Finite Group Databasebeta

← Group #6736

Character table — Group #6736

Order 240.

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

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