Finite Group Databasebeta

← Group #6033

Character table — Group #6033

Order 200.

	C₁	C₂	C₃	C₄	C₅	C₆	C₇	C₈	C₉	C₁₀	C₁₁	C₁₂	C₁₃	C₁₄	C₁₅	C₁₆	C₁₇	C₁₈	C₁₉	C₂₀
size	1	1	4	4	4	4	4	4	4	4	4	4	4	4	25	25	25	25	25	25
order	1	2	5	5	5	5	5	5	10	10	10	10	10	10	4	4	8	8	8	8
χ₁	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
χ₃	1	1	1	1	1	1	1	1	1	1	1	1	1	1	-1	-1	$i$	$i$	$- i$	$- i$
χ₄	1	1	1	1	1	1	1	1	1	1	1	1	1	1	-1	-1	$- i$	$- i$	$i$	$i$
χ₅	1	-1	1	1	1	1	1	1	-1	-1	-1	-1	-1	-1	$i$	$- i$	ζ	−ζ	ζ³	−ζ³
χ₆	1	-1	1	1	1	1	1	1	-1	-1	-1	-1	-1	-1	$i$	$- i$	−ζ	ζ	−ζ³	ζ³
χ₇	1	-1	1	1	1	1	1	1	-1	-1	-1	-1	-1	-1	$- i$	$i$	ζ³	−ζ³	ζ	−ζ
χ₈	1	-1	1	1	1	1	1	1	-1	-1	-1	-1	-1	-1	$- i$	$i$	−ζ³	ζ³	−ζ	ζ
χ₉	4	4	4	-1	-1	-1	-1	-1	4	-1	-1	-1	-1	-1	0	0	0	0	0	0
χ₁₀	4	4	-1	4	-1	-1	-1	-1	-1	4	-1	-1	-1	-1	0	0	0	0	0	0
χ₁₁	4	4	-1	-1	4	-1	-1	-1	-1	-1	4	-1	-1	-1	0	0	0	0	0	0
χ₁₂	4	4	-1	-1	-1	4	-1	-1	-1	-1	-1	4	-1	-1	0	0	0	0	0	0
χ₁₃	4	4	-1	-1	-1	-1	4	-1	-1	-1	-1	-1	4	-1	0	0	0	0	0	0
χ₁₄	4	4	-1	-1	-1	-1	-1	4	-1	-1	-1	-1	-1	4	0	0	0	0	0	0
χ₁₅	4	-4	4	-1	-1	-1	-1	-1	-4	1	1	1	1	1	0	0	0	0	0	0
χ₁₆	4	-4	-1	4	-1	-1	-1	-1	1	-4	1	1	1	1	0	0	0	0	0	0
χ₁₇	4	-4	-1	-1	4	-1	-1	-1	1	1	-4	1	1	1	0	0	0	0	0	0
χ₁₈	4	-4	-1	-1	-1	4	-1	-1	1	1	1	-4	1	1	0	0	0	0	0	0
χ₁₉	4	-4	-1	-1	-1	-1	4	-1	1	1	1	1	-4	1	0	0	0	0	0	0
χ₂₀	4	-4	-1	-1	-1	-1	-1	4	1	1	1	1	1	-4	0	0	0	0	0	0

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