Finite Group Databasebeta

← Group #4124

Character table — Group #4124

Order 160.

	C₁	C₂	C₃	C₄	C₅	C₆	C₇	C₈	C₉	C₁₀	C₁₁	C₁₂	C₁₃
size	1	1	10	10	10	16	16	16	16	16	16	16	16
order	1	2	2	4	4	5	5	5	5	10	10	10	10
χ₁	1	1	1	1	1	1	1	1	1	1	1	1	1
χ₂	1	1	1	1	1	ζ	ζ²	ζ³	ζ⁴	ζ	ζ²	ζ³	ζ⁴
χ₃	1	1	1	1	1	ζ²	ζ⁴	ζ	ζ³	ζ²	ζ⁴	ζ	ζ³
χ₄	1	1	1	1	1	ζ³	ζ	ζ⁴	ζ²	ζ³	ζ	ζ⁴	ζ²
χ₅	1	1	1	1	1	ζ⁴	ζ³	ζ²	ζ	ζ⁴	ζ³	ζ²	ζ
χ₆	4	-4	0	0	0	-1	-1	-1	-1	1	1	1	1
χ₇	4	-4	0	0	0	−ζ	−ζ²	−ζ³	−ζ⁴	ζ	ζ²	ζ³	ζ⁴
χ₈	4	-4	0	0	0	−ζ²	−ζ⁴	−ζ	−ζ³	ζ²	ζ⁴	ζ	ζ³
χ₉	4	-4	0	0	0	−ζ³	−ζ	−ζ⁴	−ζ²	ζ³	ζ	ζ⁴	ζ²
χ₁₀	4	-4	0	0	0	−ζ⁴	−ζ³	−ζ²	−ζ	ζ⁴	ζ³	ζ²	ζ
χ₁₁	5	5	1	1	-3	0	0	0	0	0	0	0	0
χ₁₂	5	5	1	-3	1	0	0	0	0	0	0	0	0
χ₁₃	5	5	-3	1	1	0	0	0	0	0	0	0	0

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