Finite Group Databasebeta

← Group #72224462

Character table — Group #72224462

Order 16320.

	C₁	C₂	C₃	C₄	C₅	C₆	C₇	C₈	C₉	C₁₀	C₁₁	C₁₂	C₁₃	C₁₄	C₁₅	C₁₆	C₁₇
size	1	68	255	272	544	680	680	960	960	1020	1088	1360	1360	1360	1632	2040	2040
order	1	2	2	3	5	4	4	17	17	4	15	6	12	12	10	8	8
χ₁	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
χ₃	1	-1	1	1	1	$i$	$- i$	1	1	-1	1	-1	$i$	$- i$	-1	$i$	$- i$
χ₄	1	-1	1	1	1	$- i$	$i$	1	1	-1	1	-1	$- i$	$i$	-1	$- i$	$i$
χ₅	16	4	0	1	1	2	2	-1	-1	0	1	1	-1	-1	-1	0	0
χ₆	16	4	0	1	1	-2	-2	-1	-1	0	1	1	1	1	-1	0	0
χ₇	16	-4	0	1	1	$2 i$	$- 2 i$	-1	-1	0	1	-1	$- i$	$i$	1	0	0
χ₈	16	-4	0	1	1	$- 2 i$	$2 i$	-1	-1	0	1	-1	$i$	$- i$	1	0	0
χ₉	17	5	1	-1	2	1	1	0	0	1	-1	-1	1	1	0	-1	-1
χ₁₀	17	5	1	-1	2	-1	-1	0	0	1	-1	-1	-1	-1	0	1	1
χ₁₁	17	-5	1	-1	2	$i$	$- i$	0	0	-1	-1	1	$i$	$- i$	0	$- i$	$i$
χ₁₂	17	-5	1	-1	2	$- i$	$i$	0	0	-1	-1	1	$- i$	$i$	0	$i$	$- i$
χ₁₃	34	6	2	4	-1	0	0	0	0	-2	-1	0	0	0	1	0	0
χ₁₄	34	-6	2	4	-1	0	0	0	0	2	-1	0	0	0	-1	0	0
χ₁₅	60	0	-4	0	0	0	0	$\frac{1 + \sqrt{17}}{2}$	$\frac{1 - \sqrt{17}}{2}$	0	0	0	0	0	0	0	0
χ₁₆	60	0	-4	0	0	0	0	$\frac{1 - \sqrt{17}}{2}$	$\frac{1 + \sqrt{17}}{2}$	0	0	0	0	0	0	0	0
χ₁₇	68	0	4	-4	-2	0	0	0	0	0	1	0	0	0	0	0	0

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