Finite Group Databasebeta

← Group #72209651

Character table — Group #72209651

Order 1536.

	C₁	C₂	C₃	C₄	C₅	C₆	C₇	C₈	C₉	C₁₀	C₁₁	C₁₂	C₁₃	C₁₄	C₁₅	C₁₆	C₁₇	C₁₈	C₁₉	C₂₀	C₂₁	C₂₂	C₂₃	C₂₄
size	1	1	2	6	6	12	12	24	48	48	48	48	96	96	96	96	96	96	96	96	128	128	128	128
order	1	2	4	2	4	4	4	4	2	4	8	8	2	4	8	8	16	16	16	16	3	6	12	12
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
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
χ₃	2	2	2	2	2	2	2	2	2	2	2	2	0	0	0	0	0	0	0	0	-1	-1	-1	-1
χ₄	3	3	3	3	3	3	3	3	-1	-1	-1	-1	1	1	1	1	-1	-1	-1	-1	0	0	0	0
χ₅	3	3	3	3	3	3	3	3	-1	-1	-1	-1	-1	-1	-1	-1	1	1	1	1	0	0	0	0
χ₆	3	3	3	3	3	-1	-1	-1	-1	-1	3	-1	1	1	-1	-1	1	1	-1	-1	0	0	0	0
χ₇	3	3	3	3	3	-1	-1	-1	-1	-1	3	-1	-1	-1	1	1	-1	-1	1	1	0	0	0	0
χ₈	3	3	3	3	3	-1	-1	-1	-1	-1	-1	3	1	1	-1	-1	-1	-1	1	1	0	0	0	0
χ₉	3	3	3	3	3	-1	-1	-1	-1	-1	-1	3	-1	-1	1	1	1	1	-1	-1	0	0	0	0
χ₁₀	4	4	-4	4	-4	0	0	0	0	0	0	0	0	0	2	-2	0	0	0	0	1	1	-1	-1
χ₁₁	4	4	-4	4	-4	0	0	0	0	0	0	0	0	0	-2	2	0	0	0	0	1	1	-1	-1
χ₁₂	6	6	6	6	6	-2	-2	-2	2	2	-2	-2	0	0	0	0	0	0	0	0	0	0	0	0
χ₁₃	6	6	-6	-2	2	2	2	-2	2	-2	0	0	0	0	0	0	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	0	0	0	0
χ₁₄	6	6	-6	-2	2	2	2	-2	2	-2	0	0	0	0	0	0	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	0	0	0	0
χ₁₅	6	6	-6	-2	2	2	2	-2	-2	2	0	0	0	0	0	0	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	0	0	0	0
χ₁₆	6	6	-6	-2	2	2	2	-2	-2	2	0	0	0	0	0	0	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	0	0	0	0
χ₁₇	8	8	-8	8	-8	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	-1	-1	1	1
χ₁₈	8	-8	0	0	0	-4	4	0	0	0	0	0	0	0	0	0	0	0	0	0	2	-2	0	0
χ₁₉	8	-8	0	0	0	-4	4	0	0	0	0	0	0	0	0	0	0	0	0	0	-1	1	$\sqrt{3}$	$- \sqrt{3}$
χ₂₀	8	-8	0	0	0	-4	4	0	0	0	0	0	0	0	0	0	0	0	0	0	-1	1	$- \sqrt{3}$	$\sqrt{3}$
χ₂₁	12	12	12	-4	-4	0	0	0	0	0	0	0	2	-2	0	0	0	0	0	0	0	0	0	0
χ₂₂	12	12	12	-4	-4	0	0	0	0	0	0	0	-2	2	0	0	0	0	0	0	0	0	0	0
χ₂₃	12	12	-12	-4	4	-4	-4	4	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₄	24	-24	0	0	0	4	-4	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0