Finite Group Databasebeta

← Group #87515

Character table — Group #87515

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	2	6	6	6	6	6	6	12	12	24	24	24	24	24	24	24	24	32	32	32	32
order	1	2	2	2	2	2	2	2	2	4	4	2	4	4	4	4	4	4	4	3	6	6	6
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	1	1	-1	-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	1	-1	-1
χ₅	2	2	2	2	2	2	2	2	2	2	2	0	0	0	0	0	0	0	0	-1	-1	-1	-1
χ₆	2	2	-2	-2	-2	-2	2	2	2	2	-2	0	0	0	0	0	0	0	0	-1	-1	1	1
χ₇	3	3	3	3	-1	-1	3	-1	-1	-1	-1	1	1	1	-1	-1	1	-1	-1	0	0	0	0
χ₈	3	3	3	3	-1	-1	3	-1	-1	-1	-1	-1	-1	-1	1	1	-1	1	1	0	0	0	0
χ₉	3	3	3	-1	3	-1	-1	3	-1	-1	-1	1	1	-1	1	-1	-1	1	-1	0	0	0	0
χ₁₀	3	3	3	-1	3	-1	-1	3	-1	-1	-1	-1	-1	1	-1	1	1	-1	1	0	0	0	0
χ₁₁	3	3	3	-1	-1	3	-1	-1	3	-1	-1	1	1	-1	-1	1	-1	-1	1	0	0	0	0
χ₁₂	3	3	3	-1	-1	3	-1	-1	3	-1	-1	-1	-1	1	1	-1	1	1	-1	0	0	0	0
χ₁₃	3	3	-3	1	1	-3	-1	-1	3	-1	1	1	-1	-1	-1	1	1	1	-1	0	0	0	0
χ₁₄	3	3	-3	1	1	-3	-1	-1	3	-1	1	-1	1	1	1	-1	-1	-1	1	0	0	0	0
χ₁₅	3	3	-3	1	-3	1	-1	3	-1	-1	1	1	-1	-1	1	-1	1	-1	1	0	0	0	0
χ₁₆	3	3	-3	1	-3	1	-1	3	-1	-1	1	-1	1	1	-1	1	-1	1	-1	0	0	0	0
χ₁₇	3	3	-3	-3	1	1	3	-1	-1	-1	1	1	-1	1	-1	-1	-1	1	1	0	0	0	0
χ₁₈	3	3	-3	-3	1	1	3	-1	-1	-1	1	-1	1	-1	1	1	1	-1	-1	0	0	0	0
χ₁₉	6	6	6	-2	-2	-2	-2	-2	-2	2	2	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₀	6	6	-6	2	2	2	-2	-2	-2	2	-2	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₁	8	-8	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	2	-2	0	0
χ₂₂	8	-8	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	-1	1	$i \sqrt{3}$	$- i \sqrt{3}$
χ₂₃	8	-8	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	-1	1	$- i \sqrt{3}$	$i \sqrt{3}$

Here i is the imaginary unit (i² = −1).