Finite Group Databasebeta

← Group #67201

Character table — Group #67201

Order 360.

	C₁	C₂	C₃	C₄	C₅	C₆	C₇	C₈	C₉	C₁₀	C₁₁	C₁₂	C₁₃	C₁₄	C₁₅	C₁₆	C₁₇	C₁₈
size	1	4	4	4	5	8	8	8	8	9	20	20	36	45	45	45	45	45
order	1	3	3	5	2	15	15	15	15	2	6	6	10	2	4	4	4	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	$i$	$i$	$- i$	$- i$
χ₄	1	1	1	1	1	1	1	1	1	-1	1	1	-1	-1	$- i$	$- i$	$i$	$i$
χ₅	1	1	1	1	-1	1	1	1	1	1	-1	-1	1	-1	$i$	$- i$	$i$	$- i$
χ₆	1	1	1	1	-1	1	1	1	1	1	-1	-1	1	-1	$- i$	$i$	$- i$	$i$
χ₇	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
χ₉	4	1	-2	4	4	1	1	-2	-2	0	1	-2	0	0	0	0	0	0
χ₁₀	4	1	-2	4	-4	1	1	-2	-2	0	-1	2	0	0	0	0	0	0
χ₁₁	4	4	4	-1	0	-1	-1	-1	-1	4	0	0	-1	0	0	0	0	0
χ₁₂	4	4	4	-1	0	-1	-1	-1	-1	-4	0	0	1	0	0	0	0	0
χ₁₃	4	-2	1	4	4	-2	-2	1	1	0	-2	1	0	0	0	0	0	0
χ₁₄	4	-2	1	4	-4	-2	-2	1	1	0	2	-1	0	0	0	0	0	0
χ₁₅	8	2	-4	-2	0	$\frac{- 1 + 3 \sqrt{5}}{2}$	$\frac{- 1 - 3 \sqrt{5}}{2}$	1	1	0	0	0	0	0	0	0	0	0
χ₁₆	8	2	-4	-2	0	$\frac{- 1 - 3 \sqrt{5}}{2}$	$\frac{- 1 + 3 \sqrt{5}}{2}$	1	1	0	0	0	0	0	0	0	0	0
χ₁₇	8	-4	2	-2	0	1	1	$\frac{- 1 + 3 \sqrt{5}}{2}$	$\frac{- 1 - 3 \sqrt{5}}{2}$	0	0	0	0	0	0	0	0	0
χ₁₈	8	-4	2	-2	0	1	1	$\frac{- 1 - 3 \sqrt{5}}{2}$	$\frac{- 1 + 3 \sqrt{5}}{2}$	0	0	0	0	0	0	0	0	0

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