Finite Group Databasebeta

← Group #66348

Character table — Group #66348

Order 324.

	C₁	C₂	C₃	C₄	C₅	C₆	C₇	C₈	C₉	C₁₀	C₁₁	C₁₂	C₁₃	C₁₄	C₁₅	C₁₆	C₁₇
size	1	2	6	6	6	6	9	18	18	18	18	18	27	27	36	54	54
order	1	3	3	9	9	9	2	3	6	18	18	18	2	2	9	6	6
χ₁	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
χ₃	1	1	1	1	1	1	-1	1	-1	-1	-1	-1	1	-1	1	1	-1
χ₄	1	1	1	1	1	1	-1	1	-1	-1	-1	-1	-1	1	1	-1	1
χ₅	2	2	2	2	2	2	0	-1	0	0	0	0	0	2	-1	0	-1
χ₆	2	2	2	2	2	2	0	-1	0	0	0	0	0	-2	-1	0	1
χ₇	2	2	2	-1	-1	-1	2	2	2	-1	-1	-1	0	0	-1	0	0
χ₈	2	2	2	-1	-1	-1	-2	2	-2	1	1	1	0	0	-1	0	0
χ₉	4	4	4	-2	-2	-2	0	-2	0	0	0	0	0	0	1	0	0
χ₁₀	6	6	-3	0	0	0	0	0	0	0	0	0	2	0	0	-1	0
χ₁₁	6	6	-3	0	0	0	0	0	0	0	0	0	-2	0	0	1	0
χ₁₂	6	-3	0	2ζ−2ζ²+ζ⁴−ζ⁵	−ζ+ζ²+ζ⁴+2ζ⁵	−ζ+ζ²−2ζ⁴−ζ⁵	2	0	-1	ζ+ζ⁸	ζ²+ζ⁷	ζ⁴+ζ⁵	0	0	0	0	0
χ₁₃	6	-3	0	2ζ−2ζ²+ζ⁴−ζ⁵	−ζ+ζ²+ζ⁴+2ζ⁵	−ζ+ζ²−2ζ⁴−ζ⁵	-2	0	1	−ζ−ζ⁸	−ζ²−ζ⁷	−ζ⁴−ζ⁵	0	0	0	0	0
χ₁₄	6	-3	0	−ζ+ζ²+ζ⁴+2ζ⁵	−ζ+ζ²−2ζ⁴−ζ⁵	2ζ−2ζ²+ζ⁴−ζ⁵	2	0	-1	ζ⁴+ζ⁵	ζ+ζ⁸	ζ²+ζ⁷	0	0	0	0	0
χ₁₅	6	-3	0	−ζ+ζ²+ζ⁴+2ζ⁵	−ζ+ζ²−2ζ⁴−ζ⁵	2ζ−2ζ²+ζ⁴−ζ⁵	-2	0	1	−ζ⁴−ζ⁵	−ζ−ζ⁸	−ζ²−ζ⁷	0	0	0	0	0
χ₁₆	6	-3	0	−ζ+ζ²−2ζ⁴−ζ⁵	2ζ−2ζ²+ζ⁴−ζ⁵	−ζ+ζ²+ζ⁴+2ζ⁵	2	0	-1	ζ²+ζ⁷	ζ⁴+ζ⁵	ζ+ζ⁸	0	0	0	0	0
χ₁₇	6	-3	0	−ζ+ζ²−2ζ⁴−ζ⁵	2ζ−2ζ²+ζ⁴−ζ⁵	−ζ+ζ²+ζ⁴+2ζ⁵	-2	0	1	−ζ²−ζ⁷	−ζ⁴−ζ⁵	−ζ−ζ⁸	0	0	0	0	0

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