Group #72342044 — 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
size	1	1	1	1	2	2	6	6	8	8	8	8	12	12	12	12	12	24	24	32	32	32	32	32	32	32	32	32	32	32	32	32	32	32	32	48	48	48	48	48	48	96	96	96	96	96	96
order	1	2	2	2	4	4	2	2	8	8	8	8	2	2	4	4	4	4	4	3	6	6	6	12	12	12	12	24	24	24	24	24	24	24	24	4	4	4	4	8	8	4	4	4	4	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
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
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
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
χ₅	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	0	0	0	0	2	2	0	0	0	0	0	0
χ₆	2	2	2	2	2	2	2	2	-2	-2	-2	-2	2	2	2	2	2	2	2	-1	-1	-1	-1	-1	-1	-1	-1	1	1	1	1	1	1	1	1	0	0	0	0	-2	-2	0	0	0	0	0	0
χ₇	2	2	2	2	-2	-2	2	2	0	0	0	0	2	2	2	-2	2	-2	-2	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
χ₈	2	2	2	2	-2	-2	2	2	0	0	0	0	2	2	2	-2	2	-2	-2	-1	-1	-1	-1	1	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	0	0	0	0	0	0
χ₉	2	2	2	2	-2	-2	2	2	0	0	0	0	2	2	2	-2	2	-2	-2	-1	-1	-1	-1	1	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	0	0	0	0	0	0
χ₁₀	2	-2	2	-2	0	0	2	-2	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	2	-2	-2	0	2	0	0	2	2	-2	-2	0	0	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	$- i \sqrt{2}$	$i \sqrt{2}$	0	0	0	0	0	0
χ₁₁	2	-2	2	-2	0	0	2	-2	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	2	-2	-2	0	2	0	0	-1	-1	1	1	$\sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	ζ⁵+ζ⁷	ζ⁵+ζ⁷	−ζ⁵−ζ⁷	−ζ⁵−ζ⁷	ζ¹³+ζ²³	ζ¹³+ζ²³	−ζ¹³−ζ²³	−ζ¹³−ζ²³	0	0	0	0	$- i \sqrt{2}$	$i \sqrt{2}$	0	0	0	0	0	0
χ₁₂	2	-2	2	-2	0	0	2	-2	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	2	-2	-2	0	2	0	0	-1	-1	1	1	$- \sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	ζ¹³+ζ²³	ζ¹³+ζ²³	−ζ¹³−ζ²³	−ζ¹³−ζ²³	ζ⁵+ζ⁷	ζ⁵+ζ⁷	−ζ⁵−ζ⁷	−ζ⁵−ζ⁷	0	0	0	0	$- i \sqrt{2}$	$i \sqrt{2}$	0	0	0	0	0	0
χ₁₃	2	-2	2	-2	0	0	2	-2	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	2	-2	-2	0	2	0	0	2	2	-2	-2	0	0	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	$i \sqrt{2}$	$- i \sqrt{2}$	0	0	0	0	0	0
χ₁₄	2	-2	2	-2	0	0	2	-2	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	2	-2	-2	0	2	0	0	-1	-1	1	1	$\sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	−ζ⁵−ζ⁷	−ζ⁵−ζ⁷	ζ⁵+ζ⁷	ζ⁵+ζ⁷	−ζ¹³−ζ²³	−ζ¹³−ζ²³	ζ¹³+ζ²³	ζ¹³+ζ²³	0	0	0	0	$i \sqrt{2}$	$- i \sqrt{2}$	0	0	0	0	0	0
χ₁₅	2	-2	2	-2	0	0	2	-2	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	2	-2	-2	0	2	0	0	-1	-1	1	1	$- \sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	−ζ¹³−ζ²³	−ζ¹³−ζ²³	ζ¹³+ζ²³	ζ¹³+ζ²³	−ζ⁵−ζ⁷	−ζ⁵−ζ⁷	ζ⁵+ζ⁷	ζ⁵+ζ⁷	0	0	0	0	$i \sqrt{2}$	$- i \sqrt{2}$	0	0	0	0	0	0
χ₁₆	3	3	3	3	3	3	3	3	3	3	3	3	-1	-1	-1	3	-1	-1	-1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	1	1	1	-1	-1	1	1	-1	-1	-1	-1
χ₁₇	3	3	3	3	3	3	3	3	3	3	3	3	-1	-1	-1	3	-1	-1	-1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	-1	-1	-1	-1	-1	-1	-1	-1	1	1	1	1
χ₁₈	3	3	3	3	3	3	3	3	-3	-3	-3	-3	-1	-1	-1	3	-1	-1	-1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	1	-1	-1	1	1	-1	1	-1	-1	1	1
χ₁₉	3	3	3	3	3	3	3	3	-3	-3	-3	-3	-1	-1	-1	3	-1	-1	-1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	-1	-1	1	1	1	1	1	-1	1	1	-1	-1
χ₂₀	4	4	-4	-4	-4	4	0	0	2	-2	2	-2	0	0	0	0	0	0	0	1	-1	-1	1	-1	-1	1	1	1	-1	1	-1	1	-1	1	-1	$2 i$	$- 2 i$	$2 i$	$- 2 i$	0	0	0	0	0	0	0	0
χ₂₁	4	4	-4	-4	-4	4	0	0	2	-2	2	-2	0	0	0	0	0	0	0	1	-1	-1	1	-1	-1	1	1	1	-1	1	-1	1	-1	1	-1	$- 2 i$	$2 i$	$- 2 i$	$2 i$	0	0	0	0	0	0	0	0
χ₂₂	4	4	-4	-4	-4	4	0	0	-2	2	-2	2	0	0	0	0	0	0	0	1	-1	-1	1	-1	-1	1	1	-1	1	-1	1	-1	1	-1	1	$2 i$	$- 2 i$	$- 2 i$	$2 i$	0	0	0	0	0	0	0	0
χ₂₃	4	4	-4	-4	-4	4	0	0	-2	2	-2	2	0	0	0	0	0	0	0	1	-1	-1	1	-1	-1	1	1	-1	1	-1	1	-1	1	-1	1	$- 2 i$	$2 i$	$2 i$	$- 2 i$	0	0	0	0	0	0	0	0
χ₂₄	6	6	6	6	6	6	-2	-2	0	0	0	0	2	2	-2	-2	-2	2	-2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	2	2	0	0	0	0	0	-2	0	0	0	0
χ₂₅	6	6	6	6	6	6	-2	-2	0	0	0	0	2	2	-2	-2	-2	2	-2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	-2	-2	0	0	0	0	0	2	0	0	0	0
χ₂₆	6	6	6	6	6	6	-2	-2	0	0	0	0	-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	2	2	0	0	-2	0	0	0	0	0
χ₂₇	6	6	6	6	6	6	-2	-2	0	0	0	0	-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	-2	-2	0	0	2	0	0	0	0	0
χ₂₈	6	6	6	6	-6	-6	6	6	0	0	0	0	-2	-2	-2	-6	-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	0	0
χ₂₉	6	6	6	6	-6	-6	-2	-2	0	0	0	0	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	0	0	0	0	2	-2	0	0
χ₃₀	6	6	6	6	-6	-6	-2	-2	0	0	0	0	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	0	0	0	0	-2	2	0	0
χ₃₁	6	6	6	6	-6	-6	-2	-2	0	0	0	0	-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	0	0	0	0	0	0	2	-2
χ₃₂	6	6	6	6	-6	-6	-2	-2	0	0	0	0	-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	0	0	0	0	0	0	-2	2
χ₃₃	6	-6	6	-6	0	0	6	-6	$- 3 i \sqrt{2}$	$- 3 i \sqrt{2}$	$3 i \sqrt{2}$	$3 i \sqrt{2}$	-2	2	2	0	-2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	$i \sqrt{2}$	$- i \sqrt{2}$	0	0	0	0	0	0
χ₃₄	6	-6	6	-6	0	0	6	-6	$3 i \sqrt{2}$	$3 i \sqrt{2}$	$- 3 i \sqrt{2}$	$- 3 i \sqrt{2}$	-2	2	2	0	-2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	$- i \sqrt{2}$	$i \sqrt{2}$	0	0	0	0	0	0
χ₃₅	8	8	-8	-8	8	-8	0	0	0	0	0	0	0	0	0	0	0	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
χ₃₆	8	8	-8	-8	8	-8	0	0	0	0	0	0	0	0	0	0	0	0	0	-1	1	1	-1	-1	-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	0	0	0	0	0	0
χ₃₇	8	8	-8	-8	8	-8	0	0	0	0	0	0	0	0	0	0	0	0	0	-1	1	1	-1	-1	-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	0	0	0	0	0	0
χ₃₈	8	8	-8	-8	-8	8	0	0	4	-4	4	-4	0	0	0	0	0	0	0	-1	1	1	-1	1	1	-1	-1	-1	1	-1	1	-1	1	-1	1	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₉	8	8	-8	-8	-8	8	0	0	-4	4	-4	4	0	0	0	0	0	0	0	-1	1	1	-1	1	1	-1	-1	1	-1	1	-1	1	-1	1	-1	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₀	8	-8	-8	8	0	0	0	0	$- 2 i \sqrt{2}$	$2 i \sqrt{2}$	$2 i \sqrt{2}$	$- 2 i \sqrt{2}$	0	0	0	0	0	0	0	2	-2	2	-2	0	0	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	0	0	0	0	0	0
χ₄₁	8	-8	-8	8	0	0	0	0	$- 2 i \sqrt{2}$	$2 i \sqrt{2}$	$2 i \sqrt{2}$	$- 2 i \sqrt{2}$	0	0	0	0	0	0	0	-1	1	-1	1	$\sqrt{3}$	$- \sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	ζ¹³+ζ²³	−ζ¹³−ζ²³	−ζ¹³−ζ²³	ζ¹³+ζ²³	ζ⁵+ζ⁷	−ζ⁵−ζ⁷	−ζ⁵−ζ⁷	ζ⁵+ζ⁷	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₂	8	-8	-8	8	0	0	0	0	$- 2 i \sqrt{2}$	$2 i \sqrt{2}$	$2 i \sqrt{2}$	$- 2 i \sqrt{2}$	0	0	0	0	0	0	0	-1	1	-1	1	$- \sqrt{3}$	$\sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	ζ⁵+ζ⁷	−ζ⁵−ζ⁷	−ζ⁵−ζ⁷	ζ⁵+ζ⁷	ζ¹³+ζ²³	−ζ¹³−ζ²³	−ζ¹³−ζ²³	ζ¹³+ζ²³	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₃	8	-8	-8	8	0	0	0	0	$2 i \sqrt{2}$	$- 2 i \sqrt{2}$	$- 2 i \sqrt{2}$	$2 i \sqrt{2}$	0	0	0	0	0	0	0	2	-2	2	-2	0	0	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	0	0	0	0	0	0
χ₄₄	8	-8	-8	8	0	0	0	0	$2 i \sqrt{2}$	$- 2 i \sqrt{2}$	$- 2 i \sqrt{2}$	$2 i \sqrt{2}$	0	0	0	0	0	0	0	-1	1	-1	1	$\sqrt{3}$	$- \sqrt{3}$	$- \sqrt{3}$	$\sqrt{3}$	−ζ¹³−ζ²³	ζ¹³+ζ²³	ζ¹³+ζ²³	−ζ¹³−ζ²³	−ζ⁵−ζ⁷	ζ⁵+ζ⁷	ζ⁵+ζ⁷	−ζ⁵−ζ⁷	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₅	8	-8	-8	8	0	0	0	0	$2 i \sqrt{2}$	$- 2 i \sqrt{2}$	$- 2 i \sqrt{2}$	$2 i \sqrt{2}$	0	0	0	0	0	0	0	-1	1	-1	1	$- \sqrt{3}$	$\sqrt{3}$	$\sqrt{3}$	$- \sqrt{3}$	−ζ⁵−ζ⁷	ζ⁵+ζ⁷	ζ⁵+ζ⁷	−ζ⁵−ζ⁷	−ζ¹³−ζ²³	ζ¹³+ζ²³	ζ¹³+ζ²³	−ζ¹³−ζ²³	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₆	12	-12	12	-12	0	0	-4	4	0	0	0	0	4	-4	4	0	-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
χ₄₇	12	-12	12	-12	0	0	-4	4	0	0	0	0	-4	4	-4	0	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

Character table — Group #72342044