Finite Group Databasebeta

← Group #3766

Character table — Group #3766

Order 144.

	C₁	C₂	C₃	C₄	C₅	C₆	C₇	C₈	C₉	C₁₀	C₁₁	C₁₂	C₁₃	C₁₄	C₁₅	C₁₆	C₁₇	C₁₈
size	1	2	3	6	8	8	8	18	18	1	2	3	6	8	8	8	18	18
order	1	3	2	6	9	9	9	2	4	2	6	2	6	18	18	18	2	4
χ₁	1	1	1	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	1	-1	-1
χ₃	2	2	2	2	-1	-1	-1	0	0	2	2	2	2	-1	-1	-1	0	0
χ₄	2	-1	2	-1	ζ+ζ⁸	ζ²+ζ⁷	ζ⁴+ζ⁵	0	0	2	-1	2	-1	ζ+ζ⁸	ζ²+ζ⁷	ζ⁴+ζ⁵	0	0
χ₅	2	-1	2	-1	ζ²+ζ⁷	ζ⁴+ζ⁵	ζ+ζ⁸	0	0	2	-1	2	-1	ζ²+ζ⁷	ζ⁴+ζ⁵	ζ+ζ⁸	0	0
χ₆	2	-1	2	-1	ζ⁴+ζ⁵	ζ+ζ⁸	ζ²+ζ⁷	0	0	2	-1	2	-1	ζ⁴+ζ⁵	ζ+ζ⁸	ζ²+ζ⁷	0	0
χ₇	3	3	-1	-1	0	0	0	1	-1	3	3	-1	-1	0	0	0	1	-1
χ₈	3	3	-1	-1	0	0	0	-1	1	3	3	-1	-1	0	0	0	-1	1
χ₉	6	-3	-2	1	0	0	0	0	0	6	-3	-2	1	0	0	0	0	0
χ₁₀	1	1	1	1	1	1	1	1	1	-1	-1	-1	-1	-1	-1	-1	-1	-1
χ₁₁	1	1	1	1	1	1	1	-1	-1	-1	-1	-1	-1	-1	-1	-1	1	1
χ₁₂	2	2	2	2	-1	-1	-1	0	0	-2	-2	-2	-2	1	1	1	0	0
χ₁₃	2	-1	2	-1	ζ+ζ⁸	ζ²+ζ⁷	ζ⁴+ζ⁵	0	0	-2	1	-2	1	−ζ−ζ⁸	−ζ²−ζ⁷	−ζ⁴−ζ⁵	0	0
χ₁₄	2	-1	2	-1	ζ²+ζ⁷	ζ⁴+ζ⁵	ζ+ζ⁸	0	0	-2	1	-2	1	−ζ²−ζ⁷	−ζ⁴−ζ⁵	−ζ−ζ⁸	0	0
χ₁₅	2	-1	2	-1	ζ⁴+ζ⁵	ζ+ζ⁸	ζ²+ζ⁷	0	0	-2	1	-2	1	−ζ⁴−ζ⁵	−ζ−ζ⁸	−ζ²−ζ⁷	0	0
χ₁₆	3	3	-1	-1	0	0	0	1	-1	-3	-3	1	1	0	0	0	-1	1
χ₁₇	3	3	-1	-1	0	0	0	-1	1	-3	-3	1	1	0	0	0	1	-1
χ₁₈	6	-3	-2	1	0	0	0	0	0	-6	3	2	-1	0	0	0	0	0

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