Group #72228084 — 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	C₅₈
size	1	1	2	3	3	3	3	4	6	6	8	8	8	8	9	9	12	12	16	16	16	16	16	16	18	24	24	24	24	32	32	32	32	36	48	48	48	48	48	48	64	64	64	64	64	64	72	72	72	72	72	72	72	72	144	144	144	144
order	1	2	4	2	2	2	2	4	4	4	3	3	6	6	2	2	4	4	12	12	12	12	12	12	4	6	6	6	6	3	3	6	6	4	12	12	12	12	12	12	12	12	12	12	12	12	8	8	8	8	8	8	8	8	2	4	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	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	-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	-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	1
χ₅	2	2	2	2	2	2	2	2	2	2	2	-1	2	-1	2	2	2	2	2	-1	2	2	-1	-1	2	2	2	-1	-1	-1	-1	-1	-1	2	2	-1	2	2	-1	-1	-1	-1	-1	-1	-1	-1	0	0	0	0	0	0	0	0	0	0	0	0
χ₆	2	2	2	2	2	2	2	2	2	2	-1	2	-1	2	2	2	2	2	-1	2	-1	-1	2	2	2	-1	-1	2	2	-1	-1	-1	-1	2	-1	2	-1	-1	2	2	-1	-1	-1	-1	-1	-1	0	0	0	0	0	0	0	0	0	0	0	0
χ₇	2	2	2	2	2	2	2	2	2	2	-1	-1	-1	-1	2	2	2	2	-1	-1	-1	-1	-1	-1	2	-1	-1	-1	-1	2	-1	2	-1	2	-1	-1	-1	-1	-1	-1	2	-1	2	2	-1	-1	0	0	0	0	0	0	0	0	0	0	0	0
χ₈	2	2	2	2	2	2	2	2	2	2	-1	-1	-1	-1	2	2	2	2	-1	-1	-1	-1	-1	-1	2	-1	-1	-1	-1	-1	2	-1	2	2	-1	-1	-1	-1	-1	-1	-1	2	-1	-1	2	2	0	0	0	0	0	0	0	0	0	0	0	0
χ₉	2	2	2	2	2	2	2	-2	2	2	2	-1	2	-1	2	2	-2	-2	2	-1	-2	-2	1	1	2	2	2	-1	-1	-1	-1	-1	-1	-2	2	-1	-2	-2	1	1	-1	-1	1	1	1	1	0	0	0	0	0	0	0	0	0	0	0	0
χ₁₀	2	2	2	2	2	2	2	-2	2	2	-1	2	-1	2	2	2	-2	-2	-1	2	1	1	-2	-2	2	-1	-1	2	2	-1	-1	-1	-1	-2	-1	2	1	1	-2	-2	-1	-1	1	1	1	1	0	0	0	0	0	0	0	0	0	0	0	0
χ₁₁	2	2	2	2	2	2	2	-2	2	2	-1	-1	-1	-1	2	2	-2	-2	-1	-1	1	1	1	1	2	-1	-1	-1	-1	2	-1	2	-1	-2	-1	-1	1	1	1	1	2	-1	-2	-2	1	1	0	0	0	0	0	0	0	0	0	0	0	0
χ₁₂	2	2	2	2	2	2	2	-2	2	2	-1	-1	-1	-1	2	2	-2	-2	-1	-1	1	1	1	1	2	-1	-1	-1	-1	-1	2	-1	2	-2	-1	-1	1	1	1	1	-1	2	1	1	-2	-2	0	0	0	0	0	0	0	0	0	0	0	0
χ₁₃	2	2	-2	2	2	2	2	0	-2	-2	2	2	2	2	2	2	0	0	-2	-2	0	0	0	0	-2	2	2	2	2	2	2	2	2	0	-2	-2	0	0	0	0	-2	-2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₁₄	2	2	-2	2	2	2	2	0	-2	-2	2	-1	2	-1	2	2	0	0	-2	1	0	0	$- i \sqrt{3}$	$i \sqrt{3}$	-2	2	2	-1	-1	-1	-1	-1	-1	0	-2	1	0	0	$- i \sqrt{3}$	$i \sqrt{3}$	1	1	$- i \sqrt{3}$	$i \sqrt{3}$	$- i \sqrt{3}$	$i \sqrt{3}$	0	0	0	0	0	0	0	0	0	0	0	0
χ₁₅	2	2	-2	2	2	2	2	0	-2	-2	2	-1	2	-1	2	2	0	0	-2	1	0	0	$i \sqrt{3}$	$- i \sqrt{3}$	-2	2	2	-1	-1	-1	-1	-1	-1	0	-2	1	0	0	$i \sqrt{3}$	$- i \sqrt{3}$	1	1	$i \sqrt{3}$	$- i \sqrt{3}$	$i \sqrt{3}$	$- i \sqrt{3}$	0	0	0	0	0	0	0	0	0	0	0	0
χ₁₆	2	2	-2	2	2	2	2	0	-2	-2	-1	2	-1	2	2	2	0	0	1	-2	$- i \sqrt{3}$	$i \sqrt{3}$	0	0	-2	-1	-1	2	2	-1	-1	-1	-1	0	1	-2	$- i \sqrt{3}$	$i \sqrt{3}$	0	0	1	1	$- i \sqrt{3}$	$i \sqrt{3}$	$i \sqrt{3}$	$- i \sqrt{3}$	0	0	0	0	0	0	0	0	0	0	0	0
χ₁₇	2	2	-2	2	2	2	2	0	-2	-2	-1	2	-1	2	2	2	0	0	1	-2	$i \sqrt{3}$	$- i \sqrt{3}$	0	0	-2	-1	-1	2	2	-1	-1	-1	-1	0	1	-2	$i \sqrt{3}$	$- i \sqrt{3}$	0	0	1	1	$i \sqrt{3}$	$- i \sqrt{3}$	$- i \sqrt{3}$	$i \sqrt{3}$	0	0	0	0	0	0	0	0	0	0	0	0
χ₁₈	2	2	-2	2	2	2	2	0	-2	-2	-1	-1	-1	-1	2	2	0	0	1	1	$- i \sqrt{3}$	$i \sqrt{3}$	$- i \sqrt{3}$	$i \sqrt{3}$	-2	-1	-1	-1	-1	-1	2	-1	2	0	1	1	$- i \sqrt{3}$	$i \sqrt{3}$	$- i \sqrt{3}$	$i \sqrt{3}$	1	-2	$i \sqrt{3}$	$- i \sqrt{3}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₁₉	2	2	-2	2	2	2	2	0	-2	-2	-1	-1	-1	-1	2	2	0	0	1	1	$- i \sqrt{3}$	$i \sqrt{3}$	$i \sqrt{3}$	$- i \sqrt{3}$	-2	-1	-1	-1	-1	2	-1	2	-1	0	1	1	$- i \sqrt{3}$	$i \sqrt{3}$	$i \sqrt{3}$	$- i \sqrt{3}$	-2	1	0	0	$- i \sqrt{3}$	$i \sqrt{3}$	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₀	2	2	-2	2	2	2	2	0	-2	-2	-1	-1	-1	-1	2	2	0	0	1	1	$i \sqrt{3}$	$- i \sqrt{3}$	$- i \sqrt{3}$	$i \sqrt{3}$	-2	-1	-1	-1	-1	2	-1	2	-1	0	1	1	$i \sqrt{3}$	$- i \sqrt{3}$	$- i \sqrt{3}$	$i \sqrt{3}$	-2	1	0	0	$i \sqrt{3}$	$- i \sqrt{3}$	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₁	2	2	-2	2	2	2	2	0	-2	-2	-1	-1	-1	-1	2	2	0	0	1	1	$i \sqrt{3}$	$- i \sqrt{3}$	$i \sqrt{3}$	$- i \sqrt{3}$	-2	-1	-1	-1	-1	-1	2	-1	2	0	1	1	$i \sqrt{3}$	$- i \sqrt{3}$	$i \sqrt{3}$	$- i \sqrt{3}$	1	-2	$- i \sqrt{3}$	$i \sqrt{3}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₂	2	-2	0	-2	-2	2	2	0	0	0	2	2	-2	-2	-2	2	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	$- i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	0	0	0	0
χ₂₃	2	-2	0	-2	-2	2	2	0	0	0	2	2	-2	-2	-2	2	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	$i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	0	0	0	0
χ₂₄	3	3	3	3	-1	3	-1	3	3	-1	0	3	0	3	-1	-1	3	-1	0	3	0	0	3	3	-1	0	0	-1	-1	0	0	0	0	-1	0	-1	0	0	-1	-1	0	0	0	0	0	0	1	1	1	-1	1	-1	-1	-1	1	1	-1	-1
χ₂₅	3	3	3	3	-1	3	-1	3	3	-1	0	3	0	3	-1	-1	3	-1	0	3	0	0	3	3	-1	0	0	-1	-1	0	0	0	0	-1	0	-1	0	0	-1	-1	0	0	0	0	0	0	-1	-1	-1	1	-1	1	1	1	-1	-1	1	1
χ₂₆	3	3	3	3	-1	3	-1	-3	3	-1	0	3	0	3	-1	-1	-3	1	0	3	0	0	-3	-3	-1	0	0	-1	-1	0	0	0	0	1	0	-1	0	0	1	1	0	0	0	0	0	0	1	1	1	-1	1	-1	-1	-1	-1	-1	1	1
χ₂₇	3	3	3	3	-1	3	-1	-3	3	-1	0	3	0	3	-1	-1	-3	1	0	3	0	0	-3	-3	-1	0	0	-1	-1	0	0	0	0	1	0	-1	0	0	1	1	0	0	0	0	0	0	-1	-1	-1	1	-1	1	1	1	1	1	-1	-1
χ₂₈	3	3	3	-1	3	-1	3	3	-1	3	3	0	3	0	-1	-1	-1	3	3	0	3	3	0	0	-1	-1	-1	0	0	0	0	0	0	-1	-1	0	-1	-1	0	0	0	0	0	0	0	0	1	1	-1	1	-1	1	-1	-1	1	-1	1	-1
χ₂₉	3	3	3	-1	3	-1	3	3	-1	3	3	0	3	0	-1	-1	-1	3	3	0	3	3	0	0	-1	-1	-1	0	0	0	0	0	0	-1	-1	0	-1	-1	0	0	0	0	0	0	0	0	-1	-1	1	-1	1	-1	1	1	-1	1	-1	1
χ₃₀	3	3	3	-1	3	-1	3	-3	-1	3	3	0	3	0	-1	-1	1	-3	3	0	-3	-3	0	0	-1	-1	-1	0	0	0	0	0	0	1	-1	0	1	1	0	0	0	0	0	0	0	0	1	1	-1	1	-1	1	-1	-1	-1	1	-1	1
χ₃₁	3	3	3	-1	3	-1	3	-3	-1	3	3	0	3	0	-1	-1	1	-3	3	0	-3	-3	0	0	-1	-1	-1	0	0	0	0	0	0	1	-1	0	1	1	0	0	0	0	0	0	0	0	-1	-1	1	-1	1	-1	1	1	1	-1	1	-1
χ₃₂	4	-4	0	-4	-4	4	4	0	0	0	4	-2	-4	2	-4	4	0	0	0	0	0	0	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
χ₃₃	4	-4	0	-4	-4	4	4	0	0	0	-2	4	2	-4	-4	4	0	0	0	0	0	0	0	0	0	-2	2	4	-4	-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
χ₃₄	4	-4	0	-4	-4	4	4	0	0	0	-2	-2	2	2	-4	4	0	0	0	0	0	0	0	0	0	-2	2	-2	2	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
χ₃₅	4	-4	0	-4	-4	4	4	0	0	0	-2	-2	2	2	-4	4	0	0	0	0	0	0	0	0	0	-2	2	-2	2	-2	4	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
χ₃₆	6	6	6	6	-2	6	-2	6	6	-2	0	-3	0	-3	-2	-2	6	-2	0	-3	0	0	-3	-3	-2	0	0	1	1	0	0	0	0	-2	0	1	0	0	1	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₇	6	6	6	6	-2	6	-2	-6	6	-2	0	-3	0	-3	-2	-2	-6	2	0	-3	0	0	3	3	-2	0	0	1	1	0	0	0	0	2	0	1	0	0	-1	-1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₈	6	6	6	-2	6	-2	6	6	-2	6	-3	0	-3	0	-2	-2	-2	6	-3	0	-3	-3	0	0	-2	1	1	0	0	0	0	0	0	-2	1	0	1	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₉	6	6	6	-2	6	-2	6	-6	-2	6	-3	0	-3	0	-2	-2	2	-6	-3	0	3	3	0	0	-2	1	1	0	0	0	0	0	0	2	1	0	-1	-1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₀	6	6	-6	6	-2	6	-2	0	-6	2	0	6	0	6	-2	-2	0	0	0	-6	0	0	0	0	2	0	0	-2	-2	0	0	0	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
χ₄₁	6	6	-6	6	-2	6	-2	0	-6	2	0	-3	0	-3	-2	-2	0	0	0	3	0	0	$- 3 i \sqrt{3}$	$3 i \sqrt{3}$	2	0	0	1	1	0	0	0	0	0	0	-1	0	0	$i \sqrt{3}$	$- i \sqrt{3}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₂	6	6	-6	6	-2	6	-2	0	-6	2	0	-3	0	-3	-2	-2	0	0	0	3	0	0	$3 i \sqrt{3}$	$- 3 i \sqrt{3}$	2	0	0	1	1	0	0	0	0	0	0	-1	0	0	$- i \sqrt{3}$	$i \sqrt{3}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₃	6	6	-6	-2	6	-2	6	0	2	-6	6	0	6	0	-2	-2	0	0	-6	0	0	0	0	0	2	-2	-2	0	0	0	0	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
χ₄₄	6	6	-6	-2	6	-2	6	0	2	-6	-3	0	-3	0	-2	-2	0	0	3	0	$- 3 i \sqrt{3}$	$3 i \sqrt{3}$	0	0	2	1	1	0	0	0	0	0	0	0	-1	0	$i \sqrt{3}$	$- i \sqrt{3}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₅	6	6	-6	-2	6	-2	6	0	2	-6	-3	0	-3	0	-2	-2	0	0	3	0	$3 i \sqrt{3}$	$- 3 i \sqrt{3}$	0	0	2	1	1	0	0	0	0	0	0	0	-1	0	$- i \sqrt{3}$	$i \sqrt{3}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₆	6	-6	0	2	-6	-2	6	0	0	0	6	0	-6	0	2	-2	0	0	0	0	0	0	0	0	0	-2	2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	0	0	0	0
χ₄₇	6	-6	0	2	-6	-2	6	0	0	0	6	0	-6	0	2	-2	0	0	0	0	0	0	0	0	0	-2	2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	0	0	0	0
χ₄₈	6	-6	0	-6	2	6	-2	0	0	0	0	6	0	-6	2	-2	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	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
χ₄₉	6	-6	0	-6	2	6	-2	0	0	0	0	6	0	-6	2	-2	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	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
χ₅₀	9	9	9	-3	-3	-3	-3	9	-3	-3	0	0	0	0	1	1	-3	-3	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	1	1	-1	-1	-1	-1	1	1	1	-1	-1	1
χ₅₁	9	9	9	-3	-3	-3	-3	9	-3	-3	0	0	0	0	1	1	-3	-3	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	-1	-1	1	1	1	1	-1	-1	-1	1	1	-1
χ₅₂	9	9	9	-3	-3	-3	-3	-9	-3	-3	0	0	0	0	1	1	3	3	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	-1	0	0	0	0	0	0	0	0	0	0	0	0	1	1	-1	-1	-1	-1	1	1	-1	1	1	-1
χ₅₃	9	9	9	-3	-3	-3	-3	-9	-3	-3	0	0	0	0	1	1	3	3	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	-1	0	0	0	0	0	0	0	0	0	0	0	0	-1	-1	1	1	1	1	-1	-1	1	-1	-1	1
χ₅₄	12	-12	0	4	-12	-4	12	0	0	0	-6	0	6	0	4	-4	0	0	0	0	0	0	0	0	0	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
χ₅₅	12	-12	0	-12	4	12	-4	0	0	0	0	-6	0	6	4	-4	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	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₅₆	18	18	-18	-6	-6	-6	-6	0	6	6	0	0	0	0	2	2	0	0	0	0	0	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
χ₅₇	18	-18	0	6	6	-6	-6	0	0	0	0	0	0	0	-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	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	0	0	0	0
χ₅₈	18	-18	0	6	6	-6	-6	0	0	0	0	0	0	0	-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	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	0	0	0	0

Character table — Group #72228084