Finite Group Databasebeta

← Group #1168

Character table — Group #1168

Order 112.

	C₁	C₂	C₃	C₄	C₅	C₆	C₇	C₈	C₉	C₁₀	C₁₁	C₁₂	C₁₃	C₁₄	C₁₅	C₁₆
size	1	7	8	8	8	8	8	8	1	7	8	8	8	8	8	8
order	1	2	7	7	7	7	7	7	2	2	14	14	14	14	14	14
χ₁	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1
χ₂	1	1	ζ	ζ²	ζ³	ζ⁴	ζ⁵	ζ⁶	1	1	ζ	ζ²	ζ³	ζ⁴	ζ⁵	ζ⁶
χ₃	1	1	ζ²	ζ⁴	ζ⁶	ζ	ζ³	ζ⁵	1	1	ζ²	ζ⁴	ζ⁶	ζ	ζ³	ζ⁵
χ₄	1	1	ζ³	ζ⁶	ζ²	ζ⁵	ζ	ζ⁴	1	1	ζ³	ζ⁶	ζ²	ζ⁵	ζ	ζ⁴
χ₅	1	1	ζ⁴	ζ	ζ⁵	ζ²	ζ⁶	ζ³	1	1	ζ⁴	ζ	ζ⁵	ζ²	ζ⁶	ζ³
χ₆	1	1	ζ⁵	ζ³	ζ	ζ⁶	ζ⁴	ζ²	1	1	ζ⁵	ζ³	ζ	ζ⁶	ζ⁴	ζ²
χ₇	1	1	ζ⁶	ζ⁵	ζ⁴	ζ³	ζ²	ζ	1	1	ζ⁶	ζ⁵	ζ⁴	ζ³	ζ²	ζ
χ₈	7	-1	0	0	0	0	0	0	7	-1	0	0	0	0	0	0
χ₉	1	1	1	1	1	1	1	1	-1	-1	-1	-1	-1	-1	-1	-1
χ₁₀	1	1	ζ	ζ²	ζ³	ζ⁴	ζ⁵	ζ⁶	-1	-1	−ζ	−ζ²	−ζ³	−ζ⁴	−ζ⁵	−ζ⁶
χ₁₁	1	1	ζ²	ζ⁴	ζ⁶	ζ	ζ³	ζ⁵	-1	-1	−ζ²	−ζ⁴	−ζ⁶	−ζ	−ζ³	−ζ⁵
χ₁₂	1	1	ζ³	ζ⁶	ζ²	ζ⁵	ζ	ζ⁴	-1	-1	−ζ³	−ζ⁶	−ζ²	−ζ⁵	−ζ	−ζ⁴
χ₁₃	1	1	ζ⁴	ζ	ζ⁵	ζ²	ζ⁶	ζ³	-1	-1	−ζ⁴	−ζ	−ζ⁵	−ζ²	−ζ⁶	−ζ³
χ₁₄	1	1	ζ⁵	ζ³	ζ	ζ⁶	ζ⁴	ζ²	-1	-1	−ζ⁵	−ζ³	−ζ	−ζ⁶	−ζ⁴	−ζ²
χ₁₅	1	1	ζ⁶	ζ⁵	ζ⁴	ζ³	ζ²	ζ	-1	-1	−ζ⁶	−ζ⁵	−ζ⁴	−ζ³	−ζ²	−ζ
χ₁₆	7	-1	0	0	0	0	0	0	-7	1	0	0	0	0	0	0

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