Finite Group Databasebeta

← Group #3874

Character table — Group #3874

Order 150.

	C₁	C₂	C₃	C₄	C₅	C₆	C₇	C₈	C₉	C₁₀	C₁₁	C₁₂	C₁₃
size	1	3	3	3	3	6	6	15	15	15	15	15	50
order	1	5	5	5	5	5	5	2	10	10	10	10	3
χ₁	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
χ₃	2	2	2	2	2	2	2	0	0	0	0	0	-1
χ₄	3	ζ+2ζ²	2ζ+ζ³	ζ²+2ζ⁴	2ζ³+ζ⁴	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	1	ζ	ζ²	ζ³	ζ⁴	0
χ₅	3	ζ+2ζ²	2ζ+ζ³	ζ²+2ζ⁴	2ζ³+ζ⁴	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	-1	−ζ	−ζ²	−ζ³	−ζ⁴	0
χ₆	3	2ζ+ζ³	2ζ³+ζ⁴	ζ+2ζ²	ζ²+2ζ⁴	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	1	ζ³	ζ	ζ⁴	ζ²	0
χ₇	3	2ζ+ζ³	2ζ³+ζ⁴	ζ+2ζ²	ζ²+2ζ⁴	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	-1	−ζ³	−ζ	−ζ⁴	−ζ²	0
χ₈	3	ζ²+2ζ⁴	ζ+2ζ²	2ζ³+ζ⁴	2ζ+ζ³	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	1	ζ²	ζ⁴	ζ	ζ³	0
χ₉	3	ζ²+2ζ⁴	ζ+2ζ²	2ζ³+ζ⁴	2ζ+ζ³	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	-1	−ζ²	−ζ⁴	−ζ	−ζ³	0
χ₁₀	3	2ζ³+ζ⁴	ζ²+2ζ⁴	2ζ+ζ³	ζ+2ζ²	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	1	ζ⁴	ζ³	ζ²	ζ	0
χ₁₁	3	2ζ³+ζ⁴	ζ²+2ζ⁴	2ζ+ζ³	ζ+2ζ²	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	-1	−ζ⁴	−ζ³	−ζ²	−ζ	0
χ₁₂	6	$1 - \sqrt{5}$	$1 + \sqrt{5}$	$1 + \sqrt{5}$	$1 - \sqrt{5}$	$\frac{- 3 + \sqrt{5}}{2}$	$\frac{- 3 - \sqrt{5}}{2}$	0	0	0	0	0	0
χ₁₃	6	$1 + \sqrt{5}$	$1 - \sqrt{5}$	$1 - \sqrt{5}$	$1 + \sqrt{5}$	$\frac{- 3 - \sqrt{5}}{2}$	$\frac{- 3 + \sqrt{5}}{2}$	0	0	0	0	0	0

Here ζ is a primitive root of unity of order 5 (ζ⁵ = 1).