Finite Group Databasebeta

← Group #5403

Character table — Group #5403

Order 192.

	C₁	C₂	C₃	C₄	C₅	C₆	C₇	C₈	C₉	C₁₀	C₁₁	C₁₂	C₁₃	C₁₄	C₁₅	C₁₆	C₁₇	C₁₈	C₁₉	C₂₀
size	1	1	2	2	2	6	6	8	8	8	8	8	8	8	8	12	24	24	24	24
order	1	2	4	8	8	2	4	3	6	12	12	24	24	24	24	8	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
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	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
χ₅	2	2	2	2	2	2	2	-1	-1	-1	-1	-1	-1	-1	-1	2	0	0	0	0
χ₆	2	2	2	-2	-2	2	2	-1	-1	-1	-1	1	1	1	1	-2	0	0	0	0
χ₇	2	2	-2	0	0	-2	2	2	2	-2	-2	0	0	0	0	0	0	0	0	0
χ₈	2	2	-2	0	0	-2	2	-1	-1	1	1	$\sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$- \sqrt{3}$	0	0	0	0	0
χ₉	2	2	-2	0	0	-2	2	-1	-1	1	1	$- \sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$\sqrt{3}$	0	0	0	0	0
χ₁₀	3	3	3	3	3	-1	-1	0	0	0	0	0	0	0	0	-1	1	1	-1	-1
χ₁₁	3	3	3	3	3	-1	-1	0	0	0	0	0	0	0	0	-1	-1	-1	1	1
χ₁₂	3	3	3	-3	-3	-1	-1	0	0	0	0	0	0	0	0	1	1	-1	-1	1
χ₁₃	3	3	3	-3	-3	-1	-1	0	0	0	0	0	0	0	0	1	-1	1	1	-1
χ₁₄	4	-4	0	$2 \sqrt{2}$	$- 2 \sqrt{2}$	0	0	1	-1	$\sqrt{3}$	$- \sqrt{3}$	ζ⁵−ζ⁷	−ζ⁵+ζ⁷	−ζ¹³+ζ²³	ζ¹³−ζ²³	0	0	0	0	0
χ₁₅	4	-4	0	$2 \sqrt{2}$	$- 2 \sqrt{2}$	0	0	1	-1	$- \sqrt{3}$	$\sqrt{3}$	ζ¹³−ζ²³	−ζ¹³+ζ²³	−ζ⁵+ζ⁷	ζ⁵−ζ⁷	0	0	0	0	0
χ₁₆	4	-4	0	$2 \sqrt{2}$	$- 2 \sqrt{2}$	0	0	-2	2	0	0	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	0	0	0	0	0
χ₁₇	4	-4	0	$- 2 \sqrt{2}$	$2 \sqrt{2}$	0	0	1	-1	$\sqrt{3}$	$- \sqrt{3}$	−ζ⁵+ζ⁷	ζ⁵−ζ⁷	ζ¹³−ζ²³	−ζ¹³+ζ²³	0	0	0	0	0
χ₁₈	4	-4	0	$- 2 \sqrt{2}$	$2 \sqrt{2}$	0	0	1	-1	$- \sqrt{3}$	$\sqrt{3}$	−ζ¹³+ζ²³	ζ¹³−ζ²³	ζ⁵−ζ⁷	−ζ⁵+ζ⁷	0	0	0	0	0
χ₁₉	4	-4	0	$- 2 \sqrt{2}$	$2 \sqrt{2}$	0	0	-2	2	0	0	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	0	0	0	0	0
χ₂₀	6	6	-6	0	0	2	-2	0	0	0	0	0	0	0	0	0	0	0	0	0

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