Finite Group Databasebeta

← Group #10623945

Character table — Group #10623945

Order 720.

	C₁	C₂	C₃	C₄	C₅	C₆	C₇	C₈	C₉	C₁₀	C₁₁	C₁₂	C₁₃	C₁₄	C₁₅	C₁₆	C₁₇	C₁₈	C₁₉	C₂₀	C₂₁
size	1	1	2	2	20	20	24	24	24	24	24	24	30	40	40	60	60	60	60	90	90
order	1	2	3	6	3	6	5	10	15	15	30	30	4	3	6	4	12	12	12	8	8
χ₁	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
χ₃	2	2	-1	-1	2	2	2	2	-1	-1	-1	-1	2	-1	-1	0	-1	0	0	0	0
χ₄	4	4	4	4	1	1	-1	-1	-1	-1	-1	-1	0	1	1	2	0	-1	-1	0	0
χ₅	4	4	4	4	1	1	-1	-1	-1	-1	-1	-1	0	1	1	-2	0	1	1	0	0
χ₆	4	-4	4	-4	1	-1	-1	1	-1	-1	1	1	0	1	-1	0	0	$\sqrt{3}$	$- \sqrt{3}$	0	0
χ₇	4	-4	4	-4	1	-1	-1	1	-1	-1	1	1	0	1	-1	0	0	$- \sqrt{3}$	$\sqrt{3}$	0	0
χ₈	4	-4	4	-4	-2	2	-1	1	-1	-1	1	1	0	-2	2	0	0	0	0	0	0
χ₉	4	-4	-2	2	-2	2	-1	1	$\frac{1 - i \sqrt{15}}{2}$	$\frac{1 + i \sqrt{15}}{2}$	$\frac{- 1 - i \sqrt{15}}{2}$	$\frac{- 1 + i \sqrt{15}}{2}$	0	1	-1	0	0	0	0	0	0
χ₁₀	4	-4	-2	2	-2	2	-1	1	$\frac{1 + i \sqrt{15}}{2}$	$\frac{1 - i \sqrt{15}}{2}$	$\frac{- 1 + i \sqrt{15}}{2}$	$\frac{- 1 - i \sqrt{15}}{2}$	0	1	-1	0	0	0	0	0	0
χ₁₁	5	5	5	5	-1	-1	0	0	0	0	0	0	1	-1	-1	1	1	1	1	-1	-1
χ₁₂	5	5	5	5	-1	-1	0	0	0	0	0	0	1	-1	-1	-1	1	-1	-1	1	1
χ₁₃	6	6	6	6	0	0	1	1	1	1	1	1	-2	0	0	0	-2	0	0	0	0
χ₁₄	6	6	-3	-3	0	0	1	1	$\frac{- 1 - i \sqrt{15}}{2}$	$\frac{- 1 + i \sqrt{15}}{2}$	$\frac{- 1 + i \sqrt{15}}{2}$	$\frac{- 1 - i \sqrt{15}}{2}$	-2	0	0	0	1	0	0	0	0
χ₁₅	6	6	-3	-3	0	0	1	1	$\frac{- 1 + i \sqrt{15}}{2}$	$\frac{- 1 - i \sqrt{15}}{2}$	$\frac{- 1 - i \sqrt{15}}{2}$	$\frac{- 1 + i \sqrt{15}}{2}$	-2	0	0	0	1	0	0	0	0
χ₁₆	6	-6	6	-6	0	0	1	-1	1	1	-1	-1	0	0	0	0	0	0	0	$\sqrt{2}$	$- \sqrt{2}$
χ₁₇	6	-6	6	-6	0	0	1	-1	1	1	-1	-1	0	0	0	0	0	0	0	$- \sqrt{2}$	$\sqrt{2}$
χ₁₈	8	8	-4	-4	2	2	-2	-2	1	1	1	1	0	-1	-1	0	0	0	0	0	0
χ₁₉	8	-8	-4	4	2	-2	-2	2	1	1	-1	-1	0	-1	1	0	0	0	0	0	0
χ₂₀	10	10	-5	-5	-2	-2	0	0	0	0	0	0	2	1	1	0	-1	0	0	0	0
χ₂₁	12	-12	-6	6	0	0	2	-2	-1	-1	1	1	0	0	0	0	0	0	0	0	0

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