Finite Group Databasebeta

← Group #89101

Character table — Group #89101

Order 432.

	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	2	2	3	4	6	6	8	9	12	16	16	16	16	18	18	18	18	27	36	36	36	36	72
order	1	3	3	2	3	6	6	3	2	6	3	3	3	3	2	2	4	4	2	6	6	12	12	6
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	2	2	2	2	2	2	2	-1	2	2	-1	-1	-1	-1	0	0	0	0	2	0	0	0	0	-1
χ₆	2	2	2	2	2	2	2	-1	-2	2	-1	-1	-1	-1	0	0	0	0	-2	0	0	0	0	1
χ₇	2	2	-1	2	-1	2	-1	2	0	-1	2	-1	-1	-1	0	2	0	2	0	0	-1	0	-1	0
χ₈	2	2	-1	2	-1	2	-1	2	0	-1	2	-1	-1	-1	0	-2	0	-2	0	0	1	0	1	0
χ₉	2	-1	2	2	-1	-1	2	2	0	-1	-1	2	-1	-1	2	0	2	0	0	-1	0	-1	0	0
χ₁₀	2	-1	2	2	-1	-1	2	2	0	-1	-1	2	-1	-1	-2	0	-2	0	0	1	0	1	0	0
χ₁₁	3	3	3	-1	3	-1	-1	0	3	-1	0	0	0	0	1	1	-1	-1	-1	1	1	-1	-1	0
χ₁₂	3	3	3	-1	3	-1	-1	0	3	-1	0	0	0	0	-1	-1	1	1	-1	-1	-1	1	1	0
χ₁₃	3	3	3	-1	3	-1	-1	0	-3	-1	0	0	0	0	1	-1	-1	1	1	1	-1	-1	1	0
χ₁₄	3	3	3	-1	3	-1	-1	0	-3	-1	0	0	0	0	-1	1	1	-1	1	-1	1	1	-1	0
χ₁₅	4	4	-2	4	-2	4	-2	-2	0	-2	-2	1	1	1	0	0	0	0	0	0	0	0	0	0
χ₁₆	4	-2	4	4	-2	-2	4	-2	0	-2	1	-2	1	1	0	0	0	0	0	0	0	0	0	0
χ₁₇	4	-2	-2	4	1	-2	-2	4	0	1	-2	-2	1	1	0	0	0	0	0	0	0	0	0	0
χ₁₈	4	-2	-2	4	1	-2	-2	-2	0	1	1	1	$\frac{- 1 + 3 i \sqrt{3}}{2}$	$\frac{- 1 - 3 i \sqrt{3}}{2}$	0	0	0	0	0	0	0	0	0	0
χ₁₉	4	-2	-2	4	1	-2	-2	-2	0	1	1	1	$\frac{- 1 - 3 i \sqrt{3}}{2}$	$\frac{- 1 + 3 i \sqrt{3}}{2}$	0	0	0	0	0	0	0	0	0	0
χ₂₀	6	6	-3	-2	-3	-2	1	0	0	1	0	0	0	0	0	2	0	-2	0	0	-1	0	1	0
χ₂₁	6	6	-3	-2	-3	-2	1	0	0	1	0	0	0	0	0	-2	0	2	0	0	1	0	-1	0
χ₂₂	6	-3	6	-2	-3	1	-2	0	0	1	0	0	0	0	2	0	-2	0	0	-1	0	1	0	0
χ₂₃	6	-3	6	-2	-3	1	-2	0	0	1	0	0	0	0	-2	0	2	0	0	1	0	-1	0	0
χ₂₄	12	-6	-6	-4	3	2	2	0	0	-1	0	0	0	0	0	0	0	0	0	0	0	0	0	0

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