Finite Group Databasebeta

← Group #3774

Character table — Group #3774

Order 144.

	C₁	C₂	C₃	C₄	C₅	C₆	C₇	C₈	C₉	C₁₀	C₁₁	C₁₂	C₁₃	C₁₄	C₁₅
size	1	1	4	4	4	4	12	12	12	12	12	12	18	18	18
order	1	2	3	3	6	6	2	2	6	6	6	6	4	8	8
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	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
χ₅	2	2	2	2	2	2	0	0	0	0	0	0	-2	0	0
χ₆	2	-2	2	2	-2	-2	0	0	0	0	0	0	0	$\sqrt{2}$	$- \sqrt{2}$
χ₇	2	-2	2	2	-2	-2	0	0	0	0	0	0	0	$- \sqrt{2}$	$\sqrt{2}$
χ₈	4	4	1	-2	1	-2	0	2	0	0	-1	-1	0	0	0
χ₉	4	4	1	-2	1	-2	0	-2	0	0	1	1	0	0	0
χ₁₀	4	4	-2	1	-2	1	2	0	-1	-1	0	0	0	0	0
χ₁₁	4	4	-2	1	-2	1	-2	0	1	1	0	0	0	0	0
χ₁₂	4	-4	1	-2	-1	2	0	0	0	0	$- i \sqrt{3}$	$i \sqrt{3}$	0	0	0
χ₁₃	4	-4	1	-2	-1	2	0	0	0	0	$i \sqrt{3}$	$- i \sqrt{3}$	0	0	0
χ₁₄	4	-4	-2	1	2	-1	0	0	$- i \sqrt{3}$	$i \sqrt{3}$	0	0	0	0	0
χ₁₅	4	-4	-2	1	2	-1	0	0	$i \sqrt{3}$	$- i \sqrt{3}$	0	0	0	0	0

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