Finite Group Databasebeta

← Group #67199

Character table — Group #67199

Order 360.

	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	4	4	5	8	8	8	8	9	10	10	15	15	15	15	20	30	30	30	30	36	45
order	1	3	3	3	5	2	15	15	15	15	2	6	6	4	4	4	4	6	12	12	12	12	10	2
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	1	1	1	1	1	-1	1	1	1	1	1	-1	-1	$i$	$- i$	$i$	$- i$	-1	$i$	$- i$	$i$	$- i$	1	-1
χ₆	1	1	1	1	1	-1	1	1	1	1	1	-1	-1	$- i$	$i$	$- i$	$i$	-1	$- i$	$i$	$- i$	$i$	1	-1
χ₇	1	1	1	1	1	-1	1	1	1	1	-1	-1	-1	$i$	$- i$	$- i$	$i$	-1	$i$	$- i$	$- i$	$i$	-1	1
χ₈	1	1	1	1	1	-1	1	1	1	1	-1	-1	-1	$- i$	$i$	$i$	$- i$	-1	$- i$	$i$	$i$	$- i$	-1	1
χ₉	2	2	-1	-1	2	2	2	-1	-1	-1	0	2	-1	0	0	2	2	-1	0	0	-1	-1	0	0
χ₁₀	2	2	-1	-1	2	2	2	-1	-1	-1	0	2	-1	0	0	-2	-2	-1	0	0	1	1	0	0
χ₁₁	2	2	-1	-1	2	-2	2	-1	-1	-1	0	-2	1	0	0	$2 i$	$- 2 i$	1	0	0	$- i$	$i$	0	0
χ₁₂	2	2	-1	-1	2	-2	2	-1	-1	-1	0	-2	1	0	0	$- 2 i$	$2 i$	1	0	0	$i$	$- i$	0	0
χ₁₃	2	-1	2	-1	2	2	-1	2	-1	-1	0	-1	2	2	2	0	0	-1	-1	-1	0	0	0	0
χ₁₄	2	-1	2	-1	2	2	-1	2	-1	-1	0	-1	2	-2	-2	0	0	-1	1	1	0	0	0	0
χ₁₅	2	-1	2	-1	2	-2	-1	2	-1	-1	0	1	-2	$2 i$	$- 2 i$	0	0	1	$- i$	$i$	0	0	0	0
χ₁₆	2	-1	2	-1	2	-2	-1	2	-1	-1	0	1	-2	$- 2 i$	$2 i$	0	0	1	$i$	$- i$	0	0	0	0
χ₁₇	4	4	4	4	-1	0	-1	-1	-1	-1	4	0	0	0	0	0	0	0	0	0	0	0	-1	0
χ₁₈	4	4	4	4	-1	0	-1	-1	-1	-1	-4	0	0	0	0	0	0	0	0	0	0	0	1	0
χ₁₉	4	-2	-2	1	4	4	-2	-2	1	1	0	-2	-2	0	0	0	0	1	0	0	0	0	0	0
χ₂₀	4	-2	-2	1	4	-4	-2	-2	1	1	0	2	2	0	0	0	0	-1	0	0	0	0	0	0
χ₂₁	8	8	-4	-4	-2	0	-2	1	1	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₂	8	-4	8	-4	-2	0	1	-2	1	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₃	8	-4	-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	0	0	0	0	0
χ₂₄	8	-4	-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	0	0	0	0	0

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