Finite Group Databasebeta

← Group #2053

Character table — Group #2053

Order 128.

	C₁	C₂	C₃	C₄	C₅	C₆	C₇	C₈	C₉	C₁₀	C₁₁	C₁₂	C₁₃	C₁₄	C₁₅	C₁₆	C₁₇	C₁₈	C₁₉	C₂₀	C₂₁	C₂₂	C₂₃	C₂₄	C₂₅	C₂₆
size	1	1	1	1	2	2	2	2	2	2	4	4	4	4	8	8	8	8	8	8	8	8	8	8	8	8
order	1	2	4	4	2	2	2	4	4	4	8	8	8	8	2	2	4	4	4	4	4	4	4	4	8	8
χ₁	1	1	1	1	1	1	1	1	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	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	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	-1	-1	-1	-1	-1	1	1	1	1
χ₅	1	1	1	1	1	1	1	1	1	1	-1	-1	-1	-1	1	1	1	1	-1	-1	-1	-1	-1	-1	1	1
χ₆	1	1	1	1	1	1	1	1	1	1	-1	-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	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	1	1	1	1	-1	-1	1	1
χ₉	2	2	2	2	2	-2	-2	2	-2	-2	0	0	0	0	0	0	0	0	0	0	$2 i$	$- 2 i$	0	0	0	0
χ₁₀	2	2	2	2	2	-2	-2	2	-2	-2	0	0	0	0	0	0	0	0	0	0	$- 2 i$	$2 i$	0	0	0	0
χ₁₁	2	2	2	2	-2	2	-2	-2	2	-2	0	0	0	0	0	0	0	0	$2 i$	$- 2 i$	0	0	0	0	0	0
χ₁₂	2	2	2	2	-2	2	-2	-2	2	-2	0	0	0	0	0	0	0	0	$- 2 i$	$2 i$	0	0	0	0	0	0
χ₁₃	2	2	2	2	-2	-2	2	-2	-2	2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	2	-2
χ₁₄	2	2	2	2	-2	-2	2	-2	-2	2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	-2	2
χ₁₅	2	2	-2	-2	2	2	2	-2	-2	-2	0	0	0	0	0	0	0	0	0	0	0	0	2	-2	0	0
χ₁₆	2	2	-2	-2	2	2	2	-2	-2	-2	0	0	0	0	0	0	0	0	0	0	0	0	-2	2	0	0
χ₁₇	2	2	-2	-2	2	-2	-2	-2	2	2	0	0	0	0	2	0	-2	0	0	0	0	0	0	0	0	0
χ₁₈	2	2	-2	-2	2	-2	-2	-2	2	2	0	0	0	0	-2	0	2	0	0	0	0	0	0	0	0	0
χ₁₉	2	2	-2	-2	-2	2	-2	2	-2	2	0	0	0	0	0	2	0	-2	0	0	0	0	0	0	0	0
χ₂₀	2	2	-2	-2	-2	2	-2	2	-2	2	0	0	0	0	0	-2	0	2	0	0	0	0	0	0	0	0
χ₂₁	2	2	-2	-2	-2	-2	2	2	2	-2	$2 i$	$2 i$	$- 2 i$	$- 2 i$	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₂	2	2	-2	-2	-2	-2	2	2	2	-2	$- 2 i$	$- 2 i$	$2 i$	$2 i$	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₃	4	-4	$4 i$	$- 4 i$	0	0	0	0	0	0	2ζ	−2ζ	2ζ³	−2ζ³	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₄	4	-4	$4 i$	$- 4 i$	0	0	0	0	0	0	−2ζ	2ζ	−2ζ³	2ζ³	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₅	4	-4	$- 4 i$	$4 i$	0	0	0	0	0	0	2ζ³	−2ζ³	2ζ	−2ζ	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₆	4	-4	$- 4 i$	$4 i$	0	0	0	0	0	0	−2ζ³	2ζ³	−2ζ	2ζ	0	0	0	0	0	0	0	0	0	0	0	0

Here ζ is a primitive root of unity of order 8 (ζ⁸ = 1); i = ζ².