Group #13165128 — 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	C₄₉	C₅₀	C₅₁
size	1	1	2	2	2	4	8	8	8	8	9	9	16	16	16	16	18	18	18	18	18	18	18	18	18	36	36	36	36	36	36	36	36	36	36	36	36	36	36	36	36	36	36	36	36	72	72	72	72	216	216
order	1	2	3	4	6	12	3	6	12	12	2	2	3	6	12	12	4	4	4	6	6	12	12	12	12	4	8	8	8	8	8	8	8	8	12	12	12	24	24	24	24	24	24	24	24	24	24	24	24	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	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	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	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	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
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	$i$	$i$	$- i$	$- i$	$i$	$i$	$- i$	$- i$	-1	1	1	$i$	$i$	$i$	$i$	$- i$	$- i$	$- i$	$- i$	$i$	$i$	$- i$	$- i$	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	$i$	$i$	$- i$	$- i$	$- i$	$- i$	$i$	$i$	-1	1	1	$- i$	$- i$	$- i$	$- i$	$i$	$i$	$i$	$i$	$i$	$i$	$- i$	$- i$	-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	$- i$	$- i$	$i$	$i$	$i$	$i$	$- i$	$- i$	-1	1	1	$i$	$i$	$i$	$i$	$- i$	$- i$	$- i$	$- i$	$- i$	$- i$	$i$	$i$	-1	1
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	$- i$	$- i$	$i$	$i$	$- i$	$- i$	$i$	$i$	-1	1	1	$- i$	$- i$	$- i$	$- i$	$i$	$i$	$i$	$i$	$- i$	$- i$	$i$	$i$	1	-1
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	-2	0	0	0	0	0	0	0	0	2	-2	-2	0	0	0	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	0	0	-2	-2	0	0	0	0	0	0	0	0	0	$- i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	-2	0	0	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	0	0	0	0	0	0
χ₁₁	2	2	2	2	2	2	2	2	2	2	-2	-2	2	2	2	2	-2	0	0	-2	-2	0	0	0	0	0	0	0	0	0	$i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	-2	0	0	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	0	0	0	0	0	0
χ₁₂	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	-2	0	0	0	0	0	0	0	0	-2	-2	-2	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₁₃	2	2	2	-2	2	-2	2	2	-2	-2	-2	-2	2	2	-2	-2	2	0	0	-2	-2	0	0	0	0	0	0	0	0	0	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	2	0	0	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	0	0	0	0	0	0
χ₁₄	2	2	2	-2	2	-2	2	2	-2	-2	-2	-2	2	2	-2	-2	2	0	0	-2	-2	0	0	0	0	0	0	0	0	0	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	2	0	0	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	0	0	0	0	0	0
χ₁₅	2	2	-1	2	-1	-1	2	2	2	2	2	2	-1	-1	-1	-1	2	2	2	-1	-1	-1	-1	-1	-1	2	0	0	0	0	2	2	2	2	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	0	0	0	0	0	0
χ₁₆	2	2	-1	2	-1	-1	2	2	2	2	2	2	-1	-1	-1	-1	2	2	2	-1	-1	-1	-1	-1	-1	2	0	0	0	0	-2	-2	-2	-2	-1	-1	-1	1	1	1	1	1	1	1	1	0	0	0	0	0	0
χ₁₇	2	2	-1	2	-1	-1	2	2	2	2	2	2	-1	-1	-1	-1	2	-2	-2	-1	-1	1	1	1	1	-2	0	0	0	0	0	0	0	0	-1	1	1	$\sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	0	0	0	0	0	0
χ₁₈	2	2	-1	2	-1	-1	2	2	2	2	2	2	-1	-1	-1	-1	2	-2	-2	-1	-1	1	1	1	1	-2	0	0	0	0	0	0	0	0	-1	1	1	$- \sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	0	0	0	0	0	0
χ₁₉	2	2	-1	2	-1	-1	2	2	2	2	-2	-2	-1	-1	-1	-1	-2	0	0	1	1	$\sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	0	0	0	0	0	$- i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	1	$\sqrt{3}$	$- \sqrt{3}$	ζ⁵+ζ⁷	ζ¹³+ζ²³	−ζ⁵−ζ⁷	−ζ¹³−ζ²³	ζ⁵+ζ⁷	ζ¹³+ζ²³	−ζ⁵−ζ⁷	−ζ¹³−ζ²³	0	0	0	0	0	0
χ₂₀	2	2	-1	2	-1	-1	2	2	2	2	-2	-2	-1	-1	-1	-1	-2	0	0	1	1	$\sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	0	0	0	0	0	$i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	1	$\sqrt{3}$	$- \sqrt{3}$	−ζ⁵−ζ⁷	−ζ¹³−ζ²³	ζ⁵+ζ⁷	ζ¹³+ζ²³	−ζ⁵−ζ⁷	−ζ¹³−ζ²³	ζ⁵+ζ⁷	ζ¹³+ζ²³	0	0	0	0	0	0
χ₂₁	2	2	-1	2	-1	-1	2	2	2	2	-2	-2	-1	-1	-1	-1	-2	0	0	1	1	$- \sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	0	0	0	0	0	$- i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	1	$- \sqrt{3}$	$\sqrt{3}$	ζ¹³+ζ²³	ζ⁵+ζ⁷	−ζ¹³−ζ²³	−ζ⁵−ζ⁷	ζ¹³+ζ²³	ζ⁵+ζ⁷	−ζ¹³−ζ²³	−ζ⁵−ζ⁷	0	0	0	0	0	0
χ₂₂	2	2	-1	2	-1	-1	2	2	2	2	-2	-2	-1	-1	-1	-1	-2	0	0	1	1	$- \sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	0	0	0	0	0	$i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	1	$- \sqrt{3}$	$\sqrt{3}$	−ζ¹³−ζ²³	−ζ⁵−ζ⁷	ζ¹³+ζ²³	ζ⁵+ζ⁷	−ζ¹³−ζ²³	−ζ⁵−ζ⁷	ζ¹³+ζ²³	ζ⁵+ζ⁷	0	0	0	0	0	0
χ₂₃	2	2	-1	-2	-1	1	2	2	-2	-2	2	2	-1	-1	1	1	-2	2	2	-1	-1	-1	-1	-1	-1	-2	0	0	0	0	0	0	0	0	1	1	1	$- i \sqrt{3}$	$i \sqrt{3}$	$- i \sqrt{3}$	$i \sqrt{3}$	$i \sqrt{3}$	$- i \sqrt{3}$	$i \sqrt{3}$	$- i \sqrt{3}$	0	0	0	0	0	0
χ₂₄	2	2	-1	-2	-1	1	2	2	-2	-2	2	2	-1	-1	1	1	-2	2	2	-1	-1	-1	-1	-1	-1	-2	0	0	0	0	0	0	0	0	1	1	1	$i \sqrt{3}$	$- i \sqrt{3}$	$i \sqrt{3}$	$- i \sqrt{3}$	$- i \sqrt{3}$	$i \sqrt{3}$	$- i \sqrt{3}$	$i \sqrt{3}$	0	0	0	0	0	0
χ₂₅	2	2	-1	-2	-1	1	2	2	-2	-2	2	2	-1	-1	1	1	-2	-2	-2	-1	-1	1	1	1	1	2	0	0	0	0	$2 i$	$2 i$	$- 2 i$	$- 2 i$	1	-1	-1	$- i$	$- i$	$- i$	$- i$	$i$	$i$	$i$	$i$	0	0	0	0	0	0
χ₂₆	2	2	-1	-2	-1	1	2	2	-2	-2	2	2	-1	-1	1	1	-2	-2	-2	-1	-1	1	1	1	1	2	0	0	0	0	$- 2 i$	$- 2 i$	$2 i$	$2 i$	1	-1	-1	$i$	$i$	$i$	$i$	$- i$	$- i$	$- i$	$- i$	0	0	0	0	0	0
χ₂₇	2	2	-1	-2	-1	1	2	2	-2	-2	-2	-2	-1	-1	1	1	2	0	0	1	1	$\sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	0	0	0	0	0	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	-1	$- \sqrt{3}$	$\sqrt{3}$	ζ⁵−ζ⁷	ζ¹³−ζ²³	−ζ⁵+ζ⁷	−ζ¹³+ζ²³	−ζ⁵+ζ⁷	−ζ¹³+ζ²³	ζ⁵−ζ⁷	ζ¹³−ζ²³	0	0	0	0	0	0
χ₂₈	2	2	-1	-2	-1	1	2	2	-2	-2	-2	-2	-1	-1	1	1	2	0	0	1	1	$\sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	0	0	0	0	0	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	-1	$- \sqrt{3}$	$\sqrt{3}$	−ζ⁵+ζ⁷	−ζ¹³+ζ²³	ζ⁵−ζ⁷	ζ¹³−ζ²³	ζ⁵−ζ⁷	ζ¹³−ζ²³	−ζ⁵+ζ⁷	−ζ¹³+ζ²³	0	0	0	0	0	0
χ₂₉	2	2	-1	-2	-1	1	2	2	-2	-2	-2	-2	-1	-1	1	1	2	0	0	1	1	$- \sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	0	0	0	0	0	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	-1	$\sqrt{3}$	$- \sqrt{3}$	ζ¹³−ζ²³	ζ⁵−ζ⁷	−ζ¹³+ζ²³	−ζ⁵+ζ⁷	−ζ¹³+ζ²³	−ζ⁵+ζ⁷	ζ¹³−ζ²³	ζ⁵−ζ⁷	0	0	0	0	0	0
χ₃₀	2	2	-1	-2	-1	1	2	2	-2	-2	-2	-2	-1	-1	1	1	2	0	0	1	1	$- \sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	0	0	0	0	0	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	-1	$\sqrt{3}$	$- \sqrt{3}$	−ζ¹³+ζ²³	−ζ⁵+ζ⁷	ζ¹³−ζ²³	ζ⁵−ζ⁷	ζ¹³−ζ²³	ζ⁵−ζ⁷	−ζ¹³+ζ²³	−ζ⁵+ζ⁷	0	0	0	0	0	0
χ₃₁	2	-2	2	0	-2	0	2	-2	0	0	-2	2	2	-2	0	0	0	2	-2	2	-2	2	2	-2	-2	0	$- i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	$- i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	0	0
χ₃₂	2	-2	2	0	-2	0	2	-2	0	0	-2	2	2	-2	0	0	0	2	-2	2	-2	2	2	-2	-2	0	$i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	$i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	0	0
χ₃₃	2	-2	2	0	-2	0	2	-2	0	0	-2	2	2	-2	0	0	0	-2	2	2	-2	-2	-2	2	2	0	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	0	0
χ₃₄	2	-2	2	0	-2	0	2	-2	0	0	-2	2	2	-2	0	0	0	-2	2	2	-2	-2	-2	2	2	0	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	0	0
χ₃₅	4	-4	4	0	-4	0	4	-4	0	0	4	-4	4	-4	0	0	0	0	0	-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
χ₃₆	4	-4	-2	0	2	0	4	-4	0	0	4	-4	-2	2	0	0	0	0	0	2	-2	$2 \sqrt{3}$	$- 2 \sqrt{3}$	$- 2 \sqrt{3}$	$2 \sqrt{3}$	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	4	-4	-2	0	2	0	4	-4	0	0	4	-4	-2	2	0	0	0	0	0	2	-2	$- 2 \sqrt{3}$	$2 \sqrt{3}$	$2 \sqrt{3}$	$- 2 \sqrt{3}$	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
χ₃₈	4	-4	-2	0	2	0	4	-4	0	0	-4	4	-2	2	0	0	0	4	-4	-2	2	-2	-2	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
χ₃₉	4	-4	-2	0	2	0	4	-4	0	0	-4	4	-2	2	0	0	0	-4	4	-2	2	2	2	-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
χ₄₀	8	8	8	8	8	8	-1	-1	-1	-1	0	0	-1	-1	-1	-1	0	0	0	0	0	0	0	0	0	0	2	2	2	2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	-1	-1	-1	-1	0	0
χ₄₁	8	8	8	8	8	8	-1	-1	-1	-1	0	0	-1	-1	-1	-1	0	0	0	0	0	0	0	0	0	0	-2	-2	-2	-2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	1	1	1	0	0
χ₄₂	8	8	8	-8	8	-8	-1	-1	1	1	0	0	-1	-1	1	1	0	0	0	0	0	0	0	0	0	0	$2 i$	$2 i$	$- 2 i$	$- 2 i$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	$- i$	$- i$	$i$	$i$	0	0
χ₄₃	8	8	8	-8	8	-8	-1	-1	1	1	0	0	-1	-1	1	1	0	0	0	0	0	0	0	0	0	0	$- 2 i$	$- 2 i$	$2 i$	$2 i$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	$i$	$i$	$- i$	$- i$	0	0
χ₄₄	8	-8	8	0	-8	0	-1	1	$3 i$	$- 3 i$	0	0	-1	1	$3 i$	$- 3 i$	0	0	0	0	0	0	0	0	0	0	2ζ⁷+2ζ²³	−2ζ⁷−2ζ²³	2ζ⁵+2ζ¹³	−2ζ⁵−2ζ¹³	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	−ζ⁷−ζ²³	ζ⁷+ζ²³	−ζ⁵−ζ¹³	ζ⁵+ζ¹³	0	0
χ₄₅	8	-8	8	0	-8	0	-1	1	$3 i$	$- 3 i$	0	0	-1	1	$3 i$	$- 3 i$	0	0	0	0	0	0	0	0	0	0	−2ζ⁷−2ζ²³	2ζ⁷+2ζ²³	−2ζ⁵−2ζ¹³	2ζ⁵+2ζ¹³	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	ζ⁷+ζ²³	−ζ⁷−ζ²³	ζ⁵+ζ¹³	−ζ⁵−ζ¹³	0	0
χ₄₆	8	-8	8	0	-8	0	-1	1	$- 3 i$	$3 i$	0	0	-1	1	$- 3 i$	$3 i$	0	0	0	0	0	0	0	0	0	0	−2ζ⁵−2ζ¹³	2ζ⁵+2ζ¹³	−2ζ⁷−2ζ²³	2ζ⁷+2ζ²³	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	ζ⁵+ζ¹³	−ζ⁵−ζ¹³	ζ⁷+ζ²³	−ζ⁷−ζ²³	0	0
χ₄₇	8	-8	8	0	-8	0	-1	1	$- 3 i$	$3 i$	0	0	-1	1	$- 3 i$	$3 i$	0	0	0	0	0	0	0	0	0	0	2ζ⁵+2ζ¹³	−2ζ⁵−2ζ¹³	2ζ⁷+2ζ²³	−2ζ⁷−2ζ²³	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	−ζ⁵−ζ¹³	ζ⁵+ζ¹³	−ζ⁷−ζ²³	ζ⁷+ζ²³	0	0
χ₄₈	16	16	-8	16	-8	-8	-2	-2	-2	-2	0	0	1	1	1	1	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	0	0	0	0
χ₄₉	16	16	-8	-16	-8	8	-2	-2	2	2	0	0	1	1	-1	-1	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	0	0	0	0
χ₅₀	16	-16	-8	0	8	0	-2	2	$6 i$	$- 6 i$	0	0	1	-1	$- 3 i$	$3 i$	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	0	0	0	0
χ₅₁	16	-16	-8	0	8	0	-2	2	$- 6 i$	$6 i$	0	0	1	-1	$3 i$	$- 3 i$	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	0	0	0	0

Character table — Group #13165128