Group #11772982 — character table

	C₁	C₂	C₃	C₄	C₅	C₆	C₇	C₈	C₉	C₁₀	C₁₁	C₁₂	C₁₃	C₁₄	C₁₅	C₁₆	C₁₇	C₁₈	C₁₉	C₂₀	C₂₁	C₂₂	C₂₃	C₂₄	C₂₅	C₂₆	C₂₇	C₂₈	C₂₉	C₃₀	C₃₁	C₃₂	C₃₃	C₃₄	C₃₅	C₃₆	C₃₇	C₃₈	C₃₉	C₄₀	C₄₁	C₄₂	C₄₃	C₄₄	C₄₅	C₄₆	C₄₇	C₄₈
size	1	1	2	2	2	4	4	4	4	4	4	8	8	8	8	8	8	8	8	8	8	8	8	8	8	16	18	18	18	18	18	18	32	32	32	32	36	36	36	36	36	36	36	36	36	144	144	144
order	1	2	4	8	8	3	3	6	6	16	16	12	12	24	24	24	24	48	48	48	48	48	48	48	48	2	2	4	16	16	16	16	6	6	6	6	8	32	32	32	32	32	32	32	32	2	8	8
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	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	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	1	1	-1	-1	-1	-1	-1	-1	1	1	1	1	-1	$i$	$i$	$i$	$i$	$- i$	$- i$	$- i$	$- i$	-1	$i$	$- i$
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	1	1	-1	-1	-1	-1	-1	-1	1	1	1	1	-1	$- i$	$- i$	$- i$	$- i$	$i$	$i$	$i$	$i$	-1	$- i$	$i$
χ₅	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	-1	1	1	1	1	1	1	-1	-1	-1	-1	1	1	1	1	1	1	1	1	1	-1	-1	-1
χ₆	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	-1	1	1	1	1	1	1	-1	-1	-1	-1	1	-1	-1	-1	-1	-1	-1	-1	-1	-1	1	1
χ₇	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	$i$	$i$	$i$	$i$	$- i$	$- i$	$- i$	$- i$	1	$- i$	$i$
χ₈	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	$- i$	$- i$	$- i$	$- i$	$i$	$i$	$i$	$i$	1	$i$	$- i$
χ₉	2	2	2	2	2	2	2	2	2	-2	-2	2	2	2	2	2	2	-2	-2	-2	-2	-2	-2	-2	-2	0	2	2	-2	-2	-2	-2	0	0	0	0	2	0	0	0	0	0	0	0	0	0	0	0
χ₁₀	2	2	2	2	2	2	2	2	2	-2	-2	2	2	2	2	2	2	-2	-2	-2	-2	-2	-2	-2	-2	0	-2	-2	2	2	2	2	0	0	0	0	-2	0	0	0	0	0	0	0	0	0	0	0
χ₁₁	2	2	2	-2	-2	2	2	2	2	0	0	2	2	-2	-2	-2	-2	0	0	0	0	0	0	0	0	0	2	2	0	0	0	0	0	0	0	0	-2	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	0	0	0
χ₁₂	2	2	2	-2	-2	2	2	2	2	0	0	2	2	-2	-2	-2	-2	0	0	0	0	0	0	0	0	0	2	2	0	0	0	0	0	0	0	0	-2	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	0	0	0
χ₁₃	2	2	2	-2	-2	2	2	2	2	0	0	2	2	-2	-2	-2	-2	0	0	0	0	0	0	0	0	0	-2	-2	0	0	0	0	0	0	0	0	2	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	0	0	0
χ₁₄	2	2	2	-2	-2	2	2	2	2	0	0	2	2	-2	-2	-2	-2	0	0	0	0	0	0	0	0	0	-2	-2	0	0	0	0	0	0	0	0	2	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	0	0	0
χ₁₅	2	2	-2	0	0	2	2	2	2	$\sqrt{2}$	$- \sqrt{2}$	-2	-2	0	0	0	0	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	0	2	-2	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	0	0	0	0	0	ζ+ζ⁷	−ζ−ζ⁷	ζ³+ζ⁵	−ζ³−ζ⁵	ζ+ζ⁷	−ζ−ζ⁷	ζ³+ζ⁵	−ζ³−ζ⁵	0	0	0
χ₁₆	2	2	-2	0	0	2	2	2	2	$\sqrt{2}$	$- \sqrt{2}$	-2	-2	0	0	0	0	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	0	2	-2	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	0	0	0	0	0	−ζ−ζ⁷	ζ+ζ⁷	−ζ³−ζ⁵	ζ³+ζ⁵	−ζ−ζ⁷	ζ+ζ⁷	−ζ³−ζ⁵	ζ³+ζ⁵	0	0	0
χ₁₇	2	2	-2	0	0	2	2	2	2	$\sqrt{2}$	$- \sqrt{2}$	-2	-2	0	0	0	0	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	0	-2	2	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	0	0	0	0	0	ζ³−ζ⁵	−ζ³+ζ⁵	ζ−ζ⁷	−ζ+ζ⁷	−ζ³+ζ⁵	ζ³−ζ⁵	−ζ+ζ⁷	ζ−ζ⁷	0	0	0
χ₁₈	2	2	-2	0	0	2	2	2	2	$\sqrt{2}$	$- \sqrt{2}$	-2	-2	0	0	0	0	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	0	-2	2	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	0	0	0	0	0	−ζ³+ζ⁵	ζ³−ζ⁵	−ζ+ζ⁷	ζ−ζ⁷	ζ³−ζ⁵	−ζ³+ζ⁵	ζ−ζ⁷	−ζ+ζ⁷	0	0	0
χ₁₉	2	2	-2	0	0	2	2	2	2	$- \sqrt{2}$	$\sqrt{2}$	-2	-2	0	0	0	0	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	0	2	-2	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	0	0	0	0	0	ζ³+ζ⁵	−ζ³−ζ⁵	−ζ−ζ⁷	ζ+ζ⁷	ζ³+ζ⁵	−ζ³−ζ⁵	−ζ−ζ⁷	ζ+ζ⁷	0	0	0
χ₂₀	2	2	-2	0	0	2	2	2	2	$- \sqrt{2}$	$\sqrt{2}$	-2	-2	0	0	0	0	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	0	2	-2	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	0	0	0	0	0	−ζ³−ζ⁵	ζ³+ζ⁵	ζ+ζ⁷	−ζ−ζ⁷	−ζ³−ζ⁵	ζ³+ζ⁵	ζ+ζ⁷	−ζ−ζ⁷	0	0	0
χ₂₁	2	2	-2	0	0	2	2	2	2	$- \sqrt{2}$	$\sqrt{2}$	-2	-2	0	0	0	0	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	0	-2	2	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	0	0	0	0	0	ζ−ζ⁷	−ζ+ζ⁷	−ζ³+ζ⁵	ζ³−ζ⁵	−ζ+ζ⁷	ζ−ζ⁷	ζ³−ζ⁵	−ζ³+ζ⁵	0	0	0
χ₂₂	2	2	-2	0	0	2	2	2	2	$- \sqrt{2}$	$\sqrt{2}$	-2	-2	0	0	0	0	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	0	-2	2	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	0	0	0	0	0	−ζ+ζ⁷	ζ−ζ⁷	ζ³−ζ⁵	−ζ³+ζ⁵	ζ−ζ⁷	−ζ+ζ⁷	−ζ³+ζ⁵	ζ³−ζ⁵	0	0	0
χ₂₃	4	4	4	4	4	1	-2	1	-2	4	4	1	-2	1	1	-2	-2	1	1	-2	-2	1	1	-2	-2	4	0	0	0	0	0	0	1	1	-2	-2	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₄	4	4	4	4	4	1	-2	1	-2	4	4	1	-2	1	1	-2	-2	1	1	-2	-2	1	1	-2	-2	-4	0	0	0	0	0	0	-1	-1	2	2	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₅	4	4	4	4	4	1	-2	1	-2	-4	-4	1	-2	1	1	-2	-2	-1	-1	2	2	-1	-1	2	2	0	0	0	0	0	0	0	3	-3	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₆	4	4	4	4	4	1	-2	1	-2	-4	-4	1	-2	1	1	-2	-2	-1	-1	2	2	-1	-1	2	2	0	0	0	0	0	0	0	-3	3	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₇	4	4	4	4	4	-2	1	-2	1	4	4	-2	1	-2	-2	1	1	-2	-2	1	1	-2	-2	1	1	4	0	0	0	0	0	0	-2	-2	1	1	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₈	4	4	4	4	4	-2	1	-2	1	4	4	-2	1	-2	-2	1	1	-2	-2	1	1	-2	-2	1	1	-4	0	0	0	0	0	0	2	2	-1	-1	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₉	4	4	4	4	4	-2	1	-2	1	-4	-4	-2	1	-2	-2	1	1	2	2	-1	-1	2	2	-1	-1	0	0	0	0	0	0	0	0	0	3	-3	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₀	4	4	4	4	4	-2	1	-2	1	-4	-4	-2	1	-2	-2	1	1	2	2	-1	-1	2	2	-1	-1	0	0	0	0	0	0	0	0	0	-3	3	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₁	4	-4	0	$2 \sqrt{2}$	$- 2 \sqrt{2}$	4	4	-4	-4	0	0	0	0	$2 \sqrt{2}$	$- 2 \sqrt{2}$	$2 \sqrt{2}$	$- 2 \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0	2ζ−2ζ⁷	−2ζ+2ζ⁷	2ζ³−2ζ⁵	−2ζ³+2ζ⁵	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₂	4	-4	0	$2 \sqrt{2}$	$- 2 \sqrt{2}$	4	4	-4	-4	0	0	0	0	$2 \sqrt{2}$	$- 2 \sqrt{2}$	$2 \sqrt{2}$	$- 2 \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0	−2ζ+2ζ⁷	2ζ−2ζ⁷	−2ζ³+2ζ⁵	2ζ³−2ζ⁵	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₃	4	-4	0	$- 2 \sqrt{2}$	$2 \sqrt{2}$	4	4	-4	-4	0	0	0	0	$- 2 \sqrt{2}$	$2 \sqrt{2}$	$- 2 \sqrt{2}$	$2 \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0	2ζ³−2ζ⁵	−2ζ³+2ζ⁵	−2ζ+2ζ⁷	2ζ−2ζ⁷	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₄	4	-4	0	$- 2 \sqrt{2}$	$2 \sqrt{2}$	4	4	-4	-4	0	0	0	0	$- 2 \sqrt{2}$	$2 \sqrt{2}$	$- 2 \sqrt{2}$	$2 \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0	−2ζ³+2ζ⁵	2ζ³−2ζ⁵	2ζ−2ζ⁷	−2ζ+2ζ⁷	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₅	8	8	8	-8	-8	2	-4	2	-4	0	0	2	-4	-2	-2	4	4	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₆	8	8	8	-8	-8	-4	2	-4	2	0	0	-4	2	4	4	-2	-2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₇	8	8	-8	0	0	2	-4	2	-4	$4 \sqrt{2}$	$- 4 \sqrt{2}$	-2	4	0	0	0	0	$\sqrt{2}$	$\sqrt{2}$	$- 2 \sqrt{2}$	$- 2 \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$2 \sqrt{2}$	$2 \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₈	8	8	-8	0	0	2	-4	2	-4	$- 4 \sqrt{2}$	$4 \sqrt{2}$	-2	4	0	0	0	0	$- \sqrt{2}$	$- \sqrt{2}$	$2 \sqrt{2}$	$2 \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- 2 \sqrt{2}$	$- 2 \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₉	8	8	-8	0	0	-4	2	-4	2	$4 \sqrt{2}$	$- 4 \sqrt{2}$	4	-2	0	0	0	0	$- 2 \sqrt{2}$	$- 2 \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$2 \sqrt{2}$	$2 \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₀	8	8	-8	0	0	-4	2	-4	2	$- 4 \sqrt{2}$	$4 \sqrt{2}$	4	-2	0	0	0	0	$2 \sqrt{2}$	$2 \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- 2 \sqrt{2}$	$- 2 \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₁	8	-8	0	$4 \sqrt{2}$	$- 4 \sqrt{2}$	2	-4	-2	4	0	0	0	0	$\sqrt{2}$	$- \sqrt{2}$	$- 2 \sqrt{2}$	$2 \sqrt{2}$	3ζ−3ζ⁷	−3ζ+3ζ⁷	0	0	3ζ³−3ζ⁵	−3ζ³+3ζ⁵	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₂	8	-8	0	$4 \sqrt{2}$	$- 4 \sqrt{2}$	2	-4	-2	4	0	0	0	0	$\sqrt{2}$	$- \sqrt{2}$	$- 2 \sqrt{2}$	$2 \sqrt{2}$	−3ζ+3ζ⁷	3ζ−3ζ⁷	0	0	−3ζ³+3ζ⁵	3ζ³−3ζ⁵	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₃	8	-8	0	$4 \sqrt{2}$	$- 4 \sqrt{2}$	-4	2	4	-2	0	0	0	0	$- 2 \sqrt{2}$	$2 \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	0	0	3ζ−3ζ⁷	−3ζ+3ζ⁷	0	0	3ζ³−3ζ⁵	−3ζ³+3ζ⁵	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₄	8	-8	0	$4 \sqrt{2}$	$- 4 \sqrt{2}$	-4	2	4	-2	0	0	0	0	$- 2 \sqrt{2}$	$2 \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	0	0	−3ζ+3ζ⁷	3ζ−3ζ⁷	0	0	−3ζ³+3ζ⁵	3ζ³−3ζ⁵	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₅	8	-8	0	$- 4 \sqrt{2}$	$4 \sqrt{2}$	2	-4	-2	4	0	0	0	0	$- \sqrt{2}$	$\sqrt{2}$	$2 \sqrt{2}$	$- 2 \sqrt{2}$	3ζ³−3ζ⁵	−3ζ³+3ζ⁵	0	0	−3ζ+3ζ⁷	3ζ−3ζ⁷	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₆	8	-8	0	$- 4 \sqrt{2}$	$4 \sqrt{2}$	2	-4	-2	4	0	0	0	0	$- \sqrt{2}$	$\sqrt{2}$	$2 \sqrt{2}$	$- 2 \sqrt{2}$	−3ζ³+3ζ⁵	3ζ³−3ζ⁵	0	0	3ζ−3ζ⁷	−3ζ+3ζ⁷	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₇	8	-8	0	$- 4 \sqrt{2}$	$4 \sqrt{2}$	-4	2	4	-2	0	0	0	0	$2 \sqrt{2}$	$- 2 \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	0	0	3ζ³−3ζ⁵	−3ζ³+3ζ⁵	0	0	−3ζ+3ζ⁷	3ζ−3ζ⁷	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₈	8	-8	0	$- 4 \sqrt{2}$	$4 \sqrt{2}$	-4	2	4	-2	0	0	0	0	$2 \sqrt{2}$	$- 2 \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	0	0	−3ζ³+3ζ⁵	3ζ³−3ζ⁵	0	0	3ζ−3ζ⁷	−3ζ+3ζ⁷	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0

Character table — Group #11772982