Finite Group Databasebeta

← Group #4160

Character table — Group #4160

Order 160.

	C₁	C₂	C₃	C₄	C₅	C₆	C₇	C₈	C₉	C₁₀	C₁₁	C₁₂	C₁₃	C₁₄	C₁₅	C₁₆
size	1	5	5	5	16	16	16	16	1	5	5	5	16	16	16	16
order	1	2	2	2	5	5	5	5	2	2	2	2	10	10	10	10
χ₁	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1
χ₂	1	1	1	1	ζ	ζ²	ζ³	ζ⁴	1	1	1	1	ζ	ζ²	ζ³	ζ⁴
χ₃	1	1	1	1	ζ²	ζ⁴	ζ	ζ³	1	1	1	1	ζ²	ζ⁴	ζ	ζ³
χ₄	1	1	1	1	ζ³	ζ	ζ⁴	ζ²	1	1	1	1	ζ³	ζ	ζ⁴	ζ²
χ₅	1	1	1	1	ζ⁴	ζ³	ζ²	ζ	1	1	1	1	ζ⁴	ζ³	ζ²	ζ
χ₆	5	1	1	-3	0	0	0	0	5	1	1	-3	0	0	0	0
χ₇	5	1	-3	1	0	0	0	0	5	1	-3	1	0	0	0	0
χ₈	5	-3	1	1	0	0	0	0	5	-3	1	1	0	0	0	0
χ₉	1	1	1	1	1	1	1	1	-1	-1	-1	-1	-1	-1	-1	-1
χ₁₀	1	1	1	1	ζ	ζ²	ζ³	ζ⁴	-1	-1	-1	-1	−ζ	−ζ²	−ζ³	−ζ⁴
χ₁₁	1	1	1	1	ζ²	ζ⁴	ζ	ζ³	-1	-1	-1	-1	−ζ²	−ζ⁴	−ζ	−ζ³
χ₁₂	1	1	1	1	ζ³	ζ	ζ⁴	ζ²	-1	-1	-1	-1	−ζ³	−ζ	−ζ⁴	−ζ²
χ₁₃	1	1	1	1	ζ⁴	ζ³	ζ²	ζ	-1	-1	-1	-1	−ζ⁴	−ζ³	−ζ²	−ζ
χ₁₄	5	1	1	-3	0	0	0	0	-5	-1	-1	3	0	0	0	0
χ₁₅	5	1	-3	1	0	0	0	0	-5	-1	3	-1	0	0	0	0
χ₁₆	5	-3	1	1	0	0	0	0	-5	3	-1	-1	0	0	0	0

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