Group #72269091 — 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	C₅₂	C₅₃	C₅₄
size	1	1	4	4	4	4	4	4	4	4	9	9	16	16	16	16	16	16	16	16	18	18	18	36	36	36	36	36	36	36	36	36	36	36	36	36	36	36	36	108	108	108	108	108	108	108	108	108	108	108	108	162	162	162
order	1	2	3	3	3	3	6	6	6	6	4	4	3	3	3	3	6	6	6	6	4	8	8	12	12	12	12	12	12	12	12	24	24	24	24	24	24	24	24	8	8	8	8	24	24	24	24	24	24	24	24	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	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	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	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	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	1	-1	-1	-1	-1	1	1	1	1	1	1	1	1	$i$	$- i$	$i$	$- i$	$i$	$i$	$- i$	$- i$	$i$	$i$	$- i$	$- i$	-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	$- i$	$i$	$- i$	$i$	$- i$	$- i$	$i$	$i$	$- i$	$- i$	$i$	$i$	-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	-1	-1	$i$	$- i$	$- i$	$i$	$i$	$i$	$- i$	$- i$	$- i$	$- i$	$i$	$i$	-1	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	1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	$- i$	$i$	$i$	$- i$	$- i$	$- i$	$i$	$i$	$i$	$i$	$- i$	$- i$	-1	1	1
χ₉	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	-2	0	0	-2	-2	-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	-2	0	0
χ₁₀	2	2	2	2	2	2	2	2	2	2	-2	-2	2	2	2	2	2	2	2	2	-2	0	0	-2	-2	-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	2	0	0
χ₁₁	2	-2	2	2	2	2	-2	-2	-2	-2	$2 i$	$- 2 i$	2	2	2	2	-2	-2	-2	-2	0	$\sqrt{2}$	$- \sqrt{2}$	0	0	0	0	$2 i$	$2 i$	$- 2 i$	$- 2 i$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0	0	0	$- i \sqrt{2}$	$i \sqrt{2}$
χ₁₂	2	-2	2	2	2	2	-2	-2	-2	-2	$2 i$	$- 2 i$	2	2	2	2	-2	-2	-2	-2	0	$- \sqrt{2}$	$\sqrt{2}$	0	0	0	0	$2 i$	$2 i$	$- 2 i$	$- 2 i$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0	0	0	$i \sqrt{2}$	$- i \sqrt{2}$
χ₁₃	2	-2	2	2	2	2	-2	-2	-2	-2	$- 2 i$	$2 i$	2	2	2	2	-2	-2	-2	-2	0	$\sqrt{2}$	$- \sqrt{2}$	0	0	0	0	$- 2 i$	$- 2 i$	$2 i$	$2 i$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0	0	0	$i \sqrt{2}$	$- i \sqrt{2}$
χ₁₄	2	-2	2	2	2	2	-2	-2	-2	-2	$- 2 i$	$2 i$	2	2	2	2	-2	-2	-2	-2	0	$- \sqrt{2}$	$\sqrt{2}$	0	0	0	0	$- 2 i$	$- 2 i$	$2 i$	$2 i$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0	0	0	$- i \sqrt{2}$	$i \sqrt{2}$
χ₁₅	4	4	1	4	4	-2	1	4	4	-2	0	0	1	1	-2	-2	1	1	-2	-2	4	4	4	1	1	-2	-2	0	0	0	0	1	1	-2	-2	1	1	-2	-2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₁₆	4	4	1	4	4	-2	1	4	4	-2	0	0	1	1	-2	-2	1	1	-2	-2	4	-4	-4	1	1	-2	-2	0	0	0	0	-1	-1	2	2	-1	-1	2	2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₁₇	4	4	1	4	4	-2	1	4	4	-2	0	0	1	1	-2	-2	1	1	-2	-2	-4	0	0	-1	-1	2	2	0	0	0	0	$3 i$	$- 3 i$	0	0	$3 i$	$- 3 i$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₁₈	4	4	1	4	4	-2	1	4	4	-2	0	0	1	1	-2	-2	1	1	-2	-2	-4	0	0	-1	-1	2	2	0	0	0	0	$- 3 i$	$3 i$	0	0	$- 3 i$	$3 i$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₁₉	4	4	4	1	-2	4	4	1	-2	4	4	4	1	-2	1	-2	1	-2	1	-2	0	0	0	0	0	0	0	1	-2	1	-2	0	0	0	0	0	0	0	0	0	0	2	2	0	0	0	0	-1	-1	-1	-1	0	0	0
χ₂₀	4	4	4	1	-2	4	4	1	-2	4	4	4	1	-2	1	-2	1	-2	1	-2	0	0	0	0	0	0	0	1	-2	1	-2	0	0	0	0	0	0	0	0	0	0	-2	-2	0	0	0	0	1	1	1	1	0	0	0
χ₂₁	4	4	4	1	-2	4	4	1	-2	4	-4	-4	1	-2	1	-2	1	-2	1	-2	0	0	0	0	0	0	0	-1	2	-1	2	0	0	0	0	0	0	0	0	0	0	$2 i$	$- 2 i$	0	0	0	0	$- i$	$- i$	$i$	$i$	0	0	0
χ₂₂	4	4	4	1	-2	4	4	1	-2	4	-4	-4	1	-2	1	-2	1	-2	1	-2	0	0	0	0	0	0	0	-1	2	-1	2	0	0	0	0	0	0	0	0	0	0	$- 2 i$	$2 i$	0	0	0	0	$i$	$i$	$- i$	$- i$	0	0	0
χ₂₃	4	4	4	-2	1	4	4	-2	1	4	4	4	-2	1	-2	1	-2	1	-2	1	0	0	0	0	0	0	0	-2	1	-2	1	0	0	0	0	0	0	0	0	2	2	0	0	-1	-1	-1	-1	0	0	0	0	0	0	0
χ₂₄	4	4	4	-2	1	4	4	-2	1	4	4	4	-2	1	-2	1	-2	1	-2	1	0	0	0	0	0	0	0	-2	1	-2	1	0	0	0	0	0	0	0	0	-2	-2	0	0	1	1	1	1	0	0	0	0	0	0	0
χ₂₅	4	4	4	-2	1	4	4	-2	1	4	-4	-4	-2	1	-2	1	-2	1	-2	1	0	0	0	0	0	0	0	2	-1	2	-1	0	0	0	0	0	0	0	0	$2 i$	$- 2 i$	0	0	$- i$	$- i$	$i$	$i$	0	0	0	0	0	0	0
χ₂₆	4	4	4	-2	1	4	4	-2	1	4	-4	-4	-2	1	-2	1	-2	1	-2	1	0	0	0	0	0	0	0	2	-1	2	-1	0	0	0	0	0	0	0	0	$- 2 i$	$2 i$	0	0	$i$	$i$	$- i$	$- i$	0	0	0	0	0	0	0
χ₂₇	4	4	-2	4	4	1	-2	4	4	1	0	0	-2	-2	1	1	-2	-2	1	1	4	4	4	-2	-2	1	1	0	0	0	0	-2	-2	1	1	-2	-2	1	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₈	4	4	-2	4	4	1	-2	4	4	1	0	0	-2	-2	1	1	-2	-2	1	1	4	-4	-4	-2	-2	1	1	0	0	0	0	2	2	-1	-1	2	2	-1	-1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₉	4	4	-2	4	4	1	-2	4	4	1	0	0	-2	-2	1	1	-2	-2	1	1	-4	0	0	2	2	-1	-1	0	0	0	0	0	0	$3 i$	$- 3 i$	0	0	$3 i$	$- 3 i$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₀	4	4	-2	4	4	1	-2	4	4	1	0	0	-2	-2	1	1	-2	-2	1	1	-4	0	0	2	2	-1	-1	0	0	0	0	0	0	$- 3 i$	$3 i$	0	0	$- 3 i$	$3 i$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₁	4	-4	1	4	4	-2	-1	-4	-4	2	0	0	1	1	-2	-2	-1	-1	2	2	0	$2 \sqrt{2}$	$- 2 \sqrt{2}$	$3 i$	$- 3 i$	0	0	0	0	0	0	−2ζ⁵−ζ⁷−2ζ¹³−ζ²³	ζ⁵+2ζ⁷+ζ¹³+2ζ²³	$- \sqrt{2}$	$- \sqrt{2}$	2ζ⁵+ζ⁷+2ζ¹³+ζ²³	−ζ⁵−2ζ⁷−ζ¹³−2ζ²³	$\sqrt{2}$	$\sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₂	4	-4	1	4	4	-2	-1	-4	-4	2	0	0	1	1	-2	-2	-1	-1	2	2	0	$2 \sqrt{2}$	$- 2 \sqrt{2}$	$- 3 i$	$3 i$	0	0	0	0	0	0	ζ⁵+2ζ⁷+ζ¹³+2ζ²³	−2ζ⁵−ζ⁷−2ζ¹³−ζ²³	$- \sqrt{2}$	$- \sqrt{2}$	−ζ⁵−2ζ⁷−ζ¹³−2ζ²³	2ζ⁵+ζ⁷+2ζ¹³+ζ²³	$\sqrt{2}$	$\sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₃	4	-4	1	4	4	-2	-1	-4	-4	2	0	0	1	1	-2	-2	-1	-1	2	2	0	$- 2 \sqrt{2}$	$2 \sqrt{2}$	$3 i$	$- 3 i$	0	0	0	0	0	0	2ζ⁵+ζ⁷+2ζ¹³+ζ²³	−ζ⁵−2ζ⁷−ζ¹³−2ζ²³	$\sqrt{2}$	$\sqrt{2}$	−2ζ⁵−ζ⁷−2ζ¹³−ζ²³	ζ⁵+2ζ⁷+ζ¹³+2ζ²³	$- \sqrt{2}$	$- \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₄	4	-4	1	4	4	-2	-1	-4	-4	2	0	0	1	1	-2	-2	-1	-1	2	2	0	$- 2 \sqrt{2}$	$2 \sqrt{2}$	$- 3 i$	$3 i$	0	0	0	0	0	0	−ζ⁵−2ζ⁷−ζ¹³−2ζ²³	2ζ⁵+ζ⁷+2ζ¹³+ζ²³	$\sqrt{2}$	$\sqrt{2}$	ζ⁵+2ζ⁷+ζ¹³+2ζ²³	−2ζ⁵−ζ⁷−2ζ¹³−ζ²³	$- \sqrt{2}$	$- \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₅	4	-4	4	1	-2	4	-4	-1	2	-4	$4 i$	$- 4 i$	1	-2	1	-2	-1	2	-1	2	0	0	0	0	0	0	0	$i$	$- 2 i$	$- i$	$2 i$	0	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	0
χ₃₆	4	-4	4	1	-2	4	-4	-1	2	-4	$4 i$	$- 4 i$	1	-2	1	-2	-1	2	-1	2	0	0	0	0	0	0	0	$i$	$- 2 i$	$- i$	$2 i$	0	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	0
χ₃₇	4	-4	4	1	-2	4	-4	-1	2	-4	$- 4 i$	$4 i$	1	-2	1	-2	-1	2	-1	2	0	0	0	0	0	0	0	$- i$	$2 i$	$i$	$- 2 i$	0	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	0
χ₃₈	4	-4	4	1	-2	4	-4	-1	2	-4	$- 4 i$	$4 i$	1	-2	1	-2	-1	2	-1	2	0	0	0	0	0	0	0	$- i$	$2 i$	$i$	$- 2 i$	0	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	0
χ₃₉	4	-4	4	-2	1	4	-4	2	-1	-4	$4 i$	$- 4 i$	-2	1	-2	1	2	-1	2	-1	0	0	0	0	0	0	0	$- 2 i$	$i$	$2 i$	$- i$	0	0	0	0	0	0	0	0	0	0	0	0	−ζ⁷+ζ²³	ζ⁷−ζ²³	ζ⁵−ζ¹³	−ζ⁵+ζ¹³	0	0	0	0	0	0	0
χ₄₀	4	-4	4	-2	1	4	-4	2	-1	-4	$4 i$	$- 4 i$	-2	1	-2	1	2	-1	2	-1	0	0	0	0	0	0	0	$- 2 i$	$i$	$2 i$	$- i$	0	0	0	0	0	0	0	0	0	0	0	0	ζ⁷−ζ²³	−ζ⁷+ζ²³	−ζ⁵+ζ¹³	ζ⁵−ζ¹³	0	0	0	0	0	0	0
χ₄₁	4	-4	4	-2	1	4	-4	2	-1	-4	$- 4 i$	$4 i$	-2	1	-2	1	2	-1	2	-1	0	0	0	0	0	0	0	$2 i$	$- i$	$- 2 i$	$i$	0	0	0	0	0	0	0	0	0	0	0	0	ζ⁵−ζ¹³	−ζ⁵+ζ¹³	−ζ⁷+ζ²³	ζ⁷−ζ²³	0	0	0	0	0	0	0
χ₄₂	4	-4	4	-2	1	4	-4	2	-1	-4	$- 4 i$	$4 i$	-2	1	-2	1	2	-1	2	-1	0	0	0	0	0	0	0	$2 i$	$- i$	$- 2 i$	$i$	0	0	0	0	0	0	0	0	0	0	0	0	−ζ⁵+ζ¹³	ζ⁵−ζ¹³	ζ⁷−ζ²³	−ζ⁷+ζ²³	0	0	0	0	0	0	0
χ₄₃	4	-4	-2	4	4	1	2	-4	-4	-1	0	0	-2	-2	1	1	2	2	-1	-1	0	$2 \sqrt{2}$	$- 2 \sqrt{2}$	0	0	$3 i$	$- 3 i$	0	0	0	0	$- \sqrt{2}$	$- \sqrt{2}$	−2ζ⁵−ζ⁷−2ζ¹³−ζ²³	ζ⁵+2ζ⁷+ζ¹³+2ζ²³	$\sqrt{2}$	$\sqrt{2}$	2ζ⁵+ζ⁷+2ζ¹³+ζ²³	−ζ⁵−2ζ⁷−ζ¹³−2ζ²³	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₄	4	-4	-2	4	4	1	2	-4	-4	-1	0	0	-2	-2	1	1	2	2	-1	-1	0	$2 \sqrt{2}$	$- 2 \sqrt{2}$	0	0	$- 3 i$	$3 i$	0	0	0	0	$- \sqrt{2}$	$- \sqrt{2}$	ζ⁵+2ζ⁷+ζ¹³+2ζ²³	−2ζ⁵−ζ⁷−2ζ¹³−ζ²³	$\sqrt{2}$	$\sqrt{2}$	−ζ⁵−2ζ⁷−ζ¹³−2ζ²³	2ζ⁵+ζ⁷+2ζ¹³+ζ²³	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₅	4	-4	-2	4	4	1	2	-4	-4	-1	0	0	-2	-2	1	1	2	2	-1	-1	0	$- 2 \sqrt{2}$	$2 \sqrt{2}$	0	0	$3 i$	$- 3 i$	0	0	0	0	$\sqrt{2}$	$\sqrt{2}$	2ζ⁵+ζ⁷+2ζ¹³+ζ²³	−ζ⁵−2ζ⁷−ζ¹³−2ζ²³	$- \sqrt{2}$	$- \sqrt{2}$	−2ζ⁵−ζ⁷−2ζ¹³−ζ²³	ζ⁵+2ζ⁷+ζ¹³+2ζ²³	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₆	4	-4	-2	4	4	1	2	-4	-4	-1	0	0	-2	-2	1	1	2	2	-1	-1	0	$- 2 \sqrt{2}$	$2 \sqrt{2}$	0	0	$- 3 i$	$3 i$	0	0	0	0	$\sqrt{2}$	$\sqrt{2}$	−ζ⁵−2ζ⁷−ζ¹³−2ζ²³	2ζ⁵+ζ⁷+2ζ¹³+ζ²³	$- \sqrt{2}$	$- \sqrt{2}$	ζ⁵+2ζ⁷+ζ¹³+2ζ²³	−2ζ⁵−ζ⁷−2ζ¹³−ζ²³	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₇	16	16	4	4	-8	-8	4	4	-8	-8	0	0	1	-2	-2	4	1	-2	-2	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	0	0	0
χ₄₈	16	16	4	-8	4	-8	4	-8	4	-8	0	0	-2	1	4	-2	-2	1	4	-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	0	0	0
χ₄₉	16	16	-8	4	-8	4	-8	4	-8	4	0	0	-2	4	1	-2	-2	4	1	-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	0	0	0
χ₅₀	16	16	-8	-8	4	4	-8	-8	4	4	0	0	4	-2	-2	1	4	-2	-2	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
χ₅₁	16	-16	4	4	-8	-8	-4	-4	8	8	0	0	1	-2	-2	4	-1	2	2	-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	0	0	0
χ₅₂	16	-16	4	-8	4	-8	-4	8	-4	8	0	0	-2	1	4	-2	2	-1	-4	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	0	0	0
χ₅₃	16	-16	-8	4	-8	4	8	-4	8	-4	0	0	-2	4	1	-2	2	-4	-1	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	0	0	0
χ₅₄	16	-16	-8	-8	4	4	8	8	-4	-4	0	0	4	-2	-2	1	-4	2	2	-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

Character table — Group #72269091