Group #13165299 — 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	C₅₅	C₅₆	C₅₇
size	1	1	2	2	2	4	4	4	4	4	4	4	8	8	8	8	8	8	8	12	12	12	16	18	18	24	24	24	24	24	24	24	24	24	24	24	24	24	24	24	36	36	36	36	48	48	48	54	54	72	72	72	72	72	72	144	216
order	1	2	3	4	6	3	3	6	6	12	12	12	3	3	6	6	12	12	12	8	8	8	12	2	4	2	6	6	24	24	24	24	24	24	24	24	24	24	24	24	2	4	6	12	6	6	6	8	8	4	6	8	12	24	24	12	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	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	-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	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	-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	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	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	-1	-1	-1	1	1	1	1	1	1	1	-1	-1	-1	1	-1	1	-1	-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	-1	1	1	1	1	-1	-1	-1	-1	-1	1	1	1	1	1	1	1	-1
χ₉	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	0	0	0	0	0	0	0	2	2	0	0	0	0	2	2	0	0	-2	-2	0	0	0	-2	-2	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	0	0	-2	2	-2	-2	0	0	0	0	0	0	0	-2	-2	0	0	0	0	-2	-2	0	0	-2	-2	0	0	0	2	2	0	0	0	0	0	0	0	0
χ₁₁	2	2	2	-2	2	2	2	2	2	-2	-2	-2	2	2	2	2	-2	-2	-2	0	0	0	-2	-2	2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	2	-2	-2	2	0	0	0	0	0	0	2	0	-2	0	0	0	0
χ₁₂	2	2	2	-2	2	2	2	2	2	-2	-2	-2	2	2	2	2	-2	-2	-2	0	0	0	-2	-2	2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	-2	2	-2	2	0	0	0	0	0	0	-2	0	2	0	0	0	0
χ₁₃	2	2	2	-2	2	2	2	2	2	-2	-2	-2	2	2	2	2	-2	-2	-2	$2 i$	$- 2 i$	0	-2	2	-2	0	0	0	$2 i$	$2 i$	$- 2 i$	$- 2 i$	0	0	$2 i$	$2 i$	$- 2 i$	$- 2 i$	0	0	0	0	2	-2	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₁₄	2	2	2	-2	2	2	2	2	2	-2	-2	-2	2	2	2	2	-2	-2	-2	$- 2 i$	$2 i$	0	-2	2	-2	0	0	0	$- 2 i$	$- 2 i$	$2 i$	$2 i$	0	0	$- 2 i$	$- 2 i$	$2 i$	$2 i$	0	0	0	0	2	-2	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₁₅	2	2	-1	2	-1	2	2	2	2	-1	2	2	-1	-1	-1	-1	2	-1	-1	2	2	0	-1	2	2	2	-1	-1	2	-1	2	-1	0	0	-1	-1	-1	-1	0	0	0	0	-1	-1	2	-1	-1	0	0	0	0	2	0	-1	-1	0	0
χ₁₆	2	2	-1	2	-1	2	2	2	2	-1	2	2	-1	-1	-1	-1	2	-1	-1	2	2	0	-1	2	2	-2	1	1	2	-1	2	-1	0	0	-1	-1	-1	-1	0	0	0	0	-1	-1	-2	1	1	0	0	0	0	-2	0	1	1	0	0
χ₁₇	2	2	-1	2	-1	2	2	2	2	-1	2	2	-1	-1	-1	-1	2	-1	-1	-2	-2	0	-1	2	2	2	-1	-1	-2	1	-2	1	0	0	1	1	1	1	0	0	0	0	-1	-1	2	-1	-1	0	0	0	0	-2	0	1	1	0	0
χ₁₈	2	2	-1	2	-1	2	2	2	2	-1	2	2	-1	-1	-1	-1	2	-1	-1	-2	-2	0	-1	2	2	-2	1	1	-2	1	-2	1	0	0	1	1	1	1	0	0	0	0	-1	-1	-2	1	1	0	0	0	0	2	0	-1	-1	0	0
χ₁₉	2	2	-1	-2	-1	2	2	2	2	1	-2	-2	-1	-1	-1	-1	-2	1	1	$2 i$	$- 2 i$	0	1	2	-2	0	$- i \sqrt{3}$	$i \sqrt{3}$	$2 i$	$- i$	$- 2 i$	$i$	0	0	$- i$	$- i$	$i$	$i$	0	0	0	0	-1	1	0	$- i \sqrt{3}$	$i \sqrt{3}$	0	0	0	0	0	0	$\sqrt{3}$	$- \sqrt{3}$	0	0
χ₂₀	2	2	-1	-2	-1	2	2	2	2	1	-2	-2	-1	-1	-1	-1	-2	1	1	$2 i$	$- 2 i$	0	1	2	-2	0	$i \sqrt{3}$	$- i \sqrt{3}$	$2 i$	$- i$	$- 2 i$	$i$	0	0	$- i$	$- i$	$i$	$i$	0	0	0	0	-1	1	0	$i \sqrt{3}$	$- i \sqrt{3}$	0	0	0	0	0	0	$- \sqrt{3}$	$\sqrt{3}$	0	0
χ₂₁	2	2	-1	-2	-1	2	2	2	2	1	-2	-2	-1	-1	-1	-1	-2	1	1	$- 2 i$	$2 i$	0	1	2	-2	0	$- i \sqrt{3}$	$i \sqrt{3}$	$- 2 i$	$i$	$2 i$	$- i$	0	0	$i$	$i$	$- i$	$- i$	0	0	0	0	-1	1	0	$- i \sqrt{3}$	$i \sqrt{3}$	0	0	0	0	0	0	$- \sqrt{3}$	$\sqrt{3}$	0	0
χ₂₂	2	2	-1	-2	-1	2	2	2	2	1	-2	-2	-1	-1	-1	-1	-2	1	1	$- 2 i$	$2 i$	0	1	2	-2	0	$i \sqrt{3}$	$- i \sqrt{3}$	$- 2 i$	$i$	$2 i$	$- i$	0	0	$i$	$i$	$- i$	$- i$	0	0	0	0	-1	1	0	$i \sqrt{3}$	$- i \sqrt{3}$	0	0	0	0	0	0	$\sqrt{3}$	$- \sqrt{3}$	0	0
χ₂₃	4	4	4	4	4	1	-2	-2	1	4	-2	-2	-2	1	-2	1	1	-2	-2	0	0	4	1	0	0	2	2	2	0	0	0	0	-2	-2	0	0	0	0	1	1	0	0	0	0	-1	-1	-1	0	0	2	0	0	0	0	0	-1	0
χ₂₄	4	4	4	4	4	1	-2	-2	1	4	-2	-2	-2	1	-2	1	1	-2	-2	0	0	4	1	0	0	-2	-2	-2	0	0	0	0	-2	-2	0	0	0	0	1	1	0	0	0	0	1	1	1	0	0	-2	0	0	0	0	0	1	0
χ₂₅	4	4	4	4	4	1	-2	-2	1	4	-2	-2	-2	1	-2	1	1	-2	-2	0	0	-4	1	0	0	2	2	2	0	0	0	0	2	2	0	0	0	0	-1	-1	0	0	0	0	-1	-1	-1	0	0	-2	0	0	0	0	0	1	0
χ₂₆	4	4	4	4	4	1	-2	-2	1	4	-2	-2	-2	1	-2	1	1	-2	-2	0	0	-4	1	0	0	-2	-2	-2	0	0	0	0	2	2	0	0	0	0	-1	-1	0	0	0	0	1	1	1	0	0	2	0	0	0	0	0	-1	0
χ₂₇	4	4	4	4	4	-2	1	1	-2	4	1	1	1	-2	1	-2	-2	1	1	2	2	4	-2	0	0	0	0	0	-1	2	-1	2	1	1	-1	-1	-1	-1	-2	-2	2	2	0	0	0	0	0	0	0	0	-1	0	-1	0	0	0	0
χ₂₈	4	4	4	4	4	-2	1	1	-2	4	1	1	1	-2	1	-2	-2	1	1	2	2	-4	-2	0	0	0	0	0	-1	2	-1	2	-1	-1	-1	-1	-1	-1	2	2	-2	-2	0	0	0	0	0	0	0	0	1	0	1	0	0	0	0
χ₂₉	4	4	4	4	4	-2	1	1	-2	4	1	1	1	-2	1	-2	-2	1	1	-2	-2	4	-2	0	0	0	0	0	1	-2	1	-2	1	1	1	1	1	1	-2	-2	-2	-2	0	0	0	0	0	0	0	0	1	0	1	0	0	0	0
χ₃₀	4	4	4	4	4	-2	1	1	-2	4	1	1	1	-2	1	-2	-2	1	1	-2	-2	-4	-2	0	0	0	0	0	1	-2	1	-2	-1	-1	1	1	1	1	2	2	2	2	0	0	0	0	0	0	0	0	-1	0	-1	0	0	0	0
χ₃₁	4	4	4	-4	4	-2	1	1	-2	-4	-1	-1	1	-2	1	-2	2	-1	-1	$2 i$	$- 2 i$	0	2	0	0	0	0	0	$- i$	$2 i$	$i$	$- 2 i$	$3 i$	$- 3 i$	$- i$	$- i$	$i$	$i$	0	0	2	-2	0	0	0	0	0	0	0	0	-1	0	1	0	0	0	0
χ₃₂	4	4	4	-4	4	-2	1	1	-2	-4	-1	-1	1	-2	1	-2	2	-1	-1	$2 i$	$- 2 i$	0	2	0	0	0	0	0	$- i$	$2 i$	$i$	$- 2 i$	$- 3 i$	$3 i$	$- i$	$- i$	$i$	$i$	0	0	-2	2	0	0	0	0	0	0	0	0	1	0	-1	0	0	0	0
χ₃₃	4	4	4	-4	4	-2	1	1	-2	-4	-1	-1	1	-2	1	-2	2	-1	-1	$- 2 i$	$2 i$	0	2	0	0	0	0	0	$i$	$- 2 i$	$- i$	$2 i$	$3 i$	$- 3 i$	$i$	$i$	$- i$	$- i$	0	0	-2	2	0	0	0	0	0	0	0	0	1	0	-1	0	0	0	0
χ₃₄	4	4	4	-4	4	-2	1	1	-2	-4	-1	-1	1	-2	1	-2	2	-1	-1	$- 2 i$	$2 i$	0	2	0	0	0	0	0	$i$	$- 2 i$	$- i$	$2 i$	$- 3 i$	$3 i$	$i$	$i$	$- i$	$- i$	0	0	2	-2	0	0	0	0	0	0	0	0	-1	0	1	0	0	0	0
χ₃₅	4	4	-2	4	-2	4	4	4	4	-2	4	4	-2	-2	-2	-2	4	-2	-2	0	0	0	-2	-4	-4	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	2	2	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₆	4	4	-2	-4	-2	4	4	4	4	2	-4	-4	-2	-2	-2	-2	-4	2	2	0	0	0	2	-4	4	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	2	-2	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₇	4	-4	4	0	-4	4	4	-4	-4	0	0	0	4	4	-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	$- 2 i \sqrt{2}$	$2 i \sqrt{2}$	0	0	0	0	0	0	0	0
χ₃₈	4	-4	4	0	-4	4	4	-4	-4	0	0	0	4	4	-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	$2 i \sqrt{2}$	$- 2 i \sqrt{2}$	0	0	0	0	0	0	0	0
χ₃₉	8	8	8	-8	8	2	-4	-4	2	-8	4	4	-4	2	-4	2	-2	4	4	0	0	0	-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
χ₄₀	8	8	-4	8	-4	2	-4	-4	2	-4	-4	-4	2	-1	2	-1	2	2	2	0	0	0	-1	0	0	4	-2	-2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	-2	1	1	0	0	0	0	0	0	0	0	0	0
χ₄₁	8	8	-4	8	-4	2	-4	-4	2	-4	-4	-4	2	-1	2	-1	2	2	2	0	0	0	-1	0	0	-4	2	2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	2	-1	-1	0	0	0	0	0	0	0	0	0	0
χ₄₂	8	8	-4	8	-4	-4	2	2	-4	-4	2	2	-1	2	-1	2	-4	-1	-1	4	4	0	2	0	0	0	0	0	-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
χ₄₃	8	8	-4	8	-4	-4	2	2	-4	-4	2	2	-1	2	-1	2	-4	-1	-1	-4	-4	0	2	0	0	0	0	0	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
χ₄₄	8	8	-4	-8	-4	2	-4	-4	2	4	4	4	2	-1	2	-1	-2	-2	-2	0	0	0	1	0	0	0	$- 2 i \sqrt{3}$	$2 i \sqrt{3}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	$i \sqrt{3}$	$- i \sqrt{3}$	0	0	0	0	0	0	0	0	0	0
χ₄₅	8	8	-4	-8	-4	2	-4	-4	2	4	4	4	2	-1	2	-1	-2	-2	-2	0	0	0	1	0	0	0	$2 i \sqrt{3}$	$- 2 i \sqrt{3}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	$- i \sqrt{3}$	$i \sqrt{3}$	0	0	0	0	0	0	0	0	0	0
χ₄₆	8	8	-4	-8	-4	-4	2	2	-4	4	-2	-2	-1	2	-1	2	4	1	1	$4 i$	$- 4 i$	0	-2	0	0	0	0	0	$- 2 i$	$- 2 i$	$2 i$	$2 i$	0	0	$i$	$i$	$- i$	$- i$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₇	8	8	-4	-8	-4	-4	2	2	-4	4	-2	-2	-1	2	-1	2	4	1	1	$- 4 i$	$4 i$	0	-2	0	0	0	0	0	$2 i$	$2 i$	$- 2 i$	$- 2 i$	0	0	$- i$	$- i$	$i$	$i$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₈	8	-8	8	0	-8	2	-4	4	-2	0	0	0	-4	2	4	-2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	$- 3 i \sqrt{2}$	$3 i \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₉	8	-8	8	0	-8	2	-4	4	-2	0	0	0	-4	2	4	-2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	$3 i \sqrt{2}$	$- 3 i \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₅₀	8	-8	8	0	-8	-4	2	-2	4	0	$6 i$	$- 6 i$	2	-4	-2	4	0	$6 i$	$- 6 i$	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	0	0	0
χ₅₁	8	-8	8	0	-8	-4	2	-2	4	0	$- 6 i$	$6 i$	2	-4	-2	4	0	$- 6 i$	$6 i$	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	0	0	0
χ₅₂	8	-8	-4	0	4	8	8	-8	-8	0	0	0	-4	-4	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	0	0	0	0	0	0	0	0	0	0
χ₅₃	8	-8	-4	0	4	-4	2	-2	4	0	$6 i$	$- 6 i$	-1	2	1	-2	0	$- 3 i$	$3 i$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	−3ζ⁵−3ζ¹³	3ζ⁵+3ζ¹³	3ζ⁷+3ζ²³	−3ζ⁷−3ζ²³	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₅₄	8	-8	-4	0	4	-4	2	-2	4	0	$6 i$	$- 6 i$	-1	2	1	-2	0	$- 3 i$	$3 i$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	3ζ⁵+3ζ¹³	−3ζ⁵−3ζ¹³	−3ζ⁷−3ζ²³	3ζ⁷+3ζ²³	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₅₅	8	-8	-4	0	4	-4	2	-2	4	0	$- 6 i$	$6 i$	-1	2	1	-2	0	$3 i$	$- 3 i$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	3ζ⁷+3ζ²³	−3ζ⁷−3ζ²³	−3ζ⁵−3ζ¹³	3ζ⁵+3ζ¹³	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₅₆	8	-8	-4	0	4	-4	2	-2	4	0	$- 6 i$	$6 i$	-1	2	1	-2	0	$3 i$	$- 3 i$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	−3ζ⁷−3ζ²³	3ζ⁷+3ζ²³	3ζ⁵+3ζ¹³	−3ζ⁵−3ζ¹³	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₅₇	16	-16	-8	0	8	4	-8	8	-4	0	0	0	4	-2	-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	0	0	0	0	0	0	0

Character table — Group #13165299