Finite Group Databasebeta

← Group #1231

Character table — Group #1231

Order 120.

	C₁	C₂	C₃	C₄	C₅	C₆	C₇	C₈	C₉	C₁₀	C₁₁	C₁₂	C₁₃	C₁₄	C₁₅	C₁₆	C₁₇	C₁₈
size	1	2	4	4	4	5	10	15	15	1	2	4	4	4	5	10	15	15
order	1	3	5	15	15	2	6	4	4	2	6	10	30	30	2	6	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	$i$	$- i$	1	1	1	1	1	-1	-1	$i$	$- i$
χ₄	1	1	1	1	1	-1	-1	$- i$	$i$	1	1	1	1	1	-1	-1	$- i$	$i$
χ₅	2	-1	2	-1	-1	2	-1	0	0	2	-1	2	-1	-1	2	-1	0	0
χ₆	2	-1	2	-1	-1	-2	1	0	0	2	-1	2	-1	-1	-2	1	0	0
χ₇	4	4	-1	-1	-1	0	0	0	0	4	4	-1	-1	-1	0	0	0	0
χ₈	4	-2	-1	$\frac{1 - i \sqrt{15}}{2}$	$\frac{1 + i \sqrt{15}}{2}$	0	0	0	0	4	-2	-1	$\frac{1 - i \sqrt{15}}{2}$	$\frac{1 + i \sqrt{15}}{2}$	0	0	0	0
χ₉	4	-2	-1	$\frac{1 + i \sqrt{15}}{2}$	$\frac{1 - i \sqrt{15}}{2}$	0	0	0	0	4	-2	-1	$\frac{1 + i \sqrt{15}}{2}$	$\frac{1 - i \sqrt{15}}{2}$	0	0	0	0
χ₁₀	1	1	1	1	1	1	1	1	1	-1	-1	-1	-1	-1	-1	-1	-1	-1
χ₁₁	1	1	1	1	1	1	1	-1	-1	-1	-1	-1	-1	-1	-1	-1	1	1
χ₁₂	1	1	1	1	1	-1	-1	$i$	$- i$	-1	-1	-1	-1	-1	1	1	$- i$	$i$
χ₁₃	1	1	1	1	1	-1	-1	$- i$	$i$	-1	-1	-1	-1	-1	1	1	$i$	$- i$
χ₁₄	2	-1	2	-1	-1	2	-1	0	0	-2	1	-2	1	1	-2	1	0	0
χ₁₅	2	-1	2	-1	-1	-2	1	0	0	-2	1	-2	1	1	2	-1	0	0
χ₁₆	4	4	-1	-1	-1	0	0	0	0	-4	-4	1	1	1	0	0	0	0
χ₁₇	4	-2	-1	$\frac{1 - i \sqrt{15}}{2}$	$\frac{1 + i \sqrt{15}}{2}$	0	0	0	0	-4	2	1	$\frac{- 1 + i \sqrt{15}}{2}$	$\frac{- 1 - i \sqrt{15}}{2}$	0	0	0	0
χ₁₈	4	-2	-1	$\frac{1 + i \sqrt{15}}{2}$	$\frac{1 - i \sqrt{15}}{2}$	0	0	0	0	-4	2	1	$\frac{- 1 - i \sqrt{15}}{2}$	$\frac{- 1 + i \sqrt{15}}{2}$	0	0	0	0

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