Finite Group Databasebeta

← Group #92537

Character table — Group #92537

Order 500.

	C₁	C₂	C₃	C₄	C₅	C₆	C₇	C₈	C₉	C₁₀	C₁₁	C₁₂	C₁₃	C₁₄
size	1	2	2	20	20	20	20	20	20	25	50	50	125	125
order	1	5	5	5	5	5	5	5	5	2	10	10	4	4
χ₁	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
χ₃	1	1	1	1	1	1	1	1	1	-1	-1	-1	$i$	$- i$
χ₄	1	1	1	1	1	1	1	1	1	-1	-1	-1	$- i$	$i$
χ₅	4	4	4	4	-1	-1	-1	-1	-1	0	0	0	0	0
χ₆	4	4	4	-1	4	-1	-1	-1	-1	0	0	0	0	0
χ₇	4	4	4	-1	-1	4	-1	-1	-1	0	0	0	0	0
χ₈	4	4	4	-1	-1	-1	4	-1	-1	0	0	0	0	0
χ₉	4	4	4	-1	-1	-1	-1	4	-1	0	0	0	0	0
χ₁₀	4	4	4	-1	-1	-1	-1	-1	4	0	0	0	0	0
χ₁₁	10	$\frac{- 5 + 5 \sqrt{5}}{2}$	$\frac{- 5 - 5 \sqrt{5}}{2}$	0	0	0	0	0	0	2	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	0	0
χ₁₂	10	$\frac{- 5 + 5 \sqrt{5}}{2}$	$\frac{- 5 - 5 \sqrt{5}}{2}$	0	0	0	0	0	0	-2	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	0	0
χ₁₃	10	$\frac{- 5 - 5 \sqrt{5}}{2}$	$\frac{- 5 + 5 \sqrt{5}}{2}$	0	0	0	0	0	0	2	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	0	0
χ₁₄	10	$\frac{- 5 - 5 \sqrt{5}}{2}$	$\frac{- 5 + 5 \sqrt{5}}{2}$	0	0	0	0	0	0	-2	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	0	0

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