Finite Group Databasebeta

Character table — Group #271

Order 54.

	C₁	C₂	C₃	C₄	C₅	C₆	C₇	C₈	C₉	C₁₀	C₁₁	C₁₂	C₁₃	C₁₄	C₁₅
size	1	2	2	2	2	2	2	2	2	2	2	2	2	2	27
order	1	3	3	3	3	9	9	9	9	9	9	9	9	9	2
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	2	2	2	2	-1	-1	-1	-1	-1	-1	-1	-1	-1	0
χ₄	2	2	-1	-1	-1	ζ+ζ⁸	ζ+ζ⁸	ζ+ζ⁸	ζ²+ζ⁷	ζ²+ζ⁷	ζ²+ζ⁷	ζ⁴+ζ⁵	ζ⁴+ζ⁵	ζ⁴+ζ⁵	0
χ₅	2	2	-1	-1	-1	ζ²+ζ⁷	ζ²+ζ⁷	ζ²+ζ⁷	ζ⁴+ζ⁵	ζ⁴+ζ⁵	ζ⁴+ζ⁵	ζ+ζ⁸	ζ+ζ⁸	ζ+ζ⁸	0
χ₆	2	2	-1	-1	-1	ζ⁴+ζ⁵	ζ⁴+ζ⁵	ζ⁴+ζ⁵	ζ+ζ⁸	ζ+ζ⁸	ζ+ζ⁸	ζ²+ζ⁷	ζ²+ζ⁷	ζ²+ζ⁷	0
χ₇	2	-1	2	-1	-1	ζ+ζ⁸	ζ²+ζ⁷	ζ⁴+ζ⁵	ζ+ζ⁸	ζ²+ζ⁷	ζ⁴+ζ⁵	ζ+ζ⁸	ζ²+ζ⁷	ζ⁴+ζ⁵	0
χ₈	2	-1	2	-1	-1	ζ²+ζ⁷	ζ⁴+ζ⁵	ζ+ζ⁸	ζ²+ζ⁷	ζ⁴+ζ⁵	ζ+ζ⁸	ζ²+ζ⁷	ζ⁴+ζ⁵	ζ+ζ⁸	0
χ₉	2	-1	2	-1	-1	ζ⁴+ζ⁵	ζ+ζ⁸	ζ²+ζ⁷	ζ⁴+ζ⁵	ζ+ζ⁸	ζ²+ζ⁷	ζ⁴+ζ⁵	ζ+ζ⁸	ζ²+ζ⁷	0
χ₁₀	2	-1	-1	2	-1	ζ+ζ⁸	ζ⁴+ζ⁵	ζ²+ζ⁷	ζ⁴+ζ⁵	ζ²+ζ⁷	ζ+ζ⁸	ζ²+ζ⁷	ζ+ζ⁸	ζ⁴+ζ⁵	0
χ₁₁	2	-1	-1	2	-1	ζ²+ζ⁷	ζ+ζ⁸	ζ⁴+ζ⁵	ζ+ζ⁸	ζ⁴+ζ⁵	ζ²+ζ⁷	ζ⁴+ζ⁵	ζ²+ζ⁷	ζ+ζ⁸	0
χ₁₂	2	-1	-1	2	-1	ζ⁴+ζ⁵	ζ²+ζ⁷	ζ+ζ⁸	ζ²+ζ⁷	ζ+ζ⁸	ζ⁴+ζ⁵	ζ+ζ⁸	ζ⁴+ζ⁵	ζ²+ζ⁷	0
χ₁₃	2	-1	-1	-1	2	2	-1	-1	-1	2	-1	-1	-1	2	0
χ₁₄	2	-1	-1	-1	2	-1	2	-1	-1	-1	2	2	-1	-1	0
χ₁₅	2	-1	-1	-1	2	-1	-1	2	2	-1	-1	-1	2	-1	0

Here ζ is a primitive root of unity of order 9 (ζ⁹ = 1).