Finite Group Databasebeta

← Group #72224455

Character table — Group #72224455

Order 2880.

	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	30	30	45	45	72	80	80	90	90	144	144	144	144	180	180	180	180	180	240	240	360
order	1	2	2	2	2	2	4	3	6	4	4	5	10	20	20	4	8	8	8	8	6	6	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	0	0	-2	2	0	2	-2	2	-2	2	-2	0	0	0	0	0	0	0	0	0	0
χ₆	9	9	3	3	1	1	1	0	0	1	1	-1	-1	1	1	-1	-1	-1	1	1	0	0	-1
χ₇	9	9	3	3	1	1	-1	0	0	1	1	-1	-1	-1	-1	-1	1	1	-1	-1	0	0	1
χ₈	9	9	-3	-3	1	1	1	0	0	1	1	-1	-1	1	1	1	-1	-1	-1	-1	0	0	1
χ₉	9	9	-3	-3	1	1	-1	0	0	1	1	-1	-1	-1	-1	1	1	1	1	1	0	0	-1
χ₁₀	10	10	2	2	2	2	0	1	1	-2	-2	0	0	0	0	2	0	0	0	0	-1	-1	0
χ₁₁	10	10	-2	-2	2	2	0	1	1	-2	-2	0	0	0	0	-2	0	0	0	0	1	1	0
χ₁₂	10	-10	2	-2	2	-2	0	1	-1	0	0	0	0	0	0	0	$i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	1	-1	0
χ₁₃	10	-10	2	-2	2	-2	0	1	-1	0	0	0	0	0	0	0	$- i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	1	-1	0
χ₁₄	10	-10	4	-4	-2	2	0	1	-1	-2	2	0	0	0	0	0	0	0	0	0	-1	1	0
χ₁₅	10	-10	-4	4	-2	2	0	1	-1	-2	2	0	0	0	0	0	0	0	0	0	1	-1	0
χ₁₆	10	-10	-2	2	2	-2	0	1	-1	0	0	0	0	0	0	0	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	-1	1	0
χ₁₇	10	-10	-2	2	2	-2	0	1	-1	0	0	0	0	0	0	0	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	-1	1	0
χ₁₈	16	16	0	0	0	0	4	-2	-2	0	0	1	1	-1	-1	0	0	0	0	0	0	0	0
χ₁₉	16	16	0	0	0	0	-4	-2	-2	0	0	1	1	1	1	0	0	0	0	0	0	0	0
χ₂₀	16	-16	0	0	0	0	0	-2	2	0	0	1	-1	$i \sqrt{5}$	$- i \sqrt{5}$	0	0	0	0	0	0	0	0
χ₂₁	16	-16	0	0	0	0	0	-2	2	0	0	1	-1	$- i \sqrt{5}$	$i \sqrt{5}$	0	0	0	0	0	0	0	0
χ₂₂	18	-18	0	0	-2	2	0	0	0	2	-2	-2	2	0	0	0	0	0	0	0	0	0	0
χ₂₃	20	20	0	0	-4	-4	0	2	2	0	0	0	0	0	0	0	0	0	0	0	0	0	0

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