Finite Group Databasebeta

← Group #5389

Character table — Group #5389

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

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