Finite Group Databasebeta

← Group #13088278

Character table — Group #13088278

Order 1440.

	C₁	C₂	C₃	C₄	C₅	C₆	C₇	C₈	C₉	C₁₀	C₁₁	C₁₂	C₁₃	C₁₄	C₁₅	C₁₆
size	1	1	45	45	80	80	90	90	90	90	90	90	144	144	180	180
order	1	2	2	2	3	6	4	4	8	8	8	8	5	10	4	4
χ₁	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
χ₃	1	-1	1	-1	1	-1	1	-1	$i$	$i$	$- i$	$- i$	1	-1	$i$	$- i$
χ₄	1	-1	1	-1	1	-1	1	-1	$- i$	$- i$	$i$	$i$	1	-1	$- i$	$i$
χ₅	9	9	1	1	0	0	1	1	1	1	1	1	-1	-1	-1	-1
χ₆	9	9	1	1	0	0	1	1	-1	-1	-1	-1	-1	-1	1	1
χ₇	9	-9	1	-1	0	0	1	-1	$i$	$i$	$- i$	$- i$	-1	1	$- i$	$i$
χ₈	9	-9	1	-1	0	0	1	-1	$- i$	$- i$	$i$	$i$	-1	1	$i$	$- i$
χ₉	10	10	2	2	1	1	-2	-2	0	0	0	0	0	0	0	0
χ₁₀	10	10	-2	-2	1	1	0	0	$i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	0	0	0	0
χ₁₁	10	10	-2	-2	1	1	0	0	$- i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	0	0	0	0
χ₁₂	10	-10	2	-2	1	-1	-2	2	0	0	0	0	0	0	0	0
χ₁₃	10	-10	-2	2	1	-1	0	0	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	0	0	0	0
χ₁₄	10	-10	-2	2	1	-1	0	0	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	0	0	0	0
χ₁₅	16	16	0	0	-2	-2	0	0	0	0	0	0	1	1	0	0
χ₁₆	16	-16	0	0	-2	2	0	0	0	0	0	0	1	-1	0	0

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