0	0	0	0
χ₂₀	2	2	-1	2	-2	-1	2	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	-1	-1	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	1	-2	1	1	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	−ζ⁴⁴+ζ⁵²−ζ⁶⁸	−ζ⁴+ζ⁴⁴−ζ⁵²	ζ⁴+ζ⁶⁸	−ζ⁴⁴+ζ⁵²−ζ⁶⁸	−ζ⁴⁴+ζ⁵²−ζ⁶⁸	−ζ⁴+ζ⁴⁴−ζ⁵²	−ζ⁴+ζ⁴⁴−ζ⁵²	ζ⁴+ζ⁶⁸	ζ⁴+ζ⁶⁸	0	$- i \sqrt{3}$	$i \sqrt{3}$	−ζ⁴⁴−ζ⁵²−ζ⁶⁸	ζ⁴+ζ⁴⁴+ζ⁵²	−ζ⁴+ζ⁶⁸	ζ⁴⁴+ζ⁵²+ζ⁶⁸	−ζ⁴−ζ⁴⁴−ζ⁵²	ζ⁴−ζ⁶⁸	0	0	0	0	0
χ₂₁	2	2	-1	2	-2	-1	2	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	-1	-1	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	1	-2	1	1	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	−ζ⁴⁴+ζ⁵²−ζ⁶⁸	−ζ⁴+ζ⁴⁴−ζ⁵²	ζ⁴+ζ⁶⁸	−ζ⁴⁴+ζ⁵²−ζ⁶⁸	−ζ⁴⁴+ζ⁵²−ζ⁶⁸	−ζ⁴+ζ⁴⁴−ζ⁵²	−ζ⁴+ζ⁴⁴−ζ⁵²	ζ⁴+ζ⁶⁸	ζ⁴+ζ⁶⁸	0	$i \sqrt{3}$	$- i \sqrt{3}$	ζ⁴⁴+ζ⁵²+ζ⁶⁸	−ζ⁴−ζ⁴⁴−ζ⁵²	ζ⁴−ζ⁶⁸	−ζ⁴⁴−ζ⁵²−ζ⁶⁸	ζ⁴+ζ⁴⁴+ζ⁵²	−ζ⁴+ζ⁶⁸	0	0	0	0	0
χ₂₂	2	2	-1	2	-2	-1	2	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	-1	-1	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	1	-2	1	1	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	−ζ⁴+ζ⁴⁴−ζ⁵²	ζ⁴+ζ⁶⁸	−ζ⁴⁴+ζ⁵²−ζ⁶⁸	−ζ⁴+ζ⁴⁴−ζ⁵²	−ζ⁴+ζ⁴⁴−ζ⁵²	ζ⁴+ζ⁶⁸	ζ⁴+ζ⁶⁸	−ζ⁴⁴+ζ⁵²−ζ⁶⁸	−ζ⁴⁴+ζ⁵²−ζ⁶⁸	0	$- i \sqrt{3}$	$i \sqrt{3}$	ζ⁴+ζ⁴⁴+ζ⁵²	−ζ⁴+ζ⁶⁸	−ζ⁴⁴−ζ⁵²−ζ⁶⁸	−ζ⁴−ζ⁴⁴−ζ⁵²	ζ⁴−ζ⁶⁸	ζ⁴⁴+ζ⁵²+ζ⁶⁸	0	0	0	0	0
χ₂₃	2	2	-1	2	-2	-1	2	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	-1	-1	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	1	-2	1	1	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	−ζ⁴+ζ⁴⁴−ζ⁵²	ζ⁴+ζ⁶⁸	−ζ⁴⁴+ζ⁵²−ζ⁶⁸	−ζ⁴+ζ⁴⁴−ζ⁵²	−ζ⁴+ζ⁴⁴−ζ⁵²	ζ⁴+ζ⁶⁸	ζ⁴+ζ⁶⁸	−ζ⁴⁴+ζ⁵²−ζ⁶⁸	−ζ⁴⁴+ζ⁵²−ζ⁶⁸	0	$i \sqrt{3}$	$- i \sqrt{3}$	−ζ⁴−ζ⁴⁴−ζ⁵²	ζ⁴−ζ⁶⁸	ζ⁴⁴+ζ⁵²+ζ⁶⁸	ζ⁴+ζ⁴⁴+ζ⁵²	−ζ⁴+ζ⁶⁸	−ζ⁴⁴−ζ⁵²−ζ⁶⁸	0	0	0	0	0
χ₂₄	2	2	-1	2	-2	-1	2	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	-1	-1	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	1	-2	1	1	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	ζ⁴+ζ⁶⁸	−ζ⁴⁴+ζ⁵²−ζ⁶⁸	−ζ⁴+ζ⁴⁴−ζ⁵²	ζ⁴+ζ⁶⁸	ζ⁴+ζ⁶⁸	−ζ⁴⁴+ζ⁵²−ζ⁶⁸	−ζ⁴⁴+ζ⁵²−ζ⁶⁸	−ζ⁴+ζ⁴⁴−ζ⁵²	−ζ⁴+ζ⁴⁴−ζ⁵²	0	$- i \sqrt{3}$	$i \sqrt{3}$	−ζ⁴+ζ⁶⁸	−ζ⁴⁴−ζ⁵²−ζ⁶⁸	ζ⁴+ζ⁴⁴+ζ⁵²	ζ⁴−ζ⁶⁸	ζ⁴⁴+ζ⁵²+ζ⁶⁸	−ζ⁴−ζ⁴⁴−ζ⁵²	0	0	0	0	0
χ₂₅	2	2	-1	2	-2	-1	2	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	-1	-1	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	1	-2	1	1	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	ζ⁴+ζ⁶⁸	−ζ⁴⁴+ζ⁵²−ζ⁶⁸	−ζ⁴+ζ⁴⁴−ζ⁵²	ζ⁴+ζ⁶⁸	ζ⁴+ζ⁶⁸	−ζ⁴⁴+ζ⁵²−ζ⁶⁸	−ζ⁴⁴+ζ⁵²−ζ⁶⁸	−ζ⁴+ζ⁴⁴−ζ⁵²	−ζ⁴+ζ⁴⁴−ζ⁵²	0	$i \sqrt{3}$	$- i \sqrt{3}$	ζ⁴−ζ⁶⁸	ζ⁴⁴+ζ⁵²+ζ⁶⁸	−ζ⁴−ζ⁴⁴−ζ⁵²	−ζ⁴+ζ⁶⁸	−ζ⁴⁴−ζ⁵²−ζ⁶⁸	ζ⁴+ζ⁴⁴+ζ⁵²	0	0	0	0	0
χ₂₆	2	-2	2	2	0	-2	-2	2	2	2	-2	-2	-2	2	-2	2	2	2	0	0	0	0	-2	-2	-2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	$\sqrt{2}$	$- \sqrt{2}$
χ₂₇	2	-2	2	2	0	-2	-2	2	2	2	-2	-2	-2	2	-2	2	2	2	0	0	0	0	-2	-2	-2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	$- \sqrt{2}$	$\sqrt{2}$
χ₂₈	4	4	4	-2	4	4	-2	-2	-2	-2	-2	-2	-2	-2	-2	1	1	1	4	-2	-2	-2	1	1	1	-2	-2	-2	1	1	1	1	1	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₉	4	4	4	-2	-4	4	-2	-2	-2	-2	-2	-2	-2	-2	-2	1	1	1	-4	2	2	2	1	1	1	2	2	2	-1	-1	-1	-1	-1	-1	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₀	4	4	-2	-2	4	-2	-2	2ζ⁴⁴−2ζ⁵²+2ζ⁶⁸	2ζ⁴−2ζ⁴⁴+2ζ⁵²	−2ζ⁴−2ζ⁶⁸	2ζ⁴⁴−2ζ⁵²+2ζ⁶⁸	2ζ⁴−2ζ⁴⁴+2ζ⁵²	−2ζ⁴−2ζ⁶⁸	1	1	−ζ⁴⁴+ζ⁵²−ζ⁶⁸	−ζ⁴+ζ⁴⁴−ζ⁵²	ζ⁴+ζ⁶⁸	-2	-2	1	1	−ζ⁴⁴+ζ⁵²−ζ⁶⁸	−ζ⁴+ζ⁴⁴−ζ⁵²	ζ⁴+ζ⁶⁸	2ζ⁴⁴−2ζ⁵²+2ζ⁶⁸	2ζ⁴−2ζ⁴⁴+2ζ⁵²	−2ζ⁴−2ζ⁶⁸	−ζ⁴⁴+ζ⁵²−ζ⁶⁸	−ζ⁴⁴+ζ⁵²−ζ⁶⁸	−ζ⁴+ζ⁴⁴−ζ⁵²	−ζ⁴+ζ⁴⁴−ζ⁵²	ζ⁴+ζ⁶⁸	ζ⁴+ζ⁶⁸	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₁	4	4	-2	-2	4	-2	-2	2ζ⁴−2ζ⁴⁴+2ζ⁵²	−2ζ⁴−2ζ⁶⁸	2ζ⁴⁴−2ζ⁵²+2ζ⁶⁸	2ζ⁴−2ζ⁴⁴+2ζ⁵²	−2ζ⁴−2ζ⁶⁸	2ζ⁴⁴−2ζ⁵²+2ζ⁶⁸	1	1	−ζ⁴+ζ⁴⁴−ζ⁵²	ζ⁴+ζ⁶⁸	−ζ⁴⁴+ζ⁵²−ζ⁶⁸	-2	-2	1	1	−ζ⁴+ζ⁴⁴−ζ⁵²	ζ⁴+ζ⁶⁸	−ζ⁴⁴+ζ⁵²−ζ⁶⁸	2ζ⁴−2ζ⁴⁴+2ζ⁵²	−2ζ⁴−2ζ⁶⁸	2ζ⁴⁴−2ζ⁵²+2ζ⁶⁸	−ζ⁴+ζ⁴⁴−ζ⁵²	−ζ⁴+ζ⁴⁴−ζ⁵²	ζ⁴+ζ⁶⁸	ζ⁴+ζ⁶⁸	−ζ⁴⁴+ζ⁵²−ζ⁶⁸	−ζ⁴⁴+ζ⁵²−ζ⁶⁸	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₂	4	4	-2	-2	4	-2	-2	−2ζ⁴−2ζ⁶⁸	2ζ⁴⁴−2ζ⁵²+2ζ⁶⁸	2ζ⁴−2ζ⁴⁴+2ζ⁵²	−2ζ⁴−2ζ⁶⁸	2ζ⁴⁴−2ζ⁵²+2ζ⁶⁸	2ζ⁴−2ζ⁴⁴+2ζ⁵²	1	1	ζ⁴+ζ⁶⁸	−ζ⁴⁴+ζ⁵²−ζ⁶⁸	−ζ⁴+ζ⁴⁴−ζ⁵²	-2	-2	1	1	ζ⁴+ζ⁶⁸	−ζ⁴⁴+ζ⁵²−ζ⁶⁸	−ζ⁴+ζ⁴⁴−ζ⁵²	−2ζ⁴−2ζ⁶⁸	2ζ⁴⁴−2ζ⁵²+2ζ⁶⁸	2ζ⁴−2ζ⁴⁴+2ζ⁵²	ζ⁴+ζ⁶⁸	ζ⁴+ζ⁶⁸	−ζ⁴⁴+ζ⁵²−ζ⁶⁸	−ζ⁴⁴+ζ⁵²−ζ⁶⁸	−ζ⁴+ζ⁴⁴−ζ⁵²	−ζ⁴+ζ⁴⁴−ζ⁵²	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₃	4	4	-2	-2	-4	-2	-2	2ζ⁴⁴−2ζ⁵²+2ζ⁶⁸	2ζ⁴−2ζ⁴⁴+2ζ⁵²	−2ζ⁴−2ζ⁶⁸	2ζ⁴⁴−2ζ⁵²+2ζ⁶⁸	2ζ⁴−2ζ⁴⁴+2ζ⁵²	−2ζ⁴−2ζ⁶⁸	1	1	−ζ⁴⁴+ζ⁵²−ζ⁶⁸	−ζ⁴+ζ⁴⁴−ζ⁵²	ζ⁴+ζ⁶⁸	2	2	-1	-1	−ζ⁴⁴+ζ⁵²−ζ⁶⁸	−ζ⁴+ζ⁴⁴−ζ⁵²	ζ⁴+ζ⁶⁸	−2ζ⁴⁴+2ζ⁵²−2ζ⁶⁸	−2ζ⁴+2ζ⁴⁴−2ζ⁵²	2ζ⁴+2ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	−ζ⁴−ζ⁶⁸	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₄	4	4	-2	-2	-4	-2	-2	2ζ⁴−2ζ⁴⁴+2ζ⁵²	−2ζ⁴−2ζ⁶⁸	2ζ⁴⁴−2ζ⁵²+2ζ⁶⁸	2ζ⁴−2ζ⁴⁴+2ζ⁵²	−2ζ⁴−2ζ⁶⁸	2ζ⁴⁴−2ζ⁵²+2ζ⁶⁸	1	1	−ζ⁴+ζ⁴⁴−ζ⁵²	ζ⁴+ζ⁶⁸	−ζ⁴⁴+ζ⁵²−ζ⁶⁸	2	2	-1	-1	−ζ⁴+ζ⁴⁴−ζ⁵²	ζ⁴+ζ⁶⁸	−ζ⁴⁴+ζ⁵²−ζ⁶⁸	−2ζ⁴+2ζ⁴⁴−2ζ⁵²	2ζ⁴+2ζ⁶⁸	−2ζ⁴⁴+2ζ⁵²−2ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₅	4	4	-2	-2	-4	-2	-2	−2ζ⁴−2ζ⁶⁸	2ζ⁴⁴−2ζ⁵²+2ζ⁶⁸	2ζ⁴−2ζ⁴⁴+2ζ⁵²	−2ζ⁴−2ζ⁶⁸	2ζ⁴⁴−2ζ⁵²+2ζ⁶⁸	2ζ⁴−2ζ⁴⁴+2ζ⁵²	1	1	ζ⁴+ζ⁶⁸	−ζ⁴⁴+ζ⁵²−ζ⁶⁸	−ζ⁴+ζ⁴⁴−ζ⁵²	2	2	-1	-1	ζ⁴+ζ⁶⁸	−ζ⁴⁴+ζ⁵²−ζ⁶⁸	−ζ⁴+ζ⁴⁴−ζ⁵²	2ζ⁴+2ζ⁶⁸	−2ζ⁴⁴+2ζ⁵²−2ζ⁶⁸	−2ζ⁴+2ζ⁴⁴−2ζ⁵²	−ζ⁴−ζ⁶⁸	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	ζ⁴−ζ⁴⁴+ζ⁵²	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₆	4	-4	4	4	0	-4	-4	-2	-2	-2	2	2	2	4	-4	-2	-2	-2	0	0	0	0	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
χ₃₇	4	-4	4	-2	0	-4	2	4	4	4	-4	-4	-4	-2	2	-2	-2	-2	0	0	0	0	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
χ₃₈	4	-4	4	-2	0	-4	2	-2	-2	-2	2	2	2	-2	2	1	1	1	0	0	0	0	-1	-1	-1	0	0	0	$3 i$	$- 3 i$	$3 i$	$- 3 i$	$3 i$	$- 3 i$	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₉	4	-4	4	-2	0	-4	2	-2	-2	-2	2	2	2	-2	2	1	1	1	0	0	0	0	-1	-1	-1	0	0	0	$- 3 i$	$3 i$	$- 3 i$	$3 i$	$- 3 i$	$3 i$	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₀	4	-4	-2	4	0	2	-4	2ζ⁴⁴−2ζ⁵²+2ζ⁶⁸	2ζ⁴−2ζ⁴⁴+2ζ⁵²	−2ζ⁴−2ζ⁶⁸	−2ζ⁴⁴+2ζ⁵²−2ζ⁶⁸	−2ζ⁴+2ζ⁴⁴−2ζ⁵²	2ζ⁴+2ζ⁶⁸	-2	2	2ζ⁴⁴−2ζ⁵²+2ζ⁶⁸	2ζ⁴−2ζ⁴⁴+2ζ⁵²	−2ζ⁴−2ζ⁶⁸	0	0	0	0	−2ζ⁴⁴+2ζ⁵²−2ζ⁶⁸	−2ζ⁴+2ζ⁴⁴−2ζ⁵²	2ζ⁴+2ζ⁶⁸	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₁	4	-4	-2	4	0	2	-4	2ζ⁴−2ζ⁴⁴+2ζ⁵²	−2ζ⁴−2ζ⁶⁸	2ζ⁴⁴−2ζ⁵²+2ζ⁶⁸	−2ζ⁴+2ζ⁴⁴−2ζ⁵²	2ζ⁴+2ζ⁶⁸	−2ζ⁴⁴+2ζ⁵²−2ζ⁶⁸	-2	2	2ζ⁴−2ζ⁴⁴+2ζ⁵²	−2ζ⁴−2ζ⁶⁸	2ζ⁴⁴−2ζ⁵²+2ζ⁶⁸	0	0	0	0	−2ζ⁴+2ζ⁴⁴−2ζ⁵²	2ζ⁴+2ζ⁶⁸	−2ζ⁴⁴+2ζ⁵²−2ζ⁶⁸	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₂	4	-4	-2	4	0	2	-4	−2ζ⁴−2ζ⁶⁸	2ζ⁴⁴−2ζ⁵²+2ζ⁶⁸	2ζ⁴−2ζ⁴⁴+2ζ⁵²	2ζ⁴+2ζ⁶⁸	−2ζ⁴⁴+2ζ⁵²−2ζ⁶⁸	−2ζ⁴+2ζ⁴⁴−2ζ⁵²	-2	2	−2ζ⁴−2ζ⁶⁸	2ζ⁴⁴−2ζ⁵²+2ζ⁶⁸	2ζ⁴−2ζ⁴⁴+2ζ⁵²	0	0	0	0	2ζ⁴+2ζ⁶⁸	−2ζ⁴⁴+2ζ⁵²−2ζ⁶⁸	−2ζ⁴+2ζ⁴⁴−2ζ⁵²	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₃	4	-4	-2	-2	0	2	2	2ζ⁴⁴−2ζ⁵²+2ζ⁶⁸	2ζ⁴−2ζ⁴⁴+2ζ⁵²	−2ζ⁴−2ζ⁶⁸	−2ζ⁴⁴+2ζ⁵²−2ζ⁶⁸	−2ζ⁴+2ζ⁴⁴−2ζ⁵²	2ζ⁴+2ζ⁶⁸	1	-1	−ζ⁴⁴+ζ⁵²−ζ⁶⁸	−ζ⁴+ζ⁴⁴−ζ⁵²	ζ⁴+ζ⁶⁸	0	0	$3 i$	$- 3 i$	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	0	0	0	−ζ¹⁴−2ζ²²+ζ⁶²−ζ⁷⁰	ζ¹⁴+2ζ²²−ζ⁶²+ζ⁷⁰	2ζ¹⁴+ζ²²+ζ⁶²−ζ⁷⁰	−2ζ¹⁴−ζ²²−ζ⁶²+ζ⁷⁰	−ζ¹⁴+ζ²²−2ζ⁶²+2ζ⁷⁰	ζ¹⁴−ζ²²+2ζ⁶²−2ζ⁷⁰	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₄	4	-4	-2	-2	0	2	2	2ζ⁴⁴−2ζ⁵²+2ζ⁶⁸	2ζ⁴−2ζ⁴⁴+2ζ⁵²	−2ζ⁴−2ζ⁶⁸	−2ζ⁴⁴+2ζ⁵²−2ζ⁶⁸	−2ζ⁴+2ζ⁴⁴−2ζ⁵²	2ζ⁴+2ζ⁶⁸	1	-1	−ζ⁴⁴+ζ⁵²−ζ⁶⁸	−ζ⁴+ζ⁴⁴−ζ⁵²	ζ⁴+ζ⁶⁸	0	0	$- 3 i$	$3 i$	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	0	0	0	ζ¹⁴+2ζ²²−ζ⁶²+ζ⁷⁰	−ζ¹⁴−2ζ²²+ζ⁶²−ζ⁷⁰	−2ζ¹⁴−ζ²²−ζ⁶²+ζ⁷⁰	2ζ¹⁴+ζ²²+ζ⁶²−ζ⁷⁰	ζ¹⁴−ζ²²+2ζ⁶²−2ζ⁷⁰	−ζ¹⁴+ζ²²−2ζ⁶²+2ζ⁷⁰	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₅	4	-4	-2	-2	0	2	2	2ζ⁴−2ζ⁴⁴+2ζ⁵²	−2ζ⁴−2ζ⁶⁸	2ζ⁴⁴−2ζ⁵²+2ζ⁶⁸	−2ζ⁴+2ζ⁴⁴−2ζ⁵²	2ζ⁴+2ζ⁶⁸	−2ζ⁴⁴+2ζ⁵²−2ζ⁶⁸	1	-1	−ζ⁴+ζ⁴⁴−ζ⁵²	ζ⁴+ζ⁶⁸	−ζ⁴⁴+ζ⁵²−ζ⁶⁸	0	0	$3 i$	$- 3 i$	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	0	0	0	2ζ¹⁴+ζ²²+ζ⁶²−ζ⁷⁰	−2ζ¹⁴−ζ²²−ζ⁶²+ζ⁷⁰	−ζ¹⁴+ζ²²−2ζ⁶²+2ζ⁷⁰	ζ¹⁴−ζ²²+2ζ⁶²−2ζ⁷⁰	−ζ¹⁴−2ζ²²+ζ⁶²−ζ⁷⁰	ζ¹⁴+2ζ²²−ζ⁶²+ζ⁷⁰	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₆	4	-4	-2	-2	0	2	2	2ζ⁴−2ζ⁴⁴+2ζ⁵²	−2ζ⁴−2ζ⁶⁸	2ζ⁴⁴−2ζ⁵²+2ζ⁶⁸	−2ζ⁴+2ζ⁴⁴−2ζ⁵²	2ζ⁴+2ζ⁶⁸	−2ζ⁴⁴+2ζ⁵²−2ζ⁶⁸	1	-1	−ζ⁴+ζ⁴⁴−ζ⁵²	ζ⁴+ζ⁶⁸	−ζ⁴⁴+ζ⁵²−ζ⁶⁸	0	0	$- 3 i$	$3 i$	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	0	0	0	−2ζ¹⁴−ζ²²−ζ⁶²+ζ⁷⁰	2ζ¹⁴+ζ²²+ζ⁶²−ζ⁷⁰	ζ¹⁴−ζ²²+2ζ⁶²−2ζ⁷⁰	−ζ¹⁴+ζ²²−2ζ⁶²+2ζ⁷⁰	ζ¹⁴+2ζ²²−ζ⁶²+ζ⁷⁰	−ζ¹⁴−2ζ²²+ζ⁶²−ζ⁷⁰	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₇	4	-4	-2	-2	0	2	2	−2ζ⁴−2ζ⁶⁸	2ζ⁴⁴−2ζ⁵²+2ζ⁶⁸	2ζ⁴−2ζ⁴⁴+2ζ⁵²	2ζ⁴+2ζ⁶⁸	−2ζ⁴⁴+2ζ⁵²−2ζ⁶⁸	−2ζ⁴+2ζ⁴⁴−2ζ⁵²	1	-1	ζ⁴+ζ⁶⁸	−ζ⁴⁴+ζ⁵²−ζ⁶⁸	−ζ⁴+ζ⁴⁴−ζ⁵²	0	0	$3 i$	$- 3 i$	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	0	0	0	−ζ¹⁴+ζ²²−2ζ⁶²+2ζ⁷⁰	ζ¹⁴−ζ²²+2ζ⁶²−2ζ⁷⁰	−ζ¹⁴−2ζ²²+ζ⁶²−ζ⁷⁰	ζ¹⁴+2ζ²²−ζ⁶²+ζ⁷⁰	2ζ¹⁴+ζ²²+ζ⁶²−ζ⁷⁰	−2ζ¹⁴−ζ²²−ζ⁶²+ζ⁷⁰	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₈	4	-4	-2	-2	0	2	2	−2ζ⁴−2ζ⁶⁸	2ζ⁴⁴−2ζ⁵²+2ζ⁶⁸	2ζ⁴−2ζ⁴⁴+2ζ⁵²	2ζ⁴+2ζ⁶⁸	−2ζ⁴⁴+2ζ⁵²−2ζ⁶⁸	−2ζ⁴+2ζ⁴⁴−2ζ⁵²	1	-1	ζ⁴+ζ⁶⁸	−ζ⁴⁴+ζ⁵²−ζ⁶⁸	−ζ⁴+ζ⁴⁴−ζ⁵²	0	0	$- 3 i$	$3 i$	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	0	0	0	ζ¹⁴−ζ²²+2ζ⁶²−2ζ⁷⁰	−ζ¹⁴+ζ²²−2ζ⁶²+2ζ⁷⁰	ζ¹⁴+2ζ²²−ζ⁶²+ζ⁷⁰	−ζ¹⁴−2ζ²²+ζ⁶²−ζ⁷⁰	−2ζ¹⁴−ζ²²−ζ⁶²+ζ⁷⁰	2ζ¹⁴+ζ²²+ζ⁶²−ζ⁷⁰	0	0	0	0	0	0	0	0	0	0	0	0	0	0

Character table — Group #88421