Group #6741 — 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
size	1	1	6	6	6	8	8	12	1	1	6	6	6	8	8	12	1	1	6	6	6	8	8	12	1	1	6	6	6	8	8	12	1	1	6	6	6	8	8	12
order	1	2	4	8	8	3	6	4	5	10	20	40	40	15	30	20	5	10	20	40	40	15	30	20	5	10	20	40	40	15	30	20	5	10	20	40	40	15	30	20
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
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
χ₃	2	2	2	0	0	-1	-1	0	2	2	2	0	0	-1	-1	0	2	2	2	0	0	-1	-1	0	2	2	2	0	0	-1	-1	0	2	2	2	0	0	-1	-1	0
χ₄	2	-2	0	$\sqrt{2}$	$- \sqrt{2}$	-1	1	0	2	-2	0	$\sqrt{2}$	$- \sqrt{2}$	-1	1	0	2	-2	0	$\sqrt{2}$	$- \sqrt{2}$	-1	1	0	2	-2	0	$\sqrt{2}$	$- \sqrt{2}$	-1	1	0	2	-2	0	$\sqrt{2}$	$- \sqrt{2}$	-1	1	0
χ₅	2	-2	0	$- \sqrt{2}$	$\sqrt{2}$	-1	1	0	2	-2	0	$- \sqrt{2}$	$\sqrt{2}$	-1	1	0	2	-2	0	$- \sqrt{2}$	$\sqrt{2}$	-1	1	0	2	-2	0	$- \sqrt{2}$	$\sqrt{2}$	-1	1	0	2	-2	0	$- \sqrt{2}$	$\sqrt{2}$	-1	1	0
χ₆	3	3	-1	1	1	0	0	-1	3	3	-1	1	1	0	0	-1	3	3	-1	1	1	0	0	-1	3	3	-1	1	1	0	0	-1	3	3	-1	1	1	0	0	-1
χ₇	3	3	-1	-1	-1	0	0	1	3	3	-1	-1	-1	0	0	1	3	3	-1	-1	-1	0	0	1	3	3	-1	-1	-1	0	0	1	3	3	-1	-1	-1	0	0	1
χ₈	4	-4	0	0	0	1	-1	0	4	-4	0	0	0	1	-1	0	4	-4	0	0	0	1	-1	0	4	-4	0	0	0	1	-1	0	4	-4	0	0	0	1	-1	0
χ₉	1	1	1	1	1	1	1	1	−ζ²⁸	−ζ²⁸	−ζ²⁸	−ζ²⁸	−ζ²⁸	−ζ²⁸	−ζ²⁸	−ζ²⁸	−ζ³⁶	−ζ³⁶	−ζ³⁶	−ζ³⁶	−ζ³⁶	−ζ³⁶	−ζ³⁶	−ζ³⁶	−ζ⁴	−ζ⁴	−ζ⁴	−ζ⁴	−ζ⁴	−ζ⁴	−ζ⁴	−ζ⁴	−ζ¹²	−ζ¹²	−ζ¹²	−ζ¹²	−ζ¹²	−ζ¹²	−ζ¹²	−ζ¹²
χ₁₀	1	1	1	-1	-1	1	1	-1	−ζ²⁸	−ζ²⁸	−ζ²⁸	ζ²⁸	ζ²⁸	−ζ²⁸	−ζ²⁸	ζ²⁸	−ζ³⁶	−ζ³⁶	−ζ³⁶	ζ³⁶	ζ³⁶	−ζ³⁶	−ζ³⁶	ζ³⁶	−ζ⁴	−ζ⁴	−ζ⁴	ζ⁴	ζ⁴	−ζ⁴	−ζ⁴	ζ⁴	−ζ¹²	−ζ¹²	−ζ¹²	ζ¹²	ζ¹²	−ζ¹²	−ζ¹²	ζ¹²
χ₁₁	2	2	2	0	0	-1	-1	0	−2ζ²⁸	−2ζ²⁸	−2ζ²⁸	0	0	ζ²⁸	ζ²⁸	0	−2ζ³⁶	−2ζ³⁶	−2ζ³⁶	0	0	ζ³⁶	ζ³⁶	0	−2ζ⁴	−2ζ⁴	−2ζ⁴	0	0	ζ⁴	ζ⁴	0	−2ζ¹²	−2ζ¹²	−2ζ¹²	0	0	ζ¹²	ζ¹²	0
χ₁₂	2	-2	0	$\sqrt{2}$	$- \sqrt{2}$	-1	1	0	−2ζ²⁸	2ζ²⁸	0	ζ¹³−ζ²³	−ζ¹³+ζ²³	ζ²⁸	−ζ²⁸	0	−2ζ³⁶	2ζ³⁶	0	ζ²¹−ζ³¹	−ζ²¹+ζ³¹	ζ³⁶	−ζ³⁶	0	−2ζ⁴	2ζ⁴	0	ζ²⁹−ζ³⁹	−ζ²⁹+ζ³⁹	ζ⁴	−ζ⁴	0	−2ζ¹²	2ζ¹²	0	−ζ⁷+ζ³⁷	ζ⁷−ζ³⁷	ζ¹²	−ζ¹²	0
χ₁₃	2	-2	0	$- \sqrt{2}$	$\sqrt{2}$	-1	1	0	−2ζ²⁸	2ζ²⁸	0	−ζ¹³+ζ²³	ζ¹³−ζ²³	ζ²⁸	−ζ²⁸	0	−2ζ³⁶	2ζ³⁶	0	−ζ²¹+ζ³¹	ζ²¹−ζ³¹	ζ³⁶	−ζ³⁶	0	−2ζ⁴	2ζ⁴	0	−ζ²⁹+ζ³⁹	ζ²⁹−ζ³⁹	ζ⁴	−ζ⁴	0	−2ζ¹²	2ζ¹²	0	ζ⁷−ζ³⁷	−ζ⁷+ζ³⁷	ζ¹²	−ζ¹²	0
χ₁₄	3	3	-1	1	1	0	0	-1	−3ζ²⁸	−3ζ²⁸	ζ²⁸	−ζ²⁸	−ζ²⁸	0	0	ζ²⁸	−3ζ³⁶	−3ζ³⁶	ζ³⁶	−ζ³⁶	−ζ³⁶	0	0	ζ³⁶	−3ζ⁴	−3ζ⁴	ζ⁴	−ζ⁴	−ζ⁴	0	0	ζ⁴	−3ζ¹²	−3ζ¹²	ζ¹²	−ζ¹²	−ζ¹²	0	0	ζ¹²
χ₁₅	3	3	-1	-1	-1	0	0	1	−3ζ²⁸	−3ζ²⁸	ζ²⁸	ζ²⁸	ζ²⁸	0	0	−ζ²⁸	−3ζ³⁶	−3ζ³⁶	ζ³⁶	ζ³⁶	ζ³⁶	0	0	−ζ³⁶	−3ζ⁴	−3ζ⁴	ζ⁴	ζ⁴	ζ⁴	0	0	−ζ⁴	−3ζ¹²	−3ζ¹²	ζ¹²	ζ¹²	ζ¹²	0	0	−ζ¹²
χ₁₆	4	-4	0	0	0	1	-1	0	−4ζ²⁸	4ζ²⁸	0	0	0	−ζ²⁸	ζ²⁸	0	−4ζ³⁶	4ζ³⁶	0	0	0	−ζ³⁶	ζ³⁶	0	−4ζ⁴	4ζ⁴	0	0	0	−ζ⁴	ζ⁴	0	−4ζ¹²	4ζ¹²	0	0	0	−ζ¹²	ζ¹²	0
χ₁₇	1	1	1	1	1	1	1	1	−ζ³⁶	−ζ³⁶	−ζ³⁶	−ζ³⁶	−ζ³⁶	−ζ³⁶	−ζ³⁶	−ζ³⁶	−ζ¹²	−ζ¹²	−ζ¹²	−ζ¹²	−ζ¹²	−ζ¹²	−ζ¹²	−ζ¹²	−ζ²⁸	−ζ²⁸	−ζ²⁸	−ζ²⁸	−ζ²⁸	−ζ²⁸	−ζ²⁸	−ζ²⁸	−ζ⁴	−ζ⁴	−ζ⁴	−ζ⁴	−ζ⁴	−ζ⁴	−ζ⁴	−ζ⁴
χ₁₈	1	1	1	-1	-1	1	1	-1	−ζ³⁶	−ζ³⁶	−ζ³⁶	ζ³⁶	ζ³⁶	−ζ³⁶	−ζ³⁶	ζ³⁶	−ζ¹²	−ζ¹²	−ζ¹²	ζ¹²	ζ¹²	−ζ¹²	−ζ¹²	ζ¹²	−ζ²⁸	−ζ²⁸	−ζ²⁸	ζ²⁸	ζ²⁸	−ζ²⁸	−ζ²⁸	ζ²⁸	−ζ⁴	−ζ⁴	−ζ⁴	ζ⁴	ζ⁴	−ζ⁴	−ζ⁴	ζ⁴
χ₁₉	2	2	2	0	0	-1	-1	0	−2ζ³⁶	−2ζ³⁶	−2ζ³⁶	0	0	ζ³⁶	ζ³⁶	0	−2ζ¹²	−2ζ¹²	−2ζ¹²	0	0	ζ¹²	ζ¹²	0	−2ζ²⁸	−2ζ²⁸	−2ζ²⁸	0	0	ζ²⁸	ζ²⁸	0	−2ζ⁴	−2ζ⁴	−2ζ⁴	0	0	ζ⁴	ζ⁴	0
χ₂₀	2	-2	0	$\sqrt{2}$	$- \sqrt{2}$	-1	1	0	−2ζ³⁶	2ζ³⁶	0	ζ²¹−ζ³¹	−ζ²¹+ζ³¹	ζ³⁶	−ζ³⁶	0	−2ζ¹²	2ζ¹²	0	−ζ⁷+ζ³⁷	ζ⁷−ζ³⁷	ζ¹²	−ζ¹²	0	−2ζ²⁸	2ζ²⁸	0	ζ¹³−ζ²³	−ζ¹³+ζ²³	ζ²⁸	−ζ²⁸	0	−2ζ⁴	2ζ⁴	0	ζ²⁹−ζ³⁹	−ζ²⁹+ζ³⁹	ζ⁴	−ζ⁴	0
χ₂₁	2	-2	0	$- \sqrt{2}$	$\sqrt{2}$	-1	1	0	−2ζ³⁶	2ζ³⁶	0	−ζ²¹+ζ³¹	ζ²¹−ζ³¹	ζ³⁶	−ζ³⁶	0	−2ζ¹²	2ζ¹²	0	ζ⁷−ζ³⁷	−ζ⁷+ζ³⁷	ζ¹²	−ζ¹²	0	−2ζ²⁸	2ζ²⁸	0	−ζ¹³+ζ²³	ζ¹³−ζ²³	ζ²⁸	−ζ²⁸	0	−2ζ⁴	2ζ⁴	0	−ζ²⁹+ζ³⁹	ζ²⁹−ζ³⁹	ζ⁴	−ζ⁴	0
χ₂₂	3	3	-1	1	1	0	0	-1	−3ζ³⁶	−3ζ³⁶	ζ³⁶	−ζ³⁶	−ζ³⁶	0	0	ζ³⁶	−3ζ¹²	−3ζ¹²	ζ¹²	−ζ¹²	−ζ¹²	0	0	ζ¹²	−3ζ²⁸	−3ζ²⁸	ζ²⁸	−ζ²⁸	−ζ²⁸	0	0	ζ²⁸	−3ζ⁴	−3ζ⁴	ζ⁴	−ζ⁴	−ζ⁴	0	0	ζ⁴
χ₂₃	3	3	-1	-1	-1	0	0	1	−3ζ³⁶	−3ζ³⁶	ζ³⁶	ζ³⁶	ζ³⁶	0	0	−ζ³⁶	−3ζ¹²	−3ζ¹²	ζ¹²	ζ¹²	ζ¹²	0	0	−ζ¹²	−3ζ²⁸	−3ζ²⁸	ζ²⁸	ζ²⁸	ζ²⁸	0	0	−ζ²⁸	−3ζ⁴	−3ζ⁴	ζ⁴	ζ⁴	ζ⁴	0	0	−ζ⁴
χ₂₄	4	-4	0	0	0	1	-1	0	−4ζ³⁶	4ζ³⁶	0	0	0	−ζ³⁶	ζ³⁶	0	−4ζ¹²	4ζ¹²	0	0	0	−ζ¹²	ζ¹²	0	−4ζ²⁸	4ζ²⁸	0	0	0	−ζ²⁸	ζ²⁸	0	−4ζ⁴	4ζ⁴	0	0	0	−ζ⁴	ζ⁴	0
χ₂₅	1	1	1	1	1	1	1	1	−ζ⁴	−ζ⁴	−ζ⁴	−ζ⁴	−ζ⁴	−ζ⁴	−ζ⁴	−ζ⁴	−ζ²⁸	−ζ²⁸	−ζ²⁸	−ζ²⁸	−ζ²⁸	−ζ²⁸	−ζ²⁸	−ζ²⁸	−ζ¹²	−ζ¹²	−ζ¹²	−ζ¹²	−ζ¹²	−ζ¹²	−ζ¹²	−ζ¹²	−ζ³⁶	−ζ³⁶	−ζ³⁶	−ζ³⁶	−ζ³⁶	−ζ³⁶	−ζ³⁶	−ζ³⁶
χ₂₆	1	1	1	-1	-1	1	1	-1	−ζ⁴	−ζ⁴	−ζ⁴	ζ⁴	ζ⁴	−ζ⁴	−ζ⁴	ζ⁴	−ζ²⁸	−ζ²⁸	−ζ²⁸	ζ²⁸	ζ²⁸	−ζ²⁸	−ζ²⁸	ζ²⁸	−ζ¹²	−ζ¹²	−ζ¹²	ζ¹²	ζ¹²	−ζ¹²	−ζ¹²	ζ¹²	−ζ³⁶	−ζ³⁶	−ζ³⁶	ζ³⁶	ζ³⁶	−ζ³⁶	−ζ³⁶	ζ³⁶
χ₂₇	2	2	2	0	0	-1	-1	0	−2ζ⁴	−2ζ⁴	−2ζ⁴	0	0	ζ⁴	ζ⁴	0	−2ζ²⁸	−2ζ²⁸	−2ζ²⁸	0	0	ζ²⁸	ζ²⁸	0	−2ζ¹²	−2ζ¹²	−2ζ¹²	0	0	ζ¹²	ζ¹²	0	−2ζ³⁶	−2ζ³⁶	−2ζ³⁶	0	0	ζ³⁶	ζ³⁶	0
χ₂₈	2	-2	0	$\sqrt{2}$	$- \sqrt{2}$	-1	1	0	−2ζ⁴	2ζ⁴	0	ζ²⁹−ζ³⁹	−ζ²⁹+ζ³⁹	ζ⁴	−ζ⁴	0	−2ζ²⁸	2ζ²⁸	0	ζ¹³−ζ²³	−ζ¹³+ζ²³	ζ²⁸	−ζ²⁸	0	−2ζ¹²	2ζ¹²	0	−ζ⁷+ζ³⁷	ζ⁷−ζ³⁷	ζ¹²	−ζ¹²	0	−2ζ³⁶	2ζ³⁶	0	ζ²¹−ζ³¹	−ζ²¹+ζ³¹	ζ³⁶	−ζ³⁶	0
χ₂₉	2	-2	0	$- \sqrt{2}$	$\sqrt{2}$	-1	1	0	−2ζ⁴	2ζ⁴	0	−ζ²⁹+ζ³⁹	ζ²⁹−ζ³⁹	ζ⁴	−ζ⁴	0	−2ζ²⁸	2ζ²⁸	0	−ζ¹³+ζ²³	ζ¹³−ζ²³	ζ²⁸	−ζ²⁸	0	−2ζ¹²	2ζ¹²	0	ζ⁷−ζ³⁷	−ζ⁷+ζ³⁷	ζ¹²	−ζ¹²	0	−2ζ³⁶	2ζ³⁶	0	−ζ²¹+ζ³¹	ζ²¹−ζ³¹	ζ³⁶	−ζ³⁶	0
χ₃₀	3	3	-1	1	1	0	0	-1	−3ζ⁴	−3ζ⁴	ζ⁴	−ζ⁴	−ζ⁴	0	0	ζ⁴	−3ζ²⁸	−3ζ²⁸	ζ²⁸	−ζ²⁸	−ζ²⁸	0	0	ζ²⁸	−3ζ¹²	−3ζ¹²	ζ¹²	−ζ¹²	−ζ¹²	0	0	ζ¹²	−3ζ³⁶	−3ζ³⁶	ζ³⁶	−ζ³⁶	−ζ³⁶	0	0	ζ³⁶
χ₃₁	3	3	-1	-1	-1	0	0	1	−3ζ⁴	−3ζ⁴	ζ⁴	ζ⁴	ζ⁴	0	0	−ζ⁴	−3ζ²⁸	−3ζ²⁸	ζ²⁸	ζ²⁸	ζ²⁸	0	0	−ζ²⁸	−3ζ¹²	−3ζ¹²	ζ¹²	ζ¹²	ζ¹²	0	0	−ζ¹²	−3ζ³⁶	−3ζ³⁶	ζ³⁶	ζ³⁶	ζ³⁶	0	0	−ζ³⁶
χ₃₂	4	-4	0	0	0	1	-1	0	−4ζ⁴	4ζ⁴	0	0	0	−ζ⁴	ζ⁴	0	−4ζ²⁸	4ζ²⁸	0	0	0	−ζ²⁸	ζ²⁸	0	−4ζ¹²	4ζ¹²	0	0	0	−ζ¹²	ζ¹²	0	−4ζ³⁶	4ζ³⁶	0	0	0	−ζ³⁶	ζ³⁶	0
χ₃₃	1	1	1	1	1	1	1	1	−ζ¹²	−ζ¹²	−ζ¹²	−ζ¹²	−ζ¹²	−ζ¹²	−ζ¹²	−ζ¹²	−ζ⁴	−ζ⁴	−ζ⁴	−ζ⁴	−ζ⁴	−ζ⁴	−ζ⁴	−ζ⁴	−ζ³⁶	−ζ³⁶	−ζ³⁶	−ζ³⁶	−ζ³⁶	−ζ³⁶	−ζ³⁶	−ζ³⁶	−ζ²⁸	−ζ²⁸	−ζ²⁸	−ζ²⁸	−ζ²⁸	−ζ²⁸	−ζ²⁸	−ζ²⁸
χ₃₄	1	1	1	-1	-1	1	1	-1	−ζ¹²	−ζ¹²	−ζ¹²	ζ¹²	ζ¹²	−ζ¹²	−ζ¹²	ζ¹²	−ζ⁴	−ζ⁴	−ζ⁴	ζ⁴	ζ⁴	−ζ⁴	−ζ⁴	ζ⁴	−ζ³⁶	−ζ³⁶	−ζ³⁶	ζ³⁶	ζ³⁶	−ζ³⁶	−ζ³⁶	ζ³⁶	−ζ²⁸	−ζ²⁸	−ζ²⁸	ζ²⁸	ζ²⁸	−ζ²⁸	−ζ²⁸	ζ²⁸
χ₃₅	2	2	2	0	0	-1	-1	0	−2ζ¹²	−2ζ¹²	−2ζ¹²	0	0	ζ¹²	ζ¹²	0	−2ζ⁴	−2ζ⁴	−2ζ⁴	0	0	ζ⁴	ζ⁴	0	−2ζ³⁶	−2ζ³⁶	−2ζ³⁶	0	0	ζ³⁶	ζ³⁶	0	−2ζ²⁸	−2ζ²⁸	−2ζ²⁸	0	0	ζ²⁸	ζ²⁸	0
χ₃₆	2	-2	0	$\sqrt{2}$	$- \sqrt{2}$	-1	1	0	−2ζ¹²	2ζ¹²	0	−ζ⁷+ζ³⁷	ζ⁷−ζ³⁷	ζ¹²	−ζ¹²	0	−2ζ⁴	2ζ⁴	0	ζ²⁹−ζ³⁹	−ζ²⁹+ζ³⁹	ζ⁴	−ζ⁴	0	−2ζ³⁶	2ζ³⁶	0	ζ²¹−ζ³¹	−ζ²¹+ζ³¹	ζ³⁶	−ζ³⁶	0	−2ζ²⁸	2ζ²⁸	0	ζ¹³−ζ²³	−ζ¹³+ζ²³	ζ²⁸	−ζ²⁸	0
χ₃₇	2	-2	0	$- \sqrt{2}$	$\sqrt{2}$	-1	1	0	−2ζ¹²	2ζ¹²	0	ζ⁷−ζ³⁷	−ζ⁷+ζ³⁷	ζ¹²	−ζ¹²	0	−2ζ⁴	2ζ⁴	0	−ζ²⁹+ζ³⁹	ζ²⁹−ζ³⁹	ζ⁴	−ζ⁴	0	−2ζ³⁶	2ζ³⁶	0	−ζ²¹+ζ³¹	ζ²¹−ζ³¹	ζ³⁶	−ζ³⁶	0	−2ζ²⁸	2ζ²⁸	0	−ζ¹³+ζ²³	ζ¹³−ζ²³	ζ²⁸	−ζ²⁸	0
χ₃₈	3	3	-1	1	1	0	0	-1	−3ζ¹²	−3ζ¹²	ζ¹²	−ζ¹²	−ζ¹²	0	0	ζ¹²	−3ζ⁴	−3ζ⁴	ζ⁴	−ζ⁴	−ζ⁴	0	0	ζ⁴	−3ζ³⁶	−3ζ³⁶	ζ³⁶	−ζ³⁶	−ζ³⁶	0	0	ζ³⁶	−3ζ²⁸	−3ζ²⁸	ζ²⁸	−ζ²⁸	−ζ²⁸	0	0	ζ²⁸
χ₃₉	3	3	-1	-1	-1	0	0	1	−3ζ¹²	−3ζ¹²	ζ¹²	ζ¹²	ζ¹²	0	0	−ζ¹²	−3ζ⁴	−3ζ⁴	ζ⁴	ζ⁴	ζ⁴	0	0	−ζ⁴	−3ζ³⁶	−3ζ³⁶	ζ³⁶	ζ³⁶	ζ³⁶	0	0	−ζ³⁶	−3ζ²⁸	−3ζ²⁸	ζ²⁸	ζ²⁸	ζ²⁸	0	0	−ζ²⁸
χ₄₀	4	-4	0	0	0	1	-1	0	−4ζ¹²	4ζ¹²	0	0	0	−ζ¹²	ζ¹²	0	−4ζ⁴	4ζ⁴	0	0	0	−ζ⁴	ζ⁴	0	−4ζ³⁶	4ζ³⁶	0	0	0	−ζ³⁶	ζ³⁶	0	−4ζ²⁸	4ζ²⁸	0	0	0	−ζ²⁸	ζ²⁸	0

Character table — Group #6741