Finite Group Databasebeta

Character table — Group #749

Order 84.

	C₁	C₂	C₃	C₄	C₅	C₆	C₇	C₈	C₉	C₁₀	C₁₁	C₁₂	C₁₃	C₁₄	C₁₅
size	1	2	2	2	7	2	4	4	4	14	3	6	6	6	21
order	1	7	7	7	2	3	21	21	21	6	2	14	14	14	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	ζ+ζ⁶	ζ²+ζ⁵	ζ³+ζ⁴	0	2	ζ+ζ⁶	ζ²+ζ⁵	ζ³+ζ⁴	0	2	ζ+ζ⁶	ζ²+ζ⁵	ζ³+ζ⁴	0
χ₄	2	ζ²+ζ⁵	ζ³+ζ⁴	ζ+ζ⁶	0	2	ζ²+ζ⁵	ζ³+ζ⁴	ζ+ζ⁶	0	2	ζ²+ζ⁵	ζ³+ζ⁴	ζ+ζ⁶	0
χ₅	2	ζ³+ζ⁴	ζ+ζ⁶	ζ²+ζ⁵	0	2	ζ³+ζ⁴	ζ+ζ⁶	ζ²+ζ⁵	0	2	ζ³+ζ⁴	ζ+ζ⁶	ζ²+ζ⁵	0
χ₆	1	1	1	1	1	1	1	1	1	1	-1	-1	-1	-1	-1
χ₇	1	1	1	1	-1	1	1	1	1	-1	-1	-1	-1	-1	1
χ₈	2	ζ+ζ⁶	ζ²+ζ⁵	ζ³+ζ⁴	0	2	ζ+ζ⁶	ζ²+ζ⁵	ζ³+ζ⁴	0	-2	−ζ−ζ⁶	−ζ²−ζ⁵	−ζ³−ζ⁴	0
χ₉	2	ζ²+ζ⁵	ζ³+ζ⁴	ζ+ζ⁶	0	2	ζ²+ζ⁵	ζ³+ζ⁴	ζ+ζ⁶	0	-2	−ζ²−ζ⁵	−ζ³−ζ⁴	−ζ−ζ⁶	0
χ₁₀	2	ζ³+ζ⁴	ζ+ζ⁶	ζ²+ζ⁵	0	2	ζ³+ζ⁴	ζ+ζ⁶	ζ²+ζ⁵	0	-2	−ζ³−ζ⁴	−ζ−ζ⁶	−ζ²−ζ⁵	0
χ₁₁	2	2	2	2	2	-1	-1	-1	-1	-1	0	0	0	0	0
χ₁₂	2	2	2	2	-2	-1	-1	-1	-1	1	0	0	0	0	0
χ₁₃	4	2ζ+2ζ⁶	2ζ²+2ζ⁵	2ζ³+2ζ⁴	0	-2	−ζ−ζ⁶	−ζ²−ζ⁵	−ζ³−ζ⁴	0	0	0	0	0	0
χ₁₄	4	2ζ²+2ζ⁵	2ζ³+2ζ⁴	2ζ+2ζ⁶	0	-2	−ζ²−ζ⁵	−ζ³−ζ⁴	−ζ−ζ⁶	0	0	0	0	0	0
χ₁₅	4	2ζ³+2ζ⁴	2ζ+2ζ⁶	2ζ²+2ζ⁵	0	-2	−ζ³−ζ⁴	−ζ−ζ⁶	−ζ²−ζ⁵	0	0	0	0	0	0

Here ζ is a primitive root of unity of order 7 (ζ⁷ = 1).