Finite Group Databasebeta

← Group #4478

Character table — Group #4478

Order 192.

	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	2	2	4	4	4	4	4	4	8	8	8	8	8	8	8	8	12	12	24	24	24
order	1	2	2	3	6	4	4	4	6	12	12	8	8	12	12	24	24	24	24	4	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	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	1	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	1
χ₅	1	1	1	1	1	1	-1	-1	1	-1	-1	$i$	$- i$	1	-1	$i$	$i$	$- i$	$- i$	1	1	-1	$i$	$- i$
χ₆	1	1	1	1	1	1	-1	-1	1	-1	-1	$i$	$- i$	1	-1	$i$	$i$	$- i$	$- i$	-1	-1	1	$- i$	$i$
χ₇	1	1	1	1	1	1	-1	-1	1	-1	-1	$- i$	$i$	1	-1	$- i$	$- i$	$i$	$i$	1	1	-1	$- i$	$i$
χ₈	1	1	1	1	1	1	-1	-1	1	-1	-1	$- i$	$i$	1	-1	$- i$	$- i$	$i$	$i$	-1	-1	1	$i$	$- i$
χ₉	2	2	2	2	2	-2	2	-2	2	2	2	0	0	-2	-2	0	0	0	0	0	0	0	0	0
χ₁₀	2	2	2	2	2	-2	-2	2	2	-2	-2	0	0	-2	2	0	0	0	0	0	0	0	0	0
χ₁₁	2	2	2	-1	-1	2	2	2	-1	-1	-1	2	2	-1	-1	-1	-1	-1	-1	0	0	0	0	0
χ₁₂	2	2	2	-1	-1	2	2	2	-1	-1	-1	-2	-2	-1	-1	1	1	1	1	0	0	0	0	0
χ₁₃	2	2	2	-1	-1	2	-2	-2	-1	1	1	$2 i$	$- 2 i$	-1	1	$- i$	$- i$	$i$	$i$	0	0	0	0	0
χ₁₄	2	2	2	-1	-1	2	-2	-2	-1	1	1	$- 2 i$	$2 i$	-1	1	$i$	$i$	$- i$	$- i$	0	0	0	0	0
χ₁₅	2	2	2	-1	-1	-2	2	-2	-1	-1	-1	0	0	1	1	$- i \sqrt{3}$	$i \sqrt{3}$	$- i \sqrt{3}$	$i \sqrt{3}$	0	0	0	0	0
χ₁₆	2	2	2	-1	-1	-2	2	-2	-1	-1	-1	0	0	1	1	$i \sqrt{3}$	$- i \sqrt{3}$	$i \sqrt{3}$	$- i \sqrt{3}$	0	0	0	0	0
χ₁₇	2	2	2	-1	-1	-2	-2	2	-1	1	1	0	0	1	-1	$\sqrt{3}$	$- \sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	0	0	0	0	0
χ₁₈	2	2	2	-1	-1	-2	-2	2	-1	1	1	0	0	1	-1	$- \sqrt{3}$	$\sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	0	0	0	0	0
χ₁₉	4	4	-4	4	4	0	0	0	-4	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₀	4	4	-4	-2	-2	0	0	0	2	$- 2 i \sqrt{3}$	$2 i \sqrt{3}$	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₁	4	4	-4	-2	-2	0	0	0	2	$2 i \sqrt{3}$	$- 2 i \sqrt{3}$	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₂	4	-4	0	4	-4	0	0	0	0	0	0	0	0	0	0	0	0	0	0	2	-2	0	0	0
χ₂₃	4	-4	0	4	-4	0	0	0	0	0	0	0	0	0	0	0	0	0	0	-2	2	0	0	0
χ₂₄	8	-8	0	-4	4	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0

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