Group #1215 — 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
size	1	1	2	2	2	2	2	6	6	1	1	2	2	2	2	2	6	6	1	1	2	2	2	2	2	6	6	1	1	2	2	2	2	2	6	6	1	1	2	2	2	2	2	6	6
order	1	2	2	3	6	6	6	2	4	5	10	10	15	30	30	30	10	20	5	10	10	15	30	30	30	10	20	5	10	10	15	30	30	30	10	20	5	10	10	15	30	30	30	10	20
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
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
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
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
χ₅	2	2	2	-1	-1	-1	-1	0	0	2	2	2	-1	-1	-1	-1	0	0	2	2	2	-1	-1	-1	-1	0	0	2	2	2	-1	-1	-1	-1	0	0	2	2	2	-1	-1	-1	-1	0	0
χ₆	2	2	-2	-1	-1	1	1	0	0	2	2	-2	-1	-1	1	1	0	0	2	2	-2	-1	-1	1	1	0	0	2	2	-2	-1	-1	1	1	0	0	2	2	-2	-1	-1	1	1	0	0
χ₇	2	-2	0	2	-2	0	0	0	0	2	-2	0	2	-2	0	0	0	0	2	-2	0	2	-2	0	0	0	0	2	-2	0	2	-2	0	0	0	0	2	-2	0	2	-2	0	0	0	0
χ₈	2	-2	0	-1	1	$i \sqrt{3}$	$- i \sqrt{3}$	0	0	2	-2	0	-1	1	$i \sqrt{3}$	$- i \sqrt{3}$	0	0	2	-2	0	-1	1	$i \sqrt{3}$	$- i \sqrt{3}$	0	0	2	-2	0	-1	1	$i \sqrt{3}$	$- i \sqrt{3}$	0	0	2	-2	0	-1	1	$i \sqrt{3}$	$- i \sqrt{3}$	0	0
χ₉	2	-2	0	-1	1	$- i \sqrt{3}$	$i \sqrt{3}$	0	0	2	-2	0	-1	1	$- i \sqrt{3}$	$i \sqrt{3}$	0	0	2	-2	0	-1	1	$- i \sqrt{3}$	$i \sqrt{3}$	0	0	2	-2	0	-1	1	$- i \sqrt{3}$	$i \sqrt{3}$	0	0	2	-2	0	-1	1	$- i \sqrt{3}$	$i \sqrt{3}$	0	0
χ₁₀	1	1	1	1	1	1	1	1	1	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷
χ₁₁	1	1	1	1	1	1	1	-1	-1	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	ζ⁸+ζ¹³	ζ⁸+ζ¹³	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	ζ+ζ¹¹	ζ+ζ¹¹	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	ζ⁴+ζ¹⁴	ζ⁴+ζ¹⁴	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	ζ²+ζ⁷	ζ²+ζ⁷
χ₁₂	1	1	-1	1	1	-1	-1	1	-1	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	ζ⁸+ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	ζ⁸+ζ¹³	ζ⁸+ζ¹³	−ζ⁸−ζ¹³	ζ⁸+ζ¹³	−ζ−ζ¹¹	−ζ−ζ¹¹	ζ+ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	ζ+ζ¹¹	ζ+ζ¹¹	−ζ−ζ¹¹	ζ+ζ¹¹	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	ζ⁴+ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	ζ⁴+ζ¹⁴	ζ⁴+ζ¹⁴	−ζ⁴−ζ¹⁴	ζ⁴+ζ¹⁴	−ζ²−ζ⁷	−ζ²−ζ⁷	ζ²+ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	ζ²+ζ⁷	ζ²+ζ⁷	−ζ²−ζ⁷	ζ²+ζ⁷
χ₁₃	1	1	-1	1	1	-1	-1	-1	1	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	ζ⁸+ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	ζ⁸+ζ¹³	ζ⁸+ζ¹³	ζ⁸+ζ¹³	−ζ⁸−ζ¹³	−ζ−ζ¹¹	−ζ−ζ¹¹	ζ+ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	ζ+ζ¹¹	ζ+ζ¹¹	ζ+ζ¹¹	−ζ−ζ¹¹	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	ζ⁴+ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	ζ⁴+ζ¹⁴	ζ⁴+ζ¹⁴	ζ⁴+ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ²−ζ⁷	−ζ²−ζ⁷	ζ²+ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	ζ²+ζ⁷	ζ²+ζ⁷	ζ²+ζ⁷	−ζ²−ζ⁷
χ₁₄	2	2	2	-1	-1	-1	-1	0	0	−2ζ⁸−2ζ¹³	−2ζ⁸−2ζ¹³	−2ζ⁸−2ζ¹³	ζ⁸+ζ¹³	ζ⁸+ζ¹³	ζ⁸+ζ¹³	ζ⁸+ζ¹³	0	0	−2ζ−2ζ¹¹	−2ζ−2ζ¹¹	−2ζ−2ζ¹¹	ζ+ζ¹¹	ζ+ζ¹¹	ζ+ζ¹¹	ζ+ζ¹¹	0	0	−2ζ⁴−2ζ¹⁴	−2ζ⁴−2ζ¹⁴	−2ζ⁴−2ζ¹⁴	ζ⁴+ζ¹⁴	ζ⁴+ζ¹⁴	ζ⁴+ζ¹⁴	ζ⁴+ζ¹⁴	0	0	−2ζ²−2ζ⁷	−2ζ²−2ζ⁷	−2ζ²−2ζ⁷	ζ²+ζ⁷	ζ²+ζ⁷	ζ²+ζ⁷	ζ²+ζ⁷	0	0
χ₁₅	2	2	-2	-1	-1	1	1	0	0	−2ζ⁸−2ζ¹³	−2ζ⁸−2ζ¹³	2ζ⁸+2ζ¹³	ζ⁸+ζ¹³	ζ⁸+ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	0	0	−2ζ−2ζ¹¹	−2ζ−2ζ¹¹	2ζ+2ζ¹¹	ζ+ζ¹¹	ζ+ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	0	0	−2ζ⁴−2ζ¹⁴	−2ζ⁴−2ζ¹⁴	2ζ⁴+2ζ¹⁴	ζ⁴+ζ¹⁴	ζ⁴+ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	0	0	−2ζ²−2ζ⁷	−2ζ²−2ζ⁷	2ζ²+2ζ⁷	ζ²+ζ⁷	ζ²+ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	0	0
χ₁₆	2	-2	0	2	-2	0	0	0	0	−2ζ⁸−2ζ¹³	2ζ⁸+2ζ¹³	0	−2ζ⁸−2ζ¹³	2ζ⁸+2ζ¹³	0	0	0	0	−2ζ−2ζ¹¹	2ζ+2ζ¹¹	0	−2ζ−2ζ¹¹	2ζ+2ζ¹¹	0	0	0	0	−2ζ⁴−2ζ¹⁴	2ζ⁴+2ζ¹⁴	0	−2ζ⁴−2ζ¹⁴	2ζ⁴+2ζ¹⁴	0	0	0	0	−2ζ²−2ζ⁷	2ζ²+2ζ⁷	0	−2ζ²−2ζ⁷	2ζ²+2ζ⁷	0	0	0	0
χ₁₇	2	-2	0	-1	1	$i \sqrt{3}$	$- i \sqrt{3}$	0	0	−2ζ⁸−2ζ¹³	2ζ⁸+2ζ¹³	0	ζ⁸+ζ¹³	−ζ⁸−ζ¹³	ζ⁸−ζ¹³	−ζ⁸+ζ¹³	0	0	−2ζ−2ζ¹¹	2ζ+2ζ¹¹	0	ζ+ζ¹¹	−ζ−ζ¹¹	−ζ+ζ¹¹	ζ−ζ¹¹	0	0	−2ζ⁴−2ζ¹⁴	2ζ⁴+2ζ¹⁴	0	ζ⁴+ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴+ζ¹⁴	ζ⁴−ζ¹⁴	0	0	−2ζ²−2ζ⁷	2ζ²+2ζ⁷	0	ζ²+ζ⁷	−ζ²−ζ⁷	ζ²−ζ⁷	−ζ²+ζ⁷	0	0
χ₁₈	2	-2	0	-1	1	$- i \sqrt{3}$	$i \sqrt{3}$	0	0	−2ζ⁸−2ζ¹³	2ζ⁸+2ζ¹³	0	ζ⁸+ζ¹³	−ζ⁸−ζ¹³	−ζ⁸+ζ¹³	ζ⁸−ζ¹³	0	0	−2ζ−2ζ¹¹	2ζ+2ζ¹¹	0	ζ+ζ¹¹	−ζ−ζ¹¹	ζ−ζ¹¹	−ζ+ζ¹¹	0	0	−2ζ⁴−2ζ¹⁴	2ζ⁴+2ζ¹⁴	0	ζ⁴+ζ¹⁴	−ζ⁴−ζ¹⁴	ζ⁴−ζ¹⁴	−ζ⁴+ζ¹⁴	0	0	−2ζ²−2ζ⁷	2ζ²+2ζ⁷	0	ζ²+ζ⁷	−ζ²−ζ⁷	−ζ²+ζ⁷	ζ²−ζ⁷	0	0
χ₁₉	1	1	1	1	1	1	1	1	1	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴
χ₂₀	1	1	1	1	1	1	1	-1	-1	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	ζ+ζ¹¹	ζ+ζ¹¹	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	ζ²+ζ⁷	ζ²+ζ⁷	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	ζ⁸+ζ¹³	ζ⁸+ζ¹³	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	ζ⁴+ζ¹⁴	ζ⁴+ζ¹⁴
χ₂₁	1	1	-1	1	1	-1	-1	1	-1	−ζ−ζ¹¹	−ζ−ζ¹¹	ζ+ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	ζ+ζ¹¹	ζ+ζ¹¹	−ζ−ζ¹¹	ζ+ζ¹¹	−ζ²−ζ⁷	−ζ²−ζ⁷	ζ²+ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	ζ²+ζ⁷	ζ²+ζ⁷	−ζ²−ζ⁷	ζ²+ζ⁷	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	ζ⁸+ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	ζ⁸+ζ¹³	ζ⁸+ζ¹³	−ζ⁸−ζ¹³	ζ⁸+ζ¹³	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	ζ⁴+ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	ζ⁴+ζ¹⁴	ζ⁴+ζ¹⁴	−ζ⁴−ζ¹⁴	ζ⁴+ζ¹⁴
χ₂₂	1	1	-1	1	1	-1	-1	-1	1	−ζ−ζ¹¹	−ζ−ζ¹¹	ζ+ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	ζ+ζ¹¹	ζ+ζ¹¹	ζ+ζ¹¹	−ζ−ζ¹¹	−ζ²−ζ⁷	−ζ²−ζ⁷	ζ²+ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	ζ²+ζ⁷	ζ²+ζ⁷	ζ²+ζ⁷	−ζ²−ζ⁷	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	ζ⁸+ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	ζ⁸+ζ¹³	ζ⁸+ζ¹³	ζ⁸+ζ¹³	−ζ⁸−ζ¹³	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	ζ⁴+ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	ζ⁴+ζ¹⁴	ζ⁴+ζ¹⁴	ζ⁴+ζ¹⁴	−ζ⁴−ζ¹⁴
χ₂₃	2	2	2	-1	-1	-1	-1	0	0	−2ζ−2ζ¹¹	−2ζ−2ζ¹¹	−2ζ−2ζ¹¹	ζ+ζ¹¹	ζ+ζ¹¹	ζ+ζ¹¹	ζ+ζ¹¹	0	0	−2ζ²−2ζ⁷	−2ζ²−2ζ⁷	−2ζ²−2ζ⁷	ζ²+ζ⁷	ζ²+ζ⁷	ζ²+ζ⁷	ζ²+ζ⁷	0	0	−2ζ⁸−2ζ¹³	−2ζ⁸−2ζ¹³	−2ζ⁸−2ζ¹³	ζ⁸+ζ¹³	ζ⁸+ζ¹³	ζ⁸+ζ¹³	ζ⁸+ζ¹³	0	0	−2ζ⁴−2ζ¹⁴	−2ζ⁴−2ζ¹⁴	−2ζ⁴−2ζ¹⁴	ζ⁴+ζ¹⁴	ζ⁴+ζ¹⁴	ζ⁴+ζ¹⁴	ζ⁴+ζ¹⁴	0	0
χ₂₄	2	2	-2	-1	-1	1	1	0	0	−2ζ−2ζ¹¹	−2ζ−2ζ¹¹	2ζ+2ζ¹¹	ζ+ζ¹¹	ζ+ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	0	0	−2ζ²−2ζ⁷	−2ζ²−2ζ⁷	2ζ²+2ζ⁷	ζ²+ζ⁷	ζ²+ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	0	0	−2ζ⁸−2ζ¹³	−2ζ⁸−2ζ¹³	2ζ⁸+2ζ¹³	ζ⁸+ζ¹³	ζ⁸+ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	0	0	−2ζ⁴−2ζ¹⁴	−2ζ⁴−2ζ¹⁴	2ζ⁴+2ζ¹⁴	ζ⁴+ζ¹⁴	ζ⁴+ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	0	0
χ₂₅	2	-2	0	2	-2	0	0	0	0	−2ζ−2ζ¹¹	2ζ+2ζ¹¹	0	−2ζ−2ζ¹¹	2ζ+2ζ¹¹	0	0	0	0	−2ζ²−2ζ⁷	2ζ²+2ζ⁷	0	−2ζ²−2ζ⁷	2ζ²+2ζ⁷	0	0	0	0	−2ζ⁸−2ζ¹³	2ζ⁸+2ζ¹³	0	−2ζ⁸−2ζ¹³	2ζ⁸+2ζ¹³	0	0	0	0	−2ζ⁴−2ζ¹⁴	2ζ⁴+2ζ¹⁴	0	−2ζ⁴−2ζ¹⁴	2ζ⁴+2ζ¹⁴	0	0	0	0
χ₂₆	2	-2	0	-1	1	$i \sqrt{3}$	$- i \sqrt{3}$	0	0	−2ζ−2ζ¹¹	2ζ+2ζ¹¹	0	ζ+ζ¹¹	−ζ−ζ¹¹	−ζ+ζ¹¹	ζ−ζ¹¹	0	0	−2ζ²−2ζ⁷	2ζ²+2ζ⁷	0	ζ²+ζ⁷	−ζ²−ζ⁷	ζ²−ζ⁷	−ζ²+ζ⁷	0	0	−2ζ⁸−2ζ¹³	2ζ⁸+2ζ¹³	0	ζ⁸+ζ¹³	−ζ⁸−ζ¹³	ζ⁸−ζ¹³	−ζ⁸+ζ¹³	0	0	−2ζ⁴−2ζ¹⁴	2ζ⁴+2ζ¹⁴	0	ζ⁴+ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴+ζ¹⁴	ζ⁴−ζ¹⁴	0	0
χ₂₇	2	-2	0	-1	1	$- i \sqrt{3}$	$i \sqrt{3}$	0	0	−2ζ−2ζ¹¹	2ζ+2ζ¹¹	0	ζ+ζ¹¹	−ζ−ζ¹¹	ζ−ζ¹¹	−ζ+ζ¹¹	0	0	−2ζ²−2ζ⁷	2ζ²+2ζ⁷	0	ζ²+ζ⁷	−ζ²−ζ⁷	−ζ²+ζ⁷	ζ²−ζ⁷	0	0	−2ζ⁸−2ζ¹³	2ζ⁸+2ζ¹³	0	ζ⁸+ζ¹³	−ζ⁸−ζ¹³	−ζ⁸+ζ¹³	ζ⁸−ζ¹³	0	0	−2ζ⁴−2ζ¹⁴	2ζ⁴+2ζ¹⁴	0	ζ⁴+ζ¹⁴	−ζ⁴−ζ¹⁴	ζ⁴−ζ¹⁴	−ζ⁴+ζ¹⁴	0	0
χ₂₈	1	1	1	1	1	1	1	1	1	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹
χ₂₉	1	1	1	1	1	1	1	-1	-1	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	ζ⁴+ζ¹⁴	ζ⁴+ζ¹⁴	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	ζ⁸+ζ¹³	ζ⁸+ζ¹³	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	ζ²+ζ⁷	ζ²+ζ⁷	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	ζ+ζ¹¹	ζ+ζ¹¹
χ₃₀	1	1	-1	1	1	-1	-1	1	-1	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	ζ⁴+ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	ζ⁴+ζ¹⁴	ζ⁴+ζ¹⁴	−ζ⁴−ζ¹⁴	ζ⁴+ζ¹⁴	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	ζ⁸+ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	ζ⁸+ζ¹³	ζ⁸+ζ¹³	−ζ⁸−ζ¹³	ζ⁸+ζ¹³	−ζ²−ζ⁷	−ζ²−ζ⁷	ζ²+ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	ζ²+ζ⁷	ζ²+ζ⁷	−ζ²−ζ⁷	ζ²+ζ⁷	−ζ−ζ¹¹	−ζ−ζ¹¹	ζ+ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	ζ+ζ¹¹	ζ+ζ¹¹	−ζ−ζ¹¹	ζ+ζ¹¹
χ₃₁	1	1	-1	1	1	-1	-1	-1	1	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	ζ⁴+ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	ζ⁴+ζ¹⁴	ζ⁴+ζ¹⁴	ζ⁴+ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	ζ⁸+ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	ζ⁸+ζ¹³	ζ⁸+ζ¹³	ζ⁸+ζ¹³	−ζ⁸−ζ¹³	−ζ²−ζ⁷	−ζ²−ζ⁷	ζ²+ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	ζ²+ζ⁷	ζ²+ζ⁷	ζ²+ζ⁷	−ζ²−ζ⁷	−ζ−ζ¹¹	−ζ−ζ¹¹	ζ+ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	ζ+ζ¹¹	ζ+ζ¹¹	ζ+ζ¹¹	−ζ−ζ¹¹
χ₃₂	2	2	2	-1	-1	-1	-1	0	0	−2ζ⁴−2ζ¹⁴	−2ζ⁴−2ζ¹⁴	−2ζ⁴−2ζ¹⁴	ζ⁴+ζ¹⁴	ζ⁴+ζ¹⁴	ζ⁴+ζ¹⁴	ζ⁴+ζ¹⁴	0	0	−2ζ⁸−2ζ¹³	−2ζ⁸−2ζ¹³	−2ζ⁸−2ζ¹³	ζ⁸+ζ¹³	ζ⁸+ζ¹³	ζ⁸+ζ¹³	ζ⁸+ζ¹³	0	0	−2ζ²−2ζ⁷	−2ζ²−2ζ⁷	−2ζ²−2ζ⁷	ζ²+ζ⁷	ζ²+ζ⁷	ζ²+ζ⁷	ζ²+ζ⁷	0	0	−2ζ−2ζ¹¹	−2ζ−2ζ¹¹	−2ζ−2ζ¹¹	ζ+ζ¹¹	ζ+ζ¹¹	ζ+ζ¹¹	ζ+ζ¹¹	0	0
χ₃₃	2	2	-2	-1	-1	1	1	0	0	−2ζ⁴−2ζ¹⁴	−2ζ⁴−2ζ¹⁴	2ζ⁴+2ζ¹⁴	ζ⁴+ζ¹⁴	ζ⁴+ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	0	0	−2ζ⁸−2ζ¹³	−2ζ⁸−2ζ¹³	2ζ⁸+2ζ¹³	ζ⁸+ζ¹³	ζ⁸+ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	0	0	−2ζ²−2ζ⁷	−2ζ²−2ζ⁷	2ζ²+2ζ⁷	ζ²+ζ⁷	ζ²+ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	0	0	−2ζ−2ζ¹¹	−2ζ−2ζ¹¹	2ζ+2ζ¹¹	ζ+ζ¹¹	ζ+ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	0	0
χ₃₄	2	-2	0	2	-2	0	0	0	0	−2ζ⁴−2ζ¹⁴	2ζ⁴+2ζ¹⁴	0	−2ζ⁴−2ζ¹⁴	2ζ⁴+2ζ¹⁴	0	0	0	0	−2ζ⁸−2ζ¹³	2ζ⁸+2ζ¹³	0	−2ζ⁸−2ζ¹³	2ζ⁸+2ζ¹³	0	0	0	0	−2ζ²−2ζ⁷	2ζ²+2ζ⁷	0	−2ζ²−2ζ⁷	2ζ²+2ζ⁷	0	0	0	0	−2ζ−2ζ¹¹	2ζ+2ζ¹¹	0	−2ζ−2ζ¹¹	2ζ+2ζ¹¹	0	0	0	0
χ₃₅	2	-2	0	-1	1	$i \sqrt{3}$	$- i \sqrt{3}$	0	0	−2ζ⁴−2ζ¹⁴	2ζ⁴+2ζ¹⁴	0	ζ⁴+ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴+ζ¹⁴	ζ⁴−ζ¹⁴	0	0	−2ζ⁸−2ζ¹³	2ζ⁸+2ζ¹³	0	ζ⁸+ζ¹³	−ζ⁸−ζ¹³	ζ⁸−ζ¹³	−ζ⁸+ζ¹³	0	0	−2ζ²−2ζ⁷	2ζ²+2ζ⁷	0	ζ²+ζ⁷	−ζ²−ζ⁷	ζ²−ζ⁷	−ζ²+ζ⁷	0	0	−2ζ−2ζ¹¹	2ζ+2ζ¹¹	0	ζ+ζ¹¹	−ζ−ζ¹¹	−ζ+ζ¹¹	ζ−ζ¹¹	0	0
χ₃₆	2	-2	0	-1	1	$- i \sqrt{3}$	$i \sqrt{3}$	0	0	−2ζ⁴−2ζ¹⁴	2ζ⁴+2ζ¹⁴	0	ζ⁴+ζ¹⁴	−ζ⁴−ζ¹⁴	ζ⁴−ζ¹⁴	−ζ⁴+ζ¹⁴	0	0	−2ζ⁸−2ζ¹³	2ζ⁸+2ζ¹³	0	ζ⁸+ζ¹³	−ζ⁸−ζ¹³	−ζ⁸+ζ¹³	ζ⁸−ζ¹³	0	0	−2ζ²−2ζ⁷	2ζ²+2ζ⁷	0	ζ²+ζ⁷	−ζ²−ζ⁷	−ζ²+ζ⁷	ζ²−ζ⁷	0	0	−2ζ−2ζ¹¹	2ζ+2ζ¹¹	0	ζ+ζ¹¹	−ζ−ζ¹¹	ζ−ζ¹¹	−ζ+ζ¹¹	0	0
χ₃₇	1	1	1	1	1	1	1	1	1	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³
χ₃₈	1	1	1	1	1	1	1	-1	-1	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	ζ²+ζ⁷	ζ²+ζ⁷	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	ζ⁴+ζ¹⁴	ζ⁴+ζ¹⁴	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	ζ+ζ¹¹	ζ+ζ¹¹	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	ζ⁸+ζ¹³	ζ⁸+ζ¹³
χ₃₉	1	1	-1	1	1	-1	-1	1	-1	−ζ²−ζ⁷	−ζ²−ζ⁷	ζ²+ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	ζ²+ζ⁷	ζ²+ζ⁷	−ζ²−ζ⁷	ζ²+ζ⁷	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	ζ⁴+ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	ζ⁴+ζ¹⁴	ζ⁴+ζ¹⁴	−ζ⁴−ζ¹⁴	ζ⁴+ζ¹⁴	−ζ−ζ¹¹	−ζ−ζ¹¹	ζ+ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	ζ+ζ¹¹	ζ+ζ¹¹	−ζ−ζ¹¹	ζ+ζ¹¹	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	ζ⁸+ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	ζ⁸+ζ¹³	ζ⁸+ζ¹³	−ζ⁸−ζ¹³	ζ⁸+ζ¹³
χ₄₀	1	1	-1	1	1	-1	-1	-1	1	−ζ²−ζ⁷	−ζ²−ζ⁷	ζ²+ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	ζ²+ζ⁷	ζ²+ζ⁷	ζ²+ζ⁷	−ζ²−ζ⁷	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	ζ⁴+ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	ζ⁴+ζ¹⁴	ζ⁴+ζ¹⁴	ζ⁴+ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ−ζ¹¹	−ζ−ζ¹¹	ζ+ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	ζ+ζ¹¹	ζ+ζ¹¹	ζ+ζ¹¹	−ζ−ζ¹¹	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	ζ⁸+ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	ζ⁸+ζ¹³	ζ⁸+ζ¹³	ζ⁸+ζ¹³	−ζ⁸−ζ¹³
χ₄₁	2	2	2	-1	-1	-1	-1	0	0	−2ζ²−2ζ⁷	−2ζ²−2ζ⁷	−2ζ²−2ζ⁷	ζ²+ζ⁷	ζ²+ζ⁷	ζ²+ζ⁷	ζ²+ζ⁷	0	0	−2ζ⁴−2ζ¹⁴	−2ζ⁴−2ζ¹⁴	−2ζ⁴−2ζ¹⁴	ζ⁴+ζ¹⁴	ζ⁴+ζ¹⁴	ζ⁴+ζ¹⁴	ζ⁴+ζ¹⁴	0	0	−2ζ−2ζ¹¹	−2ζ−2ζ¹¹	−2ζ−2ζ¹¹	ζ+ζ¹¹	ζ+ζ¹¹	ζ+ζ¹¹	ζ+ζ¹¹	0	0	−2ζ⁸−2ζ¹³	−2ζ⁸−2ζ¹³	−2ζ⁸−2ζ¹³	ζ⁸+ζ¹³	ζ⁸+ζ¹³	ζ⁸+ζ¹³	ζ⁸+ζ¹³	0	0
χ₄₂	2	2	-2	-1	-1	1	1	0	0	−2ζ²−2ζ⁷	−2ζ²−2ζ⁷	2ζ²+2ζ⁷	ζ²+ζ⁷	ζ²+ζ⁷	−ζ²−ζ⁷	−ζ²−ζ⁷	0	0	−2ζ⁴−2ζ¹⁴	−2ζ⁴−2ζ¹⁴	2ζ⁴+2ζ¹⁴	ζ⁴+ζ¹⁴	ζ⁴+ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴−ζ¹⁴	0	0	−2ζ−2ζ¹¹	−2ζ−2ζ¹¹	2ζ+2ζ¹¹	ζ+ζ¹¹	ζ+ζ¹¹	−ζ−ζ¹¹	−ζ−ζ¹¹	0	0	−2ζ⁸−2ζ¹³	−2ζ⁸−2ζ¹³	2ζ⁸+2ζ¹³	ζ⁸+ζ¹³	ζ⁸+ζ¹³	−ζ⁸−ζ¹³	−ζ⁸−ζ¹³	0	0
χ₄₃	2	-2	0	2	-2	0	0	0	0	−2ζ²−2ζ⁷	2ζ²+2ζ⁷	0	−2ζ²−2ζ⁷	2ζ²+2ζ⁷	0	0	0	0	−2ζ⁴−2ζ¹⁴	2ζ⁴+2ζ¹⁴	0	−2ζ⁴−2ζ¹⁴	2ζ⁴+2ζ¹⁴	0	0	0	0	−2ζ−2ζ¹¹	2ζ+2ζ¹¹	0	−2ζ−2ζ¹¹	2ζ+2ζ¹¹	0	0	0	0	−2ζ⁸−2ζ¹³	2ζ⁸+2ζ¹³	0	−2ζ⁸−2ζ¹³	2ζ⁸+2ζ¹³	0	0	0	0
χ₄₄	2	-2	0	-1	1	$i \sqrt{3}$	$- i \sqrt{3}$	0	0	−2ζ²−2ζ⁷	2ζ²+2ζ⁷	0	ζ²+ζ⁷	−ζ²−ζ⁷	ζ²−ζ⁷	−ζ²+ζ⁷	0	0	−2ζ⁴−2ζ¹⁴	2ζ⁴+2ζ¹⁴	0	ζ⁴+ζ¹⁴	−ζ⁴−ζ¹⁴	−ζ⁴+ζ¹⁴	ζ⁴−ζ¹⁴	0	0	−2ζ−2ζ¹¹	2ζ+2ζ¹¹	0	ζ+ζ¹¹	−ζ−ζ¹¹	−ζ+ζ¹¹	ζ−ζ¹¹	0	0	−2ζ⁸−2ζ¹³	2ζ⁸+2ζ¹³	0	ζ⁸+ζ¹³	−ζ⁸−ζ¹³	ζ⁸−ζ¹³	−ζ⁸+ζ¹³	0	0
χ₄₅	2	-2	0	-1	1	$- i \sqrt{3}$	$i \sqrt{3}$	0	0	−2ζ²−2ζ⁷	2ζ²+2ζ⁷	0	ζ²+ζ⁷	−ζ²−ζ⁷	−ζ²+ζ⁷	ζ²−ζ⁷	0	0	−2ζ⁴−2ζ¹⁴	2ζ⁴+2ζ¹⁴	0	ζ⁴+ζ¹⁴	−ζ⁴−ζ¹⁴	ζ⁴−ζ¹⁴	−ζ⁴+ζ¹⁴	0	0	−2ζ−2ζ¹¹	2ζ+2ζ¹¹	0	ζ+ζ¹¹	−ζ−ζ¹¹	ζ−ζ¹¹	−ζ+ζ¹¹	0	0	−2ζ⁸−2ζ¹³	2ζ⁸+2ζ¹³	0	ζ⁸+ζ¹³	−ζ⁸−ζ¹³	−ζ⁸+ζ¹³	ζ⁸−ζ¹³	0	0

Character table — Group #1215