Finite Group Databasebeta

← Group #72209597

Character table — Group #72209597

Order 2688.

	C₁	C₂	C₃	C₄	C₅	C₆	C₇	C₈	C₉	C₁₀	C₁₁	C₁₂	C₁₃	C₁₄	C₁₅	C₁₆	C₁₇	C₁₈	C₁₉
size	1	1	7	7	84	84	168	168	168	168	168	192	192	192	192	224	224	224	224
order	1	2	2	2	4	4	4	8	8	8	8	7	7	14	14	3	6	6	6
χ₁	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1
χ₂	3	3	3	3	-1	-1	-1	1	1	1	1	$\frac{- 1 + i \sqrt{7}}{2}$	$\frac{- 1 - i \sqrt{7}}{2}$	$\frac{- 1 + i \sqrt{7}}{2}$	$\frac{- 1 - i \sqrt{7}}{2}$	0	0	0	0
χ₃	3	3	3	3	-1	-1	-1	1	1	1	1	$\frac{- 1 - i \sqrt{7}}{2}$	$\frac{- 1 + i \sqrt{7}}{2}$	$\frac{- 1 - i \sqrt{7}}{2}$	$\frac{- 1 + i \sqrt{7}}{2}$	0	0	0	0
χ₄	4	-4	4	-4	0	0	0	0	0	0	0	$\frac{1 - i \sqrt{7}}{2}$	$\frac{1 + i \sqrt{7}}{2}$	$\frac{- 1 + i \sqrt{7}}{2}$	$\frac{- 1 - i \sqrt{7}}{2}$	1	1	-1	-1
χ₅	4	-4	4	-4	0	0	0	0	0	0	0	$\frac{1 + i \sqrt{7}}{2}$	$\frac{1 - i \sqrt{7}}{2}$	$\frac{- 1 - i \sqrt{7}}{2}$	$\frac{- 1 + i \sqrt{7}}{2}$	1	1	-1	-1
χ₆	6	6	6	6	2	2	2	0	0	0	0	-1	-1	-1	-1	0	0	0	0
χ₇	6	-6	6	-6	0	0	0	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	-1	-1	1	1	0	0	0	0
χ₈	6	-6	6	-6	0	0	0	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	-1	-1	1	1	0	0	0	0
χ₉	7	7	7	7	-1	-1	-1	-1	-1	-1	-1	0	0	0	0	1	1	1	1
χ₁₀	7	7	-1	-1	3	-1	-1	1	-1	1	-1	0	0	0	0	1	-1	1	-1
χ₁₁	7	7	-1	-1	-1	3	-1	-1	1	-1	1	0	0	0	0	1	-1	1	-1
χ₁₂	8	8	8	8	0	0	0	0	0	0	0	1	1	1	1	-1	-1	-1	-1
χ₁₃	8	-8	8	-8	0	0	0	0	0	0	0	1	1	-1	-1	-1	-1	1	1
χ₁₄	14	14	-2	-2	2	2	-2	0	0	0	0	0	0	0	0	-1	1	-1	1
χ₁₅	14	-14	-2	2	0	0	0	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	0	0	0	0	-1	1	1	-1
χ₁₆	14	-14	-2	2	0	0	0	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	0	0	0	0	-1	1	1	-1
χ₁₇	21	21	-3	-3	1	-3	1	-1	1	-1	1	0	0	0	0	0	0	0	0
χ₁₈	21	21	-3	-3	-3	1	1	1	-1	1	-1	0	0	0	0	0	0	0	0
χ₁₉	28	-28	-4	4	0	0	0	0	0	0	0	0	0	0	0	1	-1	-1	1

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