Group #91237 — 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
size	1	1	2	2	2	4	4	4	4	4	4	4	4	4	4	5	5	8	8	8	8	8	8	8	8	8	10	10	10	20	20	20	20	30	30	30	30	60	60
order	1	2	3	4	6	2	5	6	6	10	12	15	15	30	30	4	4	10	10	20	30	30	30	30	60	60	2	12	12	4	6	12	12	4	4	4	4	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
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
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	$i$	$i$	$- i$	$- i$	$i$	$- i$
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	$- i$	$- i$	$i$	$i$	$- i$	$i$
χ₅	1	1	1	1	1	-1	1	-1	-1	1	1	1	1	1	1	1	1	-1	-1	1	-1	-1	-1	-1	1	1	1	1	1	-1	1	-1	-1	1	1	1	1	-1	-1
χ₆	1	1	1	1	1	-1	1	-1	-1	1	1	1	1	1	1	1	1	-1	-1	1	-1	-1	-1	-1	1	1	1	1	1	-1	1	-1	-1	-1	-1	-1	-1	1	1
χ₇	1	1	1	1	1	-1	1	-1	-1	1	1	1	1	1	1	-1	-1	-1	-1	1	-1	-1	-1	-1	1	1	-1	-1	-1	1	-1	1	1	$i$	$i$	$- i$	$- i$	$- i$	$i$
χ₈	1	1	1	1	1	-1	1	-1	-1	1	1	1	1	1	1	-1	-1	-1	-1	1	-1	-1	-1	-1	1	1	-1	-1	-1	1	-1	1	1	$- i$	$- i$	$i$	$i$	$i$	$- i$
χ₉	2	2	2	-2	2	0	2	0	0	2	-2	2	2	2	2	2	2	0	0	-2	0	0	0	0	-2	-2	-2	2	2	0	-2	0	0	0	0	0	0	0	0
χ₁₀	2	2	2	-2	2	0	2	0	0	2	-2	2	2	2	2	-2	-2	0	0	-2	0	0	0	0	-2	-2	2	-2	-2	0	2	0	0	0	0	0	0	0	0
χ₁₁	2	2	-1	2	-1	2	2	-1	-1	2	-1	-1	-1	-1	-1	2	2	2	2	2	-1	-1	-1	-1	-1	-1	2	-1	-1	2	-1	-1	-1	0	0	0	0	0	0
χ₁₂	2	2	-1	2	-1	2	2	-1	-1	2	-1	-1	-1	-1	-1	-2	-2	2	2	2	-1	-1	-1	-1	-1	-1	-2	1	1	-2	1	1	1	0	0	0	0	0	0
χ₁₃	2	2	-1	2	-1	-2	2	1	1	2	-1	-1	-1	-1	-1	2	2	-2	-2	2	1	1	1	1	-1	-1	2	-1	-1	-2	-1	1	1	0	0	0	0	0	0
χ₁₄	2	2	-1	2	-1	-2	2	1	1	2	-1	-1	-1	-1	-1	-2	-2	-2	-2	2	1	1	1	1	-1	-1	-2	1	1	2	1	-1	-1	0	0	0	0	0	0
χ₁₅	2	2	-1	-2	-1	0	2	$- i \sqrt{3}$	$i \sqrt{3}$	2	1	-1	-1	-1	-1	2	2	0	0	-2	$- i \sqrt{3}$	$- i \sqrt{3}$	$i \sqrt{3}$	$i \sqrt{3}$	1	1	-2	-1	-1	0	1	$- i \sqrt{3}$	$i \sqrt{3}$	0	0	0	0	0	0
χ₁₆	2	2	-1	-2	-1	0	2	$- i \sqrt{3}$	$i \sqrt{3}$	2	1	-1	-1	-1	-1	-2	-2	0	0	-2	$- i \sqrt{3}$	$- i \sqrt{3}$	$i \sqrt{3}$	$i \sqrt{3}$	1	1	2	1	1	0	-1	$i \sqrt{3}$	$- i \sqrt{3}$	0	0	0	0	0	0
χ₁₇	2	2	-1	-2	-1	0	2	$i \sqrt{3}$	$- i \sqrt{3}$	2	1	-1	-1	-1	-1	2	2	0	0	-2	$i \sqrt{3}$	$i \sqrt{3}$	$- i \sqrt{3}$	$- i \sqrt{3}$	1	1	-2	-1	-1	0	1	$i \sqrt{3}$	$- i \sqrt{3}$	0	0	0	0	0	0
χ₁₈	2	2	-1	-2	-1	0	2	$i \sqrt{3}$	$- i \sqrt{3}$	2	1	-1	-1	-1	-1	-2	-2	0	0	-2	$i \sqrt{3}$	$i \sqrt{3}$	$- i \sqrt{3}$	$- i \sqrt{3}$	1	1	2	1	1	0	-1	$- i \sqrt{3}$	$i \sqrt{3}$	0	0	0	0	0	0
χ₁₉	2	-2	2	0	-2	0	2	0	0	-2	0	2	2	-2	-2	$2 i$	$- 2 i$	0	0	0	0	0	0	0	0	0	0	$2 i$	$- 2 i$	0	0	0	0	$1 + i$	$- 1 - i$	$1 - i$	$- 1 + i$	0	0
χ₂₀	2	-2	2	0	-2	0	2	0	0	-2	0	2	2	-2	-2	$2 i$	$- 2 i$	0	0	0	0	0	0	0	0	0	0	$2 i$	$- 2 i$	0	0	0	0	$- 1 - i$	$1 + i$	$- 1 + i$	$1 - i$	0	0
χ₂₁	2	-2	2	0	-2	0	2	0	0	-2	0	2	2	-2	-2	$- 2 i$	$2 i$	0	0	0	0	0	0	0	0	0	0	$- 2 i$	$2 i$	0	0	0	0	$1 - i$	$- 1 + i$	$1 + i$	$- 1 - i$	0	0
χ₂₂	2	-2	2	0	-2	0	2	0	0	-2	0	2	2	-2	-2	$- 2 i$	$2 i$	0	0	0	0	0	0	0	0	0	0	$- 2 i$	$2 i$	0	0	0	0	$- 1 + i$	$1 - i$	$- 1 - i$	$1 + i$	0	0
χ₂₃	4	4	4	4	4	4	-1	4	4	-1	4	-1	-1	-1	-1	0	0	-1	-1	-1	-1	-1	-1	-1	-1	-1	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₄	4	4	4	4	4	-4	-1	-4	-4	-1	4	-1	-1	-1	-1	0	0	1	1	-1	1	1	1	1	-1	-1	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₅	4	4	4	-4	4	0	-1	0	0	-1	-4	-1	-1	-1	-1	0	0	$- \sqrt{5}$	$\sqrt{5}$	1	$- \sqrt{5}$	$\sqrt{5}$	$- \sqrt{5}$	$\sqrt{5}$	1	1	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₆	4	4	4	-4	4	0	-1	0	0	-1	-4	-1	-1	-1	-1	0	0	$\sqrt{5}$	$- \sqrt{5}$	1	$\sqrt{5}$	$- \sqrt{5}$	$\sqrt{5}$	$- \sqrt{5}$	1	1	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₇	4	4	-2	4	-2	4	-1	-2	-2	-1	-2	$\frac{1 - i \sqrt{15}}{2}$	$\frac{1 + i \sqrt{15}}{2}$	$\frac{1 - i \sqrt{15}}{2}$	$\frac{1 + i \sqrt{15}}{2}$	0	0	-1	-1	-1	$\frac{1 - i \sqrt{15}}{2}$	$\frac{1 + i \sqrt{15}}{2}$	$\frac{1 + i \sqrt{15}}{2}$	$\frac{1 - i \sqrt{15}}{2}$	$\frac{1 - i \sqrt{15}}{2}$	$\frac{1 + i \sqrt{15}}{2}$	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₈	4	4	-2	4	-2	4	-1	-2	-2	-1	-2	$\frac{1 + i \sqrt{15}}{2}$	$\frac{1 - i \sqrt{15}}{2}$	$\frac{1 + i \sqrt{15}}{2}$	$\frac{1 - i \sqrt{15}}{2}$	0	0	-1	-1	-1	$\frac{1 + i \sqrt{15}}{2}$	$\frac{1 - i \sqrt{15}}{2}$	$\frac{1 - i \sqrt{15}}{2}$	$\frac{1 + i \sqrt{15}}{2}$	$\frac{1 + i \sqrt{15}}{2}$	$\frac{1 - i \sqrt{15}}{2}$	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₉	4	4	-2	4	-2	-4	-1	2	2	-1	-2	$\frac{1 - i \sqrt{15}}{2}$	$\frac{1 + i \sqrt{15}}{2}$	$\frac{1 - i \sqrt{15}}{2}$	$\frac{1 + i \sqrt{15}}{2}$	0	0	1	1	-1	$\frac{- 1 + i \sqrt{15}}{2}$	$\frac{- 1 - i \sqrt{15}}{2}$	$\frac{- 1 - i \sqrt{15}}{2}$	$\frac{- 1 + i \sqrt{15}}{2}$	$\frac{1 - i \sqrt{15}}{2}$	$\frac{1 + i \sqrt{15}}{2}$	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₀	4	4	-2	4	-2	-4	-1	2	2	-1	-2	$\frac{1 + i \sqrt{15}}{2}$	$\frac{1 - i \sqrt{15}}{2}$	$\frac{1 + i \sqrt{15}}{2}$	$\frac{1 - i \sqrt{15}}{2}$	0	0	1	1	-1	$\frac{- 1 - i \sqrt{15}}{2}$	$\frac{- 1 + i \sqrt{15}}{2}$	$\frac{- 1 + i \sqrt{15}}{2}$	$\frac{- 1 - i \sqrt{15}}{2}$	$\frac{1 + i \sqrt{15}}{2}$	$\frac{1 - i \sqrt{15}}{2}$	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₁	4	4	-2	-4	-2	0	-1	$- 2 i \sqrt{3}$	$2 i \sqrt{3}$	-1	2	$\frac{1 - i \sqrt{15}}{2}$	$\frac{1 + i \sqrt{15}}{2}$	$\frac{1 - i \sqrt{15}}{2}$	$\frac{1 + i \sqrt{15}}{2}$	0	0	$\sqrt{5}$	$- \sqrt{5}$	1	ζ¹⁴−ζ²²+ζ²⁶−ζ⁵⁸	ζ²−ζ³⁴+ζ³⁸−ζ⁴⁶	−ζ²+ζ³⁴−ζ³⁸+ζ⁴⁶	−ζ¹⁴+ζ²²−ζ²⁶+ζ⁵⁸	$\frac{- 1 + i \sqrt{15}}{2}$	$\frac{- 1 - i \sqrt{15}}{2}$	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₂	4	4	-2	-4	-2	0	-1	$- 2 i \sqrt{3}$	$2 i \sqrt{3}$	-1	2	$\frac{1 + i \sqrt{15}}{2}$	$\frac{1 - i \sqrt{15}}{2}$	$\frac{1 + i \sqrt{15}}{2}$	$\frac{1 - i \sqrt{15}}{2}$	0	0	$- \sqrt{5}$	$\sqrt{5}$	1	ζ²−ζ³⁴+ζ³⁸−ζ⁴⁶	ζ¹⁴−ζ²²+ζ²⁶−ζ⁵⁸	−ζ¹⁴+ζ²²−ζ²⁶+ζ⁵⁸	−ζ²+ζ³⁴−ζ³⁸+ζ⁴⁶	$\frac{- 1 - i \sqrt{15}}{2}$	$\frac{- 1 + i \sqrt{15}}{2}$	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₃	4	4	-2	-4	-2	0	-1	$2 i \sqrt{3}$	$- 2 i \sqrt{3}$	-1	2	$\frac{1 - i \sqrt{15}}{2}$	$\frac{1 + i \sqrt{15}}{2}$	$\frac{1 - i \sqrt{15}}{2}$	$\frac{1 + i \sqrt{15}}{2}$	0	0	$- \sqrt{5}$	$\sqrt{5}$	1	−ζ¹⁴+ζ²²−ζ²⁶+ζ⁵⁸	−ζ²+ζ³⁴−ζ³⁸+ζ⁴⁶	ζ²−ζ³⁴+ζ³⁸−ζ⁴⁶	ζ¹⁴−ζ²²+ζ²⁶−ζ⁵⁸	$\frac{- 1 + i \sqrt{15}}{2}$	$\frac{- 1 - i \sqrt{15}}{2}$	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₄	4	4	-2	-4	-2	0	-1	$2 i \sqrt{3}$	$- 2 i \sqrt{3}$	-1	2	$\frac{1 + i \sqrt{15}}{2}$	$\frac{1 - i \sqrt{15}}{2}$	$\frac{1 + i \sqrt{15}}{2}$	$\frac{1 - i \sqrt{15}}{2}$	0	0	$\sqrt{5}$	$- \sqrt{5}$	1	−ζ²+ζ³⁴−ζ³⁸+ζ⁴⁶	−ζ¹⁴+ζ²²−ζ²⁶+ζ⁵⁸	ζ¹⁴−ζ²²+ζ²⁶−ζ⁵⁸	ζ²−ζ³⁴+ζ³⁸−ζ⁴⁶	$\frac{- 1 - i \sqrt{15}}{2}$	$\frac{- 1 + i \sqrt{15}}{2}$	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₅	4	-4	-2	0	2	0	4	0	0	-4	0	-2	-2	2	2	$4 i$	$- 4 i$	0	0	0	0	0	0	0	0	0	0	$- 2 i$	$2 i$	0	0	0	0	0	0	0	0	0	0
χ₃₆	4	-4	-2	0	2	0	4	0	0	-4	0	-2	-2	2	2	$- 4 i$	$4 i$	0	0	0	0	0	0	0	0	0	0	$2 i$	$- 2 i$	0	0	0	0	0	0	0	0	0	0
χ₃₇	8	-8	8	0	-8	0	-2	0	0	2	0	-2	-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	0
χ₃₈	8	-8	-4	0	4	0	-2	0	0	2	0	$1 - i \sqrt{15}$	$1 + i \sqrt{15}$	$- 1 + i \sqrt{15}$	$- 1 - i \sqrt{15}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₉	8	-8	-4	0	4	0	-2	0	0	2	0	$1 + i \sqrt{15}$	$1 - i \sqrt{15}$	$- 1 - i \sqrt{15}$	$- 1 + i \sqrt{15}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0

Character table — Group #91237