Finite Group Databasebeta

Character table — Group #204

Order 48.

	C₁	C₂	C₃	C₄	C₅	C₆	C₇	C₈	C₉	C₁₀	C₁₁	C₁₂	C₁₃	C₁₄	C₁₅
size	1	1	2	2	2	2	2	2	2	2	2	2	2	12	12
order	1	2	3	4	6	8	8	12	12	24	24	24	24	2	4
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	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
χ₅	2	2	2	-2	2	0	0	-2	-2	0	0	0	0	0	0
χ₆	2	2	-1	2	-1	2	2	-1	-1	-1	-1	-1	-1	0	0
χ₇	2	2	-1	2	-1	-2	-2	-1	-1	1	1	1	1	0	0
χ₈	2	2	-1	-2	-1	0	0	1	1	$\sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$- \sqrt{3}$	0	0
χ₉	2	2	-1	-2	-1	0	0	1	1	$- \sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$\sqrt{3}$	0	0
χ₁₀	2	-2	2	0	-2	$- i \sqrt{2}$	$i \sqrt{2}$	0	0	$- i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	0	0
χ₁₁	2	-2	2	0	-2	$i \sqrt{2}$	$- i \sqrt{2}$	0	0	$i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	0	0
χ₁₂	2	-2	-1	0	1	$- i \sqrt{2}$	$i \sqrt{2}$	$\sqrt{3}$	$- \sqrt{3}$	ζ⁵+ζ⁷	−ζ⁵−ζ⁷	ζ¹³+ζ²³	−ζ¹³−ζ²³	0	0
χ₁₃	2	-2	-1	0	1	$- i \sqrt{2}$	$i \sqrt{2}$	$- \sqrt{3}$	$\sqrt{3}$	ζ¹³+ζ²³	−ζ¹³−ζ²³	ζ⁵+ζ⁷	−ζ⁵−ζ⁷	0	0
χ₁₄	2	-2	-1	0	1	$i \sqrt{2}$	$- i \sqrt{2}$	$\sqrt{3}$	$- \sqrt{3}$	−ζ⁵−ζ⁷	ζ⁵+ζ⁷	−ζ¹³−ζ²³	ζ¹³+ζ²³	0	0
χ₁₅	2	-2	-1	0	1	$i \sqrt{2}$	$- i \sqrt{2}$	$- \sqrt{3}$	$\sqrt{3}$	−ζ¹³−ζ²³	ζ¹³+ζ²³	−ζ⁵−ζ⁷	ζ⁵+ζ⁷	0	0

Here ζ is a primitive root of unity of order 24 (ζ²⁴ = 1); i = ζ⁶.