Finite Group Databasebeta

← Group #4621

Character table — Group #4621

Order 192.

	C₁	C₂	C₃	C₄	C₅	C₆	C₇	C₈	C₉	C₁₀	C₁₁	C₁₂	C₁₃	C₁₄	C₁₅
size	1	1	3	3	6	6	12	12	12	12	12	24	24	32	32
order	1	2	2	2	4	4	4	8	8	8	8	4	4	3	6
χ₁	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
χ₃	2	2	2	2	2	2	2	0	0	0	0	0	0	-1	-1
χ₄	2	-2	2	-2	0	0	0	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	0	0	-1	1
χ₅	2	-2	2	-2	0	0	0	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	0	0	-1	1
χ₆	3	3	3	3	-1	-1	-1	1	1	1	1	-1	-1	0	0
χ₇	3	3	3	3	-1	-1	-1	-1	-1	-1	-1	1	1	0	0
χ₈	3	3	-1	-1	$- 1 + 2 i$	$- 1 - 2 i$	1	$i$	$- i$	$i$	$- i$	-1	1	0	0
χ₉	3	3	-1	-1	$- 1 + 2 i$	$- 1 - 2 i$	1	$- i$	$i$	$- i$	$i$	1	-1	0	0
χ₁₀	3	3	-1	-1	$- 1 - 2 i$	$- 1 + 2 i$	1	$i$	$- i$	$i$	$- i$	1	-1	0	0
χ₁₁	3	3	-1	-1	$- 1 - 2 i$	$- 1 + 2 i$	1	$- i$	$i$	$- i$	$i$	-1	1	0	0
χ₁₂	4	-4	4	-4	0	0	0	0	0	0	0	0	0	1	-1
χ₁₃	6	6	-2	-2	2	2	-2	0	0	0	0	0	0	0	0
χ₁₄	6	-6	-2	2	0	0	0	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	0	0	0	0
χ₁₅	6	-6	-2	2	0	0	0	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	0	0	0	0

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