Finite Group Databasebeta

← Group #64379

Character table — Group #64379

Order 288.

	C₁	C₂	C₃	C₄	C₅	C₆	C₇	C₈	C₉	C₁₀	C₁₁	C₁₂	C₁₃	C₁₄	C₁₅	C₁₆	C₁₇	C₁₈
size	1	8	9	12	18	18	18	24	36	1	8	9	12	18	18	18	24	36
order	1	3	2	2	4	8	8	6	4	2	6	2	2	4	8	8	6	4
χ₁	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
χ₃	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
χ₅	2	2	2	0	-2	0	0	0	0	2	2	2	0	-2	0	0	0	0
χ₆	2	2	-2	0	0	$i \sqrt{2}$	$- i \sqrt{2}$	0	0	2	2	-2	0	0	$i \sqrt{2}$	$- i \sqrt{2}$	0	0
χ₇	2	2	-2	0	0	$- i \sqrt{2}$	$i \sqrt{2}$	0	0	2	2	-2	0	0	$- i \sqrt{2}$	$i \sqrt{2}$	0	0
χ₈	8	-1	0	2	0	0	0	-1	0	8	-1	0	2	0	0	0	-1	0
χ₉	8	-1	0	-2	0	0	0	1	0	8	-1	0	-2	0	0	0	1	0
χ₁₀	1	1	1	1	1	1	1	1	1	-1	-1	-1	-1	-1	-1	-1	-1	-1
χ₁₁	1	1	1	1	1	-1	-1	1	-1	-1	-1	-1	-1	-1	1	1	-1	1
χ₁₂	1	1	1	-1	1	1	1	-1	-1	-1	-1	-1	1	-1	-1	-1	1	1
χ₁₃	1	1	1	-1	1	-1	-1	-1	1	-1	-1	-1	1	-1	1	1	1	-1
χ₁₄	2	2	2	0	-2	0	0	0	0	-2	-2	-2	0	2	0	0	0	0
χ₁₅	2	2	-2	0	0	$i \sqrt{2}$	$- i \sqrt{2}$	0	0	-2	-2	2	0	0	$- i \sqrt{2}$	$i \sqrt{2}$	0	0
χ₁₆	2	2	-2	0	0	$- i \sqrt{2}$	$i \sqrt{2}$	0	0	-2	-2	2	0	0	$i \sqrt{2}$	$- i \sqrt{2}$	0	0
χ₁₇	8	-1	0	2	0	0	0	-1	0	-8	1	0	-2	0	0	0	1	0
χ₁₈	8	-1	0	-2	0	0	0	1	0	-8	1	0	2	0	0	0	-1	0

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