Group #1233 — 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
size	1	3	4	4	1	3	4	4	1	3	4	4	1	3	4	4	1	3	4	4	1	3	4	4	1	3	4	4	1	3	4	4	1	3	4	4	1	3	4	4
order	1	2	3	3	5	10	15	15	5	10	15	15	5	10	15	15	5	10	15	15	2	2	6	6	10	10	30	30	10	10	30	30	10	10	30	30	10	10	30	30
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
χ₂	1	1	$\frac{- 1 + i \sqrt{3}}{2}$	$\frac{- 1 - i \sqrt{3}}{2}$	1	1	$\frac{- 1 + i \sqrt{3}}{2}$	$\frac{- 1 - i \sqrt{3}}{2}$	1	1	$\frac{- 1 + i \sqrt{3}}{2}$	$\frac{- 1 - i \sqrt{3}}{2}$	1	1	$\frac{- 1 + i \sqrt{3}}{2}$	$\frac{- 1 - i \sqrt{3}}{2}$	1	1	$\frac{- 1 + i \sqrt{3}}{2}$	$\frac{- 1 - i \sqrt{3}}{2}$	1	1	$\frac{- 1 + i \sqrt{3}}{2}$	$\frac{- 1 - i \sqrt{3}}{2}$	1	1	$\frac{- 1 + i \sqrt{3}}{2}$	$\frac{- 1 - i \sqrt{3}}{2}$	1	1	$\frac{- 1 + i \sqrt{3}}{2}$	$\frac{- 1 - i \sqrt{3}}{2}$	1	1	$\frac{- 1 + i \sqrt{3}}{2}$	$\frac{- 1 - i \sqrt{3}}{2}$	1	1	$\frac{- 1 + i \sqrt{3}}{2}$	$\frac{- 1 - i \sqrt{3}}{2}$
χ₃	1	1	$\frac{- 1 - i \sqrt{3}}{2}$	$\frac{- 1 + i \sqrt{3}}{2}$	1	1	$\frac{- 1 - i \sqrt{3}}{2}$	$\frac{- 1 + i \sqrt{3}}{2}$	1	1	$\frac{- 1 - i \sqrt{3}}{2}$	$\frac{- 1 + i \sqrt{3}}{2}$	1	1	$\frac{- 1 - i \sqrt{3}}{2}$	$\frac{- 1 + i \sqrt{3}}{2}$	1	1	$\frac{- 1 - i \sqrt{3}}{2}$	$\frac{- 1 + i \sqrt{3}}{2}$	1	1	$\frac{- 1 - i \sqrt{3}}{2}$	$\frac{- 1 + i \sqrt{3}}{2}$	1	1	$\frac{- 1 - i \sqrt{3}}{2}$	$\frac{- 1 + i \sqrt{3}}{2}$	1	1	$\frac{- 1 - i \sqrt{3}}{2}$	$\frac{- 1 + i \sqrt{3}}{2}$	1	1	$\frac{- 1 - i \sqrt{3}}{2}$	$\frac{- 1 + i \sqrt{3}}{2}$	1	1	$\frac{- 1 - i \sqrt{3}}{2}$	$\frac{- 1 + i \sqrt{3}}{2}$
χ₄	3	-1	0	0	3	-1	0	0	3	-1	0	0	3	-1	0	0	3	-1	0	0	3	-1	0	0	3	-1	0	0	3	-1	0	0	3	-1	0	0	3	-1	0	0
χ₅	1	1	1	1	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	1	1	1	1	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷
χ₆	1	1	$\frac{- 1 + i \sqrt{3}}{2}$	$\frac{- 1 - i \sqrt{3}}{2}$	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	ζ⁸	ζ¹³	−ζ−ζ¹¹	−ζ−ζ¹¹	ζ¹¹	ζ	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	ζ¹⁴	ζ⁴	−ζ²−ζ⁷	−ζ²−ζ⁷	ζ²	ζ⁷	1	1	$\frac{- 1 + i \sqrt{3}}{2}$	$\frac{- 1 - i \sqrt{3}}{2}$	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	ζ⁸	ζ¹³	−ζ−ζ¹¹	−ζ−ζ¹¹	ζ¹¹	ζ	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	ζ¹⁴	ζ⁴	−ζ²−ζ⁷	−ζ²−ζ⁷	ζ²	ζ⁷
χ₇	1	1	$\frac{- 1 - i \sqrt{3}}{2}$	$\frac{- 1 + i \sqrt{3}}{2}$	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	ζ¹³	ζ⁸	−ζ−ζ¹¹	−ζ−ζ¹¹	ζ	ζ¹¹	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	ζ⁴	ζ¹⁴	−ζ²−ζ⁷	−ζ²−ζ⁷	ζ⁷	ζ²	1	1	$\frac{- 1 - i \sqrt{3}}{2}$	$\frac{- 1 + i \sqrt{3}}{2}$	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	ζ¹³	ζ⁸	−ζ−ζ¹¹	−ζ−ζ¹¹	ζ	ζ¹¹	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	ζ⁴	ζ¹⁴	−ζ²−ζ⁷	−ζ²−ζ⁷	ζ⁷	ζ²
χ₈	3	-1	0	0	−3ζ⁸−3ζ¹³	ζ⁸+ζ¹³	0	0	−3ζ−3ζ¹¹	ζ+ζ¹¹	0	0	−3ζ⁴−3ζ¹⁴	ζ⁴+ζ¹⁴	0	0	−3ζ²−3ζ⁷	ζ²+ζ⁷	0	0	3	-1	0	0	−3ζ⁸−3ζ¹³	ζ⁸+ζ¹³	0	0	−3ζ−3ζ¹¹	ζ+ζ¹¹	0	0	−3ζ⁴−3ζ¹⁴	ζ⁴+ζ¹⁴	0	0	−3ζ²−3ζ⁷	ζ²+ζ⁷	0	0
χ₉	1	1	1	1	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	1	1	1	1	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴
χ₁₀	1	1	$\frac{- 1 + i \sqrt{3}}{2}$	$\frac{- 1 - i \sqrt{3}}{2}$	−ζ−ζ¹¹	−ζ−ζ¹¹	ζ¹¹	ζ	−ζ²−ζ⁷	−ζ²−ζ⁷	ζ²	ζ⁷	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	ζ⁸	ζ¹³	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	ζ¹⁴	ζ⁴	1	1	$\frac{- 1 + i \sqrt{3}}{2}$	$\frac{- 1 - i \sqrt{3}}{2}$	−ζ−ζ¹¹	−ζ−ζ¹¹	ζ¹¹	ζ	−ζ²−ζ⁷	−ζ²−ζ⁷	ζ²	ζ⁷	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	ζ⁸	ζ¹³	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	ζ¹⁴	ζ⁴
χ₁₁	1	1	$\frac{- 1 - i \sqrt{3}}{2}$	$\frac{- 1 + i \sqrt{3}}{2}$	−ζ−ζ¹¹	−ζ−ζ¹¹	ζ	ζ¹¹	−ζ²−ζ⁷	−ζ²−ζ⁷	ζ⁷	ζ²	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	ζ¹³	ζ⁸	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	ζ⁴	ζ¹⁴	1	1	$\frac{- 1 - i \sqrt{3}}{2}$	$\frac{- 1 + i \sqrt{3}}{2}$	−ζ−ζ¹¹	−ζ−ζ¹¹	ζ	ζ¹¹	−ζ²−ζ⁷	−ζ²−ζ⁷	ζ⁷	ζ²	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	ζ¹³	ζ⁸	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	ζ⁴	ζ¹⁴
χ₁₂	3	-1	0	0	−3ζ−3ζ¹¹	ζ+ζ¹¹	0	0	−3ζ²−3ζ⁷	ζ²+ζ⁷	0	0	−3ζ⁸−3ζ¹³	ζ⁸+ζ¹³	0	0	−3ζ⁴−3ζ¹⁴	ζ⁴+ζ¹⁴	0	0	3	-1	0	0	−3ζ−3ζ¹¹	ζ+ζ¹¹	0	0	−3ζ²−3ζ⁷	ζ²+ζ⁷	0	0	−3ζ⁸−3ζ¹³	ζ⁸+ζ¹³	0	0	−3ζ⁴−3ζ¹⁴	ζ⁴+ζ¹⁴	0	0
χ₁₃	1	1	1	1	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	1	1	1	1	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹
χ₁₄	1	1	$\frac{- 1 + i \sqrt{3}}{2}$	$\frac{- 1 - i \sqrt{3}}{2}$	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	ζ¹⁴	ζ⁴	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	ζ⁸	ζ¹³	−ζ²−ζ⁷	−ζ²−ζ⁷	ζ²	ζ⁷	−ζ−ζ¹¹	−ζ−ζ¹¹	ζ¹¹	ζ	1	1	$\frac{- 1 + i \sqrt{3}}{2}$	$\frac{- 1 - i \sqrt{3}}{2}$	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	ζ¹⁴	ζ⁴	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	ζ⁸	ζ¹³	−ζ²−ζ⁷	−ζ²−ζ⁷	ζ²	ζ⁷	−ζ−ζ¹¹	−ζ−ζ¹¹	ζ¹¹	ζ
χ₁₅	1	1	$\frac{- 1 - i \sqrt{3}}{2}$	$\frac{- 1 + i \sqrt{3}}{2}$	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	ζ⁴	ζ¹⁴	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	ζ¹³	ζ⁸	−ζ²−ζ⁷	−ζ²−ζ⁷	ζ⁷	ζ²	−ζ−ζ¹¹	−ζ−ζ¹¹	ζ	ζ¹¹	1	1	$\frac{- 1 - i \sqrt{3}}{2}$	$\frac{- 1 + i \sqrt{3}}{2}$	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	ζ⁴	ζ¹⁴	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	ζ¹³	ζ⁸	−ζ²−ζ⁷	−ζ²−ζ⁷	ζ⁷	ζ²	−ζ−ζ¹¹	−ζ−ζ¹¹	ζ	ζ¹¹
χ₁₆	3	-1	0	0	−3ζ⁴−3ζ¹⁴	ζ⁴+ζ¹⁴	0	0	−3ζ⁸−3ζ¹³	ζ⁸+ζ¹³	0	0	−3ζ²−3ζ⁷	ζ²+ζ⁷	0	0	−3ζ−3ζ¹¹	ζ+ζ¹¹	0	0	3	-1	0	0	−3ζ⁴−3ζ¹⁴	ζ⁴+ζ¹⁴	0	0	−3ζ⁸−3ζ¹³	ζ⁸+ζ¹³	0	0	−3ζ²−3ζ⁷	ζ²+ζ⁷	0	0	−3ζ−3ζ¹¹	ζ+ζ¹¹	0	0
χ₁₇	1	1	1	1	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	1	1	1	1	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³
χ₁₈	1	1	$\frac{- 1 + i \sqrt{3}}{2}$	$\frac{- 1 - i \sqrt{3}}{2}$	−ζ²−ζ⁷	−ζ²−ζ⁷	ζ²	ζ⁷	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	ζ¹⁴	ζ⁴	−ζ−ζ¹¹	−ζ−ζ¹¹	ζ¹¹	ζ	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	ζ⁸	ζ¹³	1	1	$\frac{- 1 + i \sqrt{3}}{2}$	$\frac{- 1 - i \sqrt{3}}{2}$	−ζ²−ζ⁷	−ζ²−ζ⁷	ζ²	ζ⁷	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	ζ¹⁴	ζ⁴	−ζ−ζ¹¹	−ζ−ζ¹¹	ζ¹¹	ζ	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	ζ⁸	ζ¹³
χ₁₉	1	1	$\frac{- 1 - i \sqrt{3}}{2}$	$\frac{- 1 + i \sqrt{3}}{2}$	−ζ²−ζ⁷	−ζ²−ζ⁷	ζ⁷	ζ²	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	ζ⁴	ζ¹⁴	−ζ−ζ¹¹	−ζ−ζ¹¹	ζ	ζ¹¹	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	ζ¹³	ζ⁸	1	1	$\frac{- 1 - i \sqrt{3}}{2}$	$\frac{- 1 + i \sqrt{3}}{2}$	−ζ²−ζ⁷	−ζ²−ζ⁷	ζ⁷	ζ²	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	ζ⁴	ζ¹⁴	−ζ−ζ¹¹	−ζ−ζ¹¹	ζ	ζ¹¹	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	ζ¹³	ζ⁸
χ₂₀	3	-1	0	0	−3ζ²−3ζ⁷	ζ²+ζ⁷	0	0	−3ζ⁴−3ζ¹⁴	ζ⁴+ζ¹⁴	0	0	−3ζ−3ζ¹¹	ζ+ζ¹¹	0	0	−3ζ⁸−3ζ¹³	ζ⁸+ζ¹³	0	0	3	-1	0	0	−3ζ²−3ζ⁷	ζ²+ζ⁷	0	0	−3ζ⁴−3ζ¹⁴	ζ⁴+ζ¹⁴	0	0	−3ζ−3ζ¹¹	ζ+ζ¹¹	0	0	−3ζ⁸−3ζ¹³	ζ⁸+ζ¹³	0	0
χ₂₁	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
χ₂₂	1	1	$\frac{- 1 + i \sqrt{3}}{2}$	$\frac{- 1 - i \sqrt{3}}{2}$	1	1	$\frac{- 1 + i \sqrt{3}}{2}$	$\frac{- 1 - i \sqrt{3}}{2}$	1	1	$\frac{- 1 + i \sqrt{3}}{2}$	$\frac{- 1 - i \sqrt{3}}{2}$	1	1	$\frac{- 1 + i \sqrt{3}}{2}$	$\frac{- 1 - i \sqrt{3}}{2}$	1	1	$\frac{- 1 + i \sqrt{3}}{2}$	$\frac{- 1 - i \sqrt{3}}{2}$	-1	-1	$\frac{1 - i \sqrt{3}}{2}$	$\frac{1 + i \sqrt{3}}{2}$	-1	-1	$\frac{1 - i \sqrt{3}}{2}$	$\frac{1 + i \sqrt{3}}{2}$	-1	-1	$\frac{1 - i \sqrt{3}}{2}$	$\frac{1 + i \sqrt{3}}{2}$	-1	-1	$\frac{1 - i \sqrt{3}}{2}$	$\frac{1 + i \sqrt{3}}{2}$	-1	-1	$\frac{1 - i \sqrt{3}}{2}$	$\frac{1 + i \sqrt{3}}{2}$
χ₂₃	1	1	$\frac{- 1 - i \sqrt{3}}{2}$	$\frac{- 1 + i \sqrt{3}}{2}$	1	1	$\frac{- 1 - i \sqrt{3}}{2}$	$\frac{- 1 + i \sqrt{3}}{2}$	1	1	$\frac{- 1 - i \sqrt{3}}{2}$	$\frac{- 1 + i \sqrt{3}}{2}$	1	1	$\frac{- 1 - i \sqrt{3}}{2}$	$\frac{- 1 + i \sqrt{3}}{2}$	1	1	$\frac{- 1 - i \sqrt{3}}{2}$	$\frac{- 1 + i \sqrt{3}}{2}$	-1	-1	$\frac{1 + i \sqrt{3}}{2}$	$\frac{1 - i \sqrt{3}}{2}$	-1	-1	$\frac{1 + i \sqrt{3}}{2}$	$\frac{1 - i \sqrt{3}}{2}$	-1	-1	$\frac{1 + i \sqrt{3}}{2}$	$\frac{1 - i \sqrt{3}}{2}$	-1	-1	$\frac{1 + i \sqrt{3}}{2}$	$\frac{1 - i \sqrt{3}}{2}$	-1	-1	$\frac{1 + i \sqrt{3}}{2}$	$\frac{1 - i \sqrt{3}}{2}$
χ₂₄	3	-1	0	0	3	-1	0	0	3	-1	0	0	3	-1	0	0	3	-1	0	0	-3	1	0	0	-3	1	0	0	-3	1	0	0	-3	1	0	0	-3	1	0	0
χ₂₅	1	1	1	1	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	-1	-1	-1	-1	ζ⁸+ζ¹³	ζ⁸+ζ¹³	ζ⁸+ζ¹³	ζ⁸+ζ¹³	ζ+ζ¹¹	ζ+ζ¹¹	ζ+ζ¹¹	ζ+ζ¹¹	ζ⁴+ζ¹⁴	ζ⁴+ζ¹⁴	ζ⁴+ζ¹⁴	ζ⁴+ζ¹⁴	ζ²+ζ⁷	ζ²+ζ⁷	ζ²+ζ⁷	ζ²+ζ⁷
χ₂₆	1	1	$\frac{- 1 + i \sqrt{3}}{2}$	$\frac{- 1 - i \sqrt{3}}{2}$	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	ζ⁸	ζ¹³	−ζ−ζ¹¹	−ζ−ζ¹¹	ζ¹¹	ζ	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	ζ¹⁴	ζ⁴	−ζ²−ζ⁷	−ζ²−ζ⁷	ζ²	ζ⁷	-1	-1	$\frac{1 - i \sqrt{3}}{2}$	$\frac{1 + i \sqrt{3}}{2}$	ζ⁸+ζ¹³	ζ⁸+ζ¹³	−ζ⁸	−ζ¹³	ζ+ζ¹¹	ζ+ζ¹¹	−ζ¹¹	−ζ	ζ⁴+ζ¹⁴	ζ⁴+ζ¹⁴	−ζ¹⁴	−ζ⁴	ζ²+ζ⁷	ζ²+ζ⁷	−ζ²	−ζ⁷
χ₂₇	1	1	$\frac{- 1 - i \sqrt{3}}{2}$	$\frac{- 1 + i \sqrt{3}}{2}$	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	ζ¹³	ζ⁸	−ζ−ζ¹¹	−ζ−ζ¹¹	ζ	ζ¹¹	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	ζ⁴	ζ¹⁴	−ζ²−ζ⁷	−ζ²−ζ⁷	ζ⁷	ζ²	-1	-1	$\frac{1 + i \sqrt{3}}{2}$	$\frac{1 - i \sqrt{3}}{2}$	ζ⁸+ζ¹³	ζ⁸+ζ¹³	−ζ¹³	−ζ⁸	ζ+ζ¹¹	ζ+ζ¹¹	−ζ	−ζ¹¹	ζ⁴+ζ¹⁴	ζ⁴+ζ¹⁴	−ζ⁴	−ζ¹⁴	ζ²+ζ⁷	ζ²+ζ⁷	−ζ⁷	−ζ²
χ₂₈	3	-1	0	0	−3ζ⁸−3ζ¹³	ζ⁸+ζ¹³	0	0	−3ζ−3ζ¹¹	ζ+ζ¹¹	0	0	−3ζ⁴−3ζ¹⁴	ζ⁴+ζ¹⁴	0	0	−3ζ²−3ζ⁷	ζ²+ζ⁷	0	0	-3	1	0	0	3ζ⁸+3ζ¹³	−ζ⁸−ζ¹³	0	0	3ζ+3ζ¹¹	−ζ−ζ¹¹	0	0	3ζ⁴+3ζ¹⁴	−ζ⁴−ζ¹⁴	0	0	3ζ²+3ζ⁷	−ζ²−ζ⁷	0	0
χ₂₉	1	1	1	1	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	-1	-1	-1	-1	ζ+ζ¹¹	ζ+ζ¹¹	ζ+ζ¹¹	ζ+ζ¹¹	ζ²+ζ⁷	ζ²+ζ⁷	ζ²+ζ⁷	ζ²+ζ⁷	ζ⁸+ζ¹³	ζ⁸+ζ¹³	ζ⁸+ζ¹³	ζ⁸+ζ¹³	ζ⁴+ζ¹⁴	ζ⁴+ζ¹⁴	ζ⁴+ζ¹⁴	ζ⁴+ζ¹⁴
χ₃₀	1	1	$\frac{- 1 + i \sqrt{3}}{2}$	$\frac{- 1 - i \sqrt{3}}{2}$	−ζ−ζ¹¹	−ζ−ζ¹¹	ζ¹¹	ζ	−ζ²−ζ⁷	−ζ²−ζ⁷	ζ²	ζ⁷	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	ζ⁸	ζ¹³	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	ζ¹⁴	ζ⁴	-1	-1	$\frac{1 - i \sqrt{3}}{2}$	$\frac{1 + i \sqrt{3}}{2}$	ζ+ζ¹¹	ζ+ζ¹¹	−ζ¹¹	−ζ	ζ²+ζ⁷	ζ²+ζ⁷	−ζ²	−ζ⁷	ζ⁸+ζ¹³	ζ⁸+ζ¹³	−ζ⁸	−ζ¹³	ζ⁴+ζ¹⁴	ζ⁴+ζ¹⁴	−ζ¹⁴	−ζ⁴
χ₃₁	1	1	$\frac{- 1 - i \sqrt{3}}{2}$	$\frac{- 1 + i \sqrt{3}}{2}$	−ζ−ζ¹¹	−ζ−ζ¹¹	ζ	ζ¹¹	−ζ²−ζ⁷	−ζ²−ζ⁷	ζ⁷	ζ²	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	ζ¹³	ζ⁸	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	ζ⁴	ζ¹⁴	-1	-1	$\frac{1 + i \sqrt{3}}{2}$	$\frac{1 - i \sqrt{3}}{2}$	ζ+ζ¹¹	ζ+ζ¹¹	−ζ	−ζ¹¹	ζ²+ζ⁷	ζ²+ζ⁷	−ζ⁷	−ζ²	ζ⁸+ζ¹³	ζ⁸+ζ¹³	−ζ¹³	−ζ⁸	ζ⁴+ζ¹⁴	ζ⁴+ζ¹⁴	−ζ⁴	−ζ¹⁴
χ₃₂	3	-1	0	0	−3ζ−3ζ¹¹	ζ+ζ¹¹	0	0	−3ζ²−3ζ⁷	ζ²+ζ⁷	0	0	−3ζ⁸−3ζ¹³	ζ⁸+ζ¹³	0	0	−3ζ⁴−3ζ¹⁴	ζ⁴+ζ¹⁴	0	0	-3	1	0	0	3ζ+3ζ¹¹	−ζ−ζ¹¹	0	0	3ζ²+3ζ⁷	−ζ²−ζ⁷	0	0	3ζ⁸+3ζ¹³	−ζ⁸−ζ¹³	0	0	3ζ⁴+3ζ¹⁴	−ζ⁴−ζ¹⁴	0	0
χ₃₃	1	1	1	1	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	-1	-1	-1	-1	ζ⁴+ζ¹⁴	ζ⁴+ζ¹⁴	ζ⁴+ζ¹⁴	ζ⁴+ζ¹⁴	ζ⁸+ζ¹³	ζ⁸+ζ¹³	ζ⁸+ζ¹³	ζ⁸+ζ¹³	ζ²+ζ⁷	ζ²+ζ⁷	ζ²+ζ⁷	ζ²+ζ⁷	ζ+ζ¹¹	ζ+ζ¹¹	ζ+ζ¹¹	ζ+ζ¹¹
χ₃₄	1	1	$\frac{- 1 + i \sqrt{3}}{2}$	$\frac{- 1 - i \sqrt{3}}{2}$	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	ζ¹⁴	ζ⁴	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	ζ⁸	ζ¹³	−ζ²−ζ⁷	−ζ²−ζ⁷	ζ²	ζ⁷	−ζ−ζ¹¹	−ζ−ζ¹¹	ζ¹¹	ζ	-1	-1	$\frac{1 - i \sqrt{3}}{2}$	$\frac{1 + i \sqrt{3}}{2}$	ζ⁴+ζ¹⁴	ζ⁴+ζ¹⁴	−ζ¹⁴	−ζ⁴	ζ⁸+ζ¹³	ζ⁸+ζ¹³	−ζ⁸	−ζ¹³	ζ²+ζ⁷	ζ²+ζ⁷	−ζ²	−ζ⁷	ζ+ζ¹¹	ζ+ζ¹¹	−ζ¹¹	−ζ
χ₃₅	1	1	$\frac{- 1 - i \sqrt{3}}{2}$	$\frac{- 1 + i \sqrt{3}}{2}$	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	ζ⁴	ζ¹⁴	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	ζ¹³	ζ⁸	−ζ²−ζ⁷	−ζ²−ζ⁷	ζ⁷	ζ²	−ζ−ζ¹¹	−ζ−ζ¹¹	ζ	ζ¹¹	-1	-1	$\frac{1 + i \sqrt{3}}{2}$	$\frac{1 - i \sqrt{3}}{2}$	ζ⁴+ζ¹⁴	ζ⁴+ζ¹⁴	−ζ⁴	−ζ¹⁴	ζ⁸+ζ¹³	ζ⁸+ζ¹³	−ζ¹³	−ζ⁸	ζ²+ζ⁷	ζ²+ζ⁷	−ζ⁷	−ζ²	ζ+ζ¹¹	ζ+ζ¹¹	−ζ	−ζ¹¹
χ₃₆	3	-1	0	0	−3ζ⁴−3ζ¹⁴	ζ⁴+ζ¹⁴	0	0	−3ζ⁸−3ζ¹³	ζ⁸+ζ¹³	0	0	−3ζ²−3ζ⁷	ζ²+ζ⁷	0	0	−3ζ−3ζ¹¹	ζ+ζ¹¹	0	0	-3	1	0	0	3ζ⁴+3ζ¹⁴	−ζ⁴−ζ¹⁴	0	0	3ζ⁸+3ζ¹³	−ζ⁸−ζ¹³	0	0	3ζ²+3ζ⁷	−ζ²−ζ⁷	0	0	3ζ+3ζ¹¹	−ζ−ζ¹¹	0	0
χ₃₇	1	1	1	1	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	-1	-1	-1	-1	ζ²+ζ⁷	ζ²+ζ⁷	ζ²+ζ⁷	ζ²+ζ⁷	ζ⁴+ζ¹⁴	ζ⁴+ζ¹⁴	ζ⁴+ζ¹⁴	ζ⁴+ζ¹⁴	ζ+ζ¹¹	ζ+ζ¹¹	ζ+ζ¹¹	ζ+ζ¹¹	ζ⁸+ζ¹³	ζ⁸+ζ¹³	ζ⁸+ζ¹³	ζ⁸+ζ¹³
χ₃₈	1	1	$\frac{- 1 + i \sqrt{3}}{2}$	$\frac{- 1 - i \sqrt{3}}{2}$	−ζ²−ζ⁷	−ζ²−ζ⁷	ζ²	ζ⁷	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	ζ¹⁴	ζ⁴	−ζ−ζ¹¹	−ζ−ζ¹¹	ζ¹¹	ζ	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	ζ⁸	ζ¹³	-1	-1	$\frac{1 - i \sqrt{3}}{2}$	$\frac{1 + i \sqrt{3}}{2}$	ζ²+ζ⁷	ζ²+ζ⁷	−ζ²	−ζ⁷	ζ⁴+ζ¹⁴	ζ⁴+ζ¹⁴	−ζ¹⁴	−ζ⁴	ζ+ζ¹¹	ζ+ζ¹¹	−ζ¹¹	−ζ	ζ⁸+ζ¹³	ζ⁸+ζ¹³	−ζ⁸	−ζ¹³
χ₃₉	1	1	$\frac{- 1 - i \sqrt{3}}{2}$	$\frac{- 1 + i \sqrt{3}}{2}$	−ζ²−ζ⁷	−ζ²−ζ⁷	ζ⁷	ζ²	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	ζ⁴	ζ¹⁴	−ζ−ζ¹¹	−ζ−ζ¹¹	ζ	ζ¹¹	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	ζ¹³	ζ⁸	-1	-1	$\frac{1 + i \sqrt{3}}{2}$	$\frac{1 - i \sqrt{3}}{2}$	ζ²+ζ⁷	ζ²+ζ⁷	−ζ⁷	−ζ²	ζ⁴+ζ¹⁴	ζ⁴+ζ¹⁴	−ζ⁴	−ζ¹⁴	ζ+ζ¹¹	ζ+ζ¹¹	−ζ	−ζ¹¹	ζ⁸+ζ¹³	ζ⁸+ζ¹³	−ζ¹³	−ζ⁸
χ₄₀	3	-1	0	0	−3ζ²−3ζ⁷	ζ²+ζ⁷	0	0	−3ζ⁴−3ζ¹⁴	ζ⁴+ζ¹⁴	0	0	−3ζ−3ζ¹¹	ζ+ζ¹¹	0	0	−3ζ⁸−3ζ¹³	ζ⁸+ζ¹³	0	0	-3	1	0	0	3ζ²+3ζ⁷	−ζ²−ζ⁷	0	0	3ζ⁴+3ζ¹⁴	−ζ⁴−ζ¹⁴	0	0	3ζ+3ζ¹¹	−ζ−ζ¹¹	0	0	3ζ⁸+3ζ¹³	−ζ⁸−ζ¹³	0	0

Character table — Group #1233