Finite Group Databasebeta

← Group #10621462

Character table — Group #10621462

Order 672.

	C₁	C₂	C₃	C₄	C₅	C₆	C₇	C₈	C₉	C₁₀	C₁₁	C₁₂	C₁₃	C₁₄	C₁₅	C₁₆
size	1	1	42	42	42	42	42	42	42	48	48	56	56	56	56	56
order	1	2	4	8	8	16	16	16	16	7	14	2	3	6	6	6
χ₁	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
χ₃	6	6	2	0	0	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	-1	-1	0	0	0	0	0
χ₄	6	6	2	0	0	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	-1	-1	0	0	0	0	0
χ₅	6	6	-2	2	2	0	0	0	0	-1	-1	0	0	0	0	0
χ₆	6	-6	0	$\sqrt{2}$	$- \sqrt{2}$	−ζ²⁵−ζ³¹−ζ⁴¹−ζ⁴⁷	ζ²⁵+ζ³¹+ζ⁴¹+ζ⁴⁷	ζ¹¹+ζ¹³+ζ²⁹+ζ⁴³	−ζ¹¹−ζ¹³−ζ²⁹−ζ⁴³	-1	1	0	0	0	0	0
χ₇	6	-6	0	$\sqrt{2}$	$- \sqrt{2}$	ζ²⁵+ζ³¹+ζ⁴¹+ζ⁴⁷	−ζ²⁵−ζ³¹−ζ⁴¹−ζ⁴⁷	−ζ¹¹−ζ¹³−ζ²⁹−ζ⁴³	ζ¹¹+ζ¹³+ζ²⁹+ζ⁴³	-1	1	0	0	0	0	0
χ₈	6	-6	0	$- \sqrt{2}$	$\sqrt{2}$	ζ¹¹+ζ¹³+ζ²⁹+ζ⁴³	−ζ¹¹−ζ¹³−ζ²⁹−ζ⁴³	ζ²⁵+ζ³¹+ζ⁴¹+ζ⁴⁷	−ζ²⁵−ζ³¹−ζ⁴¹−ζ⁴⁷	-1	1	0	0	0	0	0
χ₉	6	-6	0	$- \sqrt{2}$	$\sqrt{2}$	−ζ¹¹−ζ¹³−ζ²⁹−ζ⁴³	ζ¹¹+ζ¹³+ζ²⁹+ζ⁴³	−ζ²⁵−ζ³¹−ζ⁴¹−ζ⁴⁷	ζ²⁵+ζ³¹+ζ⁴¹+ζ⁴⁷	-1	1	0	0	0	0	0
χ₁₀	7	7	-1	-1	-1	1	1	1	1	0	0	-1	1	1	-1	-1
χ₁₁	7	7	-1	-1	-1	-1	-1	-1	-1	0	0	1	1	1	1	1
χ₁₂	8	8	0	0	0	0	0	0	0	1	1	2	-1	-1	-1	-1
χ₁₃	8	8	0	0	0	0	0	0	0	1	1	-2	-1	-1	1	1
χ₁₄	8	-8	0	0	0	0	0	0	0	1	-1	0	2	-2	0	0
χ₁₅	8	-8	0	0	0	0	0	0	0	1	-1	0	-1	1	$- i \sqrt{3}$	$i \sqrt{3}$
χ₁₆	8	-8	0	0	0	0	0	0	0	1	-1	0	-1	1	$i \sqrt{3}$	$- i \sqrt{3}$

Here ζ is a primitive root of unity of order 48 (ζ⁴⁸ = 1); i = ζ¹².