Finite Group Databasebeta

← Group #64224

Character table — Group #64224

Order 288.

	C₁	C₂	C₃	C₄	C₅	C₆	C₇	C₈	C₉	C₁₀	C₁₁	C₁₂	C₁₃	C₁₄	C₁₅	C₁₆	C₁₇	C₁₈	C₁₉	C₂₀	C₂₁	C₂₂	C₂₃	C₂₄
size	1	1	2	4	4	4	4	4	4	8	12	12	12	12	12	12	12	12	18	18	24	24	36	36
order	1	2	4	3	3	6	6	12	12	12	2	2	2	4	6	6	12	12	2	4	6	6	8	8
χ₁	1	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	-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	-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	1
χ₅	1	1	-1	1	1	1	1	-1	-1	-1	1	-1	1	-1	1	1	-1	-1	-1	1	1	-1	1	-1
χ₆	1	1	-1	1	1	1	1	-1	-1	-1	1	-1	-1	1	-1	-1	1	1	-1	1	1	-1	-1	1
χ₇	1	1	-1	1	1	1	1	-1	-1	-1	-1	1	1	-1	1	1	-1	-1	-1	1	-1	1	-1	1
χ₈	1	1	-1	1	1	1	1	-1	-1	-1	-1	1	-1	1	-1	-1	1	1	-1	1	-1	1	1	-1
χ₉	2	2	2	2	2	2	2	2	2	2	0	0	0	0	0	0	0	0	-2	-2	0	0	0	0
χ₁₀	2	2	-2	2	2	2	2	-2	-2	-2	0	0	0	0	0	0	0	0	2	-2	0	0	0	0
χ₁₁	4	4	4	1	-2	-2	1	1	1	-2	0	0	2	2	-1	-1	-1	-1	0	0	0	0	0	0
χ₁₂	4	4	4	1	-2	-2	1	1	1	-2	0	0	-2	-2	1	1	1	1	0	0	0	0	0	0
χ₁₃	4	4	4	-2	1	1	-2	-2	-2	1	2	2	0	0	0	0	0	0	0	0	-1	-1	0	0
χ₁₄	4	4	4	-2	1	1	-2	-2	-2	1	-2	-2	0	0	0	0	0	0	0	0	1	1	0	0
χ₁₅	4	4	-4	1	-2	-2	1	-1	-1	2	0	0	2	-2	-1	-1	1	1	0	0	0	0	0	0
χ₁₆	4	4	-4	1	-2	-2	1	-1	-1	2	0	0	-2	2	1	1	-1	-1	0	0	0	0	0	0
χ₁₇	4	4	-4	-2	1	1	-2	2	2	-1	2	-2	0	0	0	0	0	0	0	0	-1	1	0	0
χ₁₈	4	4	-4	-2	1	1	-2	2	2	-1	-2	2	0	0	0	0	0	0	0	0	1	-1	0	0
χ₁₉	4	-4	0	1	-2	2	-1	$3 i$	$- 3 i$	0	0	0	0	0	$- i \sqrt{3}$	$i \sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	0	0	0	0	0	0
χ₂₀	4	-4	0	1	-2	2	-1	$3 i$	$- 3 i$	0	0	0	0	0	$i \sqrt{3}$	$- i \sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	0	0	0	0	0	0
χ₂₁	4	-4	0	1	-2	2	-1	$- 3 i$	$3 i$	0	0	0	0	0	$- i \sqrt{3}$	$i \sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	0	0	0	0	0	0
χ₂₂	4	-4	0	1	-2	2	-1	$- 3 i$	$3 i$	0	0	0	0	0	$i \sqrt{3}$	$- i \sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	0	0	0	0	0	0
χ₂₃	4	-4	0	4	4	-4	-4	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₄	8	-8	0	-4	2	-2	4	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0

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