Finite Group Databasebeta

← Group #10621461

Character table — Group #10621461

Order 672.

	C₁	C₂	C₃	C₄	C₅	C₆	C₇	C₈	C₉	C₁₀	C₁₁	C₁₂	C₁₃	C₁₄	C₁₅	C₁₆	C₁₇	C₁₈
size	1	1	21	21	28	28	42	42	42	42	42	42	48	48	56	56	56	56
order	1	2	2	2	4	4	4	4	8	8	8	8	7	14	3	6	12	12
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	$i$	$- i$	1	-1	$i$	$i$	$- i$	$- i$	1	-1	1	-1	$i$	$- i$
χ₄	1	-1	-1	1	$- i$	$i$	1	-1	$- i$	$- i$	$i$	$i$	1	-1	1	-1	$- i$	$i$
χ₅	6	6	2	2	0	0	0	0	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	-1	-1	0	0	0	0
χ₆	6	6	2	2	0	0	0	0	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	-1	-1	0	0	0	0
χ₇	6	6	-2	-2	0	0	2	2	0	0	0	0	-1	-1	0	0	0	0
χ₈	6	-6	2	-2	0	0	2	-2	0	0	0	0	-1	1	0	0	0	0
χ₉	6	-6	-2	2	0	0	0	0	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	-1	1	0	0	0	0
χ₁₀	6	-6	-2	2	0	0	0	0	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	-1	1	0	0	0	0
χ₁₁	7	7	-1	-1	1	1	-1	-1	-1	-1	-1	-1	0	0	1	1	1	1
χ₁₂	7	7	-1	-1	-1	-1	-1	-1	1	1	1	1	0	0	1	1	-1	-1
χ₁₃	7	-7	1	-1	$i$	$- i$	-1	1	$- i$	$- i$	$i$	$i$	0	0	1	-1	$i$	$- i$
χ₁₄	7	-7	1	-1	$- i$	$i$	-1	1	$i$	$i$	$- i$	$- i$	0	0	1	-1	$- i$	$i$
χ₁₅	8	8	0	0	2	2	0	0	0	0	0	0	1	1	-1	-1	-1	-1
χ₁₆	8	8	0	0	-2	-2	0	0	0	0	0	0	1	1	-1	-1	1	1
χ₁₇	8	-8	0	0	$2 i$	$- 2 i$	0	0	0	0	0	0	1	-1	-1	1	$- i$	$i$
χ₁₈	8	-8	0	0	$- 2 i$	$2 i$	0	0	0	0	0	0	1	-1	-1	1	$i$	$- i$

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