Finite Group Databasebeta

← Group #1089

Character table — Group #1089

Order 108.

	C₁	C₂	C₃	C₄	C₅	C₆	C₇	C₈	C₉	C₁₀	C₁₁	C₁₂	C₁₃	C₁₄	C₁₅	C₁₆	C₁₇	C₁₈
size	1	2	2	2	2	9	2	4	4	4	4	18	3	6	6	6	6	27
order	1	3	9	9	9	2	3	3	9	9	9	6	2	6	18	18	18	2
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	-1	-1	-1	0	2	2	-1	-1	-1	0	2	2	-1	-1	-1	0
χ₄	2	-1	ζ+ζ⁸	ζ²+ζ⁷	ζ⁴+ζ⁵	0	2	-1	ζ+ζ⁸	ζ²+ζ⁷	ζ⁴+ζ⁵	0	2	-1	ζ+ζ⁸	ζ²+ζ⁷	ζ⁴+ζ⁵	0
χ₅	2	-1	ζ²+ζ⁷	ζ⁴+ζ⁵	ζ+ζ⁸	0	2	-1	ζ²+ζ⁷	ζ⁴+ζ⁵	ζ+ζ⁸	0	2	-1	ζ²+ζ⁷	ζ⁴+ζ⁵	ζ+ζ⁸	0
χ₆	2	-1	ζ⁴+ζ⁵	ζ+ζ⁸	ζ²+ζ⁷	0	2	-1	ζ⁴+ζ⁵	ζ+ζ⁸	ζ²+ζ⁷	0	2	-1	ζ⁴+ζ⁵	ζ+ζ⁸	ζ²+ζ⁷	0
χ₇	1	1	1	1	1	1	1	1	1	1	1	1	-1	-1	-1	-1	-1	-1
χ₈	1	1	1	1	1	-1	1	1	1	1	1	-1	-1	-1	-1	-1	-1	1
χ₉	2	2	-1	-1	-1	0	2	2	-1	-1	-1	0	-2	-2	1	1	1	0
χ₁₀	2	-1	ζ+ζ⁸	ζ²+ζ⁷	ζ⁴+ζ⁵	0	2	-1	ζ+ζ⁸	ζ²+ζ⁷	ζ⁴+ζ⁵	0	-2	1	−ζ−ζ⁸	−ζ²−ζ⁷	−ζ⁴−ζ⁵	0
χ₁₁	2	-1	ζ²+ζ⁷	ζ⁴+ζ⁵	ζ+ζ⁸	0	2	-1	ζ²+ζ⁷	ζ⁴+ζ⁵	ζ+ζ⁸	0	-2	1	−ζ²−ζ⁷	−ζ⁴−ζ⁵	−ζ−ζ⁸	0
χ₁₂	2	-1	ζ⁴+ζ⁵	ζ+ζ⁸	ζ²+ζ⁷	0	2	-1	ζ⁴+ζ⁵	ζ+ζ⁸	ζ²+ζ⁷	0	-2	1	−ζ⁴−ζ⁵	−ζ−ζ⁸	−ζ²−ζ⁷	0
χ₁₃	2	2	2	2	2	2	-1	-1	-1	-1	-1	-1	0	0	0	0	0	0
χ₁₄	2	2	2	2	2	-2	-1	-1	-1	-1	-1	1	0	0	0	0	0	0
χ₁₅	4	4	-2	-2	-2	0	-2	-2	1	1	1	0	0	0	0	0	0	0
χ₁₆	4	-2	2ζ+2ζ⁸	2ζ²+2ζ⁷	2ζ⁴+2ζ⁵	0	-2	1	−ζ−ζ⁸	−ζ²−ζ⁷	−ζ⁴−ζ⁵	0	0	0	0	0	0	0
χ₁₇	4	-2	2ζ²+2ζ⁷	2ζ⁴+2ζ⁵	2ζ+2ζ⁸	0	-2	1	−ζ²−ζ⁷	−ζ⁴−ζ⁵	−ζ−ζ⁸	0	0	0	0	0	0	0
χ₁₈	4	-2	2ζ⁴+2ζ⁵	2ζ+2ζ⁸	2ζ²+2ζ⁷	0	-2	1	−ζ⁴−ζ⁵	−ζ−ζ⁸	−ζ²−ζ⁷	0	0	0	0	0	0	0

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