Finite Group Databasebeta

Character table — Group #89

Order 30.

	C₁	C₂	C₃	C₄	C₅	C₆	C₇	C₈	C₉	C₁₀	C₁₁	C₁₂	C₁₃	C₁₄	C₁₅
size	1	2	3	1	2	3	1	2	3	1	2	3	1	2	3
order	1	3	2	5	15	10	5	15	10	5	15	10	5	15	10
χ₁	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
χ₃	2	-1	0	2	-1	0	2	-1	0	2	-1	0	2	-1	0
χ₄	1	1	1	ζ	ζ	ζ	ζ²	ζ²	ζ²	ζ³	ζ³	ζ³	ζ⁴	ζ⁴	ζ⁴
χ₅	1	1	-1	ζ	ζ	−ζ	ζ²	ζ²	−ζ²	ζ³	ζ³	−ζ³	ζ⁴	ζ⁴	−ζ⁴
χ₆	2	-1	0	2ζ	−ζ	0	2ζ²	−ζ²	0	2ζ³	−ζ³	0	2ζ⁴	−ζ⁴	0
χ₇	1	1	1	ζ²	ζ²	ζ²	ζ⁴	ζ⁴	ζ⁴	ζ	ζ	ζ	ζ³	ζ³	ζ³
χ₈	1	1	-1	ζ²	ζ²	−ζ²	ζ⁴	ζ⁴	−ζ⁴	ζ	ζ	−ζ	ζ³	ζ³	−ζ³
χ₉	2	-1	0	2ζ²	−ζ²	0	2ζ⁴	−ζ⁴	0	2ζ	−ζ	0	2ζ³	−ζ³	0
χ₁₀	1	1	1	ζ³	ζ³	ζ³	ζ	ζ	ζ	ζ⁴	ζ⁴	ζ⁴	ζ²	ζ²	ζ²
χ₁₁	1	1	-1	ζ³	ζ³	−ζ³	ζ	ζ	−ζ	ζ⁴	ζ⁴	−ζ⁴	ζ²	ζ²	−ζ²
χ₁₂	2	-1	0	2ζ³	−ζ³	0	2ζ	−ζ	0	2ζ⁴	−ζ⁴	0	2ζ²	−ζ²	0
χ₁₃	1	1	1	ζ⁴	ζ⁴	ζ⁴	ζ³	ζ³	ζ³	ζ²	ζ²	ζ²	ζ	ζ	ζ
χ₁₄	1	1	-1	ζ⁴	ζ⁴	−ζ⁴	ζ³	ζ³	−ζ³	ζ²	ζ²	−ζ²	ζ	ζ	−ζ
χ₁₅	2	-1	0	2ζ⁴	−ζ⁴	0	2ζ³	−ζ³	0	2ζ²	−ζ²	0	2ζ	−ζ	0

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