Finite Group Databasebeta

← Group #85553

Character table — Group #85553

Order 384.

	C₁	C₂	C₃	C₄	C₅	C₆	C₇	C₈	C₉	C₁₀	C₁₁	C₁₂	C₁₃	C₁₄	C₁₅	C₁₆	C₁₇	C₁₈	C₁₉	C₂₀	C₂₁	C₂₂	C₂₃
size	1	1	1	1	6	6	6	6	12	12	12	12	12	24	24	24	24	24	32	32	32	32	48
order	1	2	2	2	4	4	4	4	4	8	8	8	8	4	8	8	8	8	3	6	6	6	4
χ₁	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
χ₃	2	2	2	2	2	2	2	2	2	0	0	0	0	2	0	0	0	0	-1	-1	-1	-1	0
χ₄	2	2	-2	-2	0	2	0	-2	0	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	0	0	0	$\sqrt{2}$	$- \sqrt{2}$	-1	1	1	-1	0
χ₅	2	2	-2	-2	0	2	0	-2	0	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	0	0	0	$- \sqrt{2}$	$\sqrt{2}$	-1	1	1	-1	0
χ₆	2	-2	2	-2	2	0	-2	0	0	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	0	$\sqrt{2}$	$- \sqrt{2}$	0	0	-1	1	-1	1	0
χ₇	2	-2	2	-2	2	0	-2	0	0	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	0	$- \sqrt{2}$	$\sqrt{2}$	0	0	-1	1	-1	1	0
χ₈	3	3	3	3	3	-1	3	-1	-1	1	1	1	1	-1	1	1	-1	-1	0	0	0	0	-1
χ₉	3	3	3	3	3	-1	3	-1	-1	-1	-1	-1	-1	-1	-1	-1	1	1	0	0	0	0	1
χ₁₀	3	3	3	3	-1	3	-1	3	-1	1	1	1	1	-1	-1	-1	1	1	0	0	0	0	-1
χ₁₁	3	3	3	3	-1	3	-1	3	-1	-1	-1	-1	-1	-1	1	1	-1	-1	0	0	0	0	1
χ₁₂	3	3	3	3	-1	-1	-1	-1	3	1	1	1	1	-1	-1	-1	-1	-1	0	0	0	0	1
χ₁₃	3	3	3	3	-1	-1	-1	-1	3	-1	-1	-1	-1	-1	1	1	1	1	0	0	0	0	-1
χ₁₄	4	4	-4	-4	0	4	0	-4	0	0	0	0	0	0	0	0	0	0	1	-1	-1	1	0
χ₁₅	4	-4	4	-4	4	0	-4	0	0	0	0	0	0	0	0	0	0	0	1	-1	1	-1	0
χ₁₆	4	-4	-4	4	0	0	0	0	0	2	-2	-2	2	0	0	0	0	0	1	1	-1	-1	0
χ₁₇	4	-4	-4	4	0	0	0	0	0	-2	2	2	-2	0	0	0	0	0	1	1	-1	-1	0
χ₁₈	6	6	6	6	-2	-2	-2	-2	-2	0	0	0	0	2	0	0	0	0	0	0	0	0	0
χ₁₉	6	6	-6	-6	0	-2	0	2	0	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	0	0	0	$- \sqrt{2}$	$\sqrt{2}$	0	0	0	0	0
χ₂₀	6	6	-6	-6	0	-2	0	2	0	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	0	0	0	$\sqrt{2}$	$- \sqrt{2}$	0	0	0	0	0
χ₂₁	6	-6	6	-6	-2	0	2	0	0	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	0	$- \sqrt{2}$	$\sqrt{2}$	0	0	0	0	0	0	0
χ₂₂	6	-6	6	-6	-2	0	2	0	0	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	0	$\sqrt{2}$	$- \sqrt{2}$	0	0	0	0	0	0	0
χ₂₃	8	-8	-8	8	0	0	0	0	0	0	0	0	0	0	0	0	0	0	-1	-1	1	1	0