Finite Group Databasebeta

← Group #6860

Character table — Group #6860

Order 243.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35
size11111111199999999999999999999999999
order13333333333999999999999999999999999
χ111111111111111111111111111111111111
χ211111111111111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32
χ311111111111111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32
χ411111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32
χ511111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111−1−i32−1−i32−1−i32111−1+i32−1+i32−1+i32
χ611111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111
χ711111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32
χ811111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111
χ911111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111−1+i32−1+i32−1+i32111−1−i32−1−i32−1−i32
χ10333333333−3+3i32−3−3i32000000000000000000000000
χ11333333333−3−3i32−3+3i32000000000000000000000000
χ12333−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32−3−3i3200000000000000ζ+2ζ4ζ−ζ4−2ζ−ζ40002ζ2+ζ5−ζ2+ζ5−ζ2−2ζ5000
χ13333−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32−3−3i3200000000000000ζ−ζ4−2ζ−ζ4ζ+2ζ4000−ζ2+ζ5−ζ2−2ζ52ζ2+ζ5000
χ14333−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32−3−3i3200000000000000−2ζ−ζ4ζ+2ζ4ζ−ζ4000−ζ2−2ζ52ζ2+ζ5−ζ2+ζ5000
χ15333−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i32000000000000002ζ2+ζ5−ζ2+ζ5−ζ2−2ζ5000ζ−ζ4−2ζ−ζ4ζ+2ζ4000
χ16333−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i3200000000000000−ζ2+ζ5−ζ2−2ζ52ζ2+ζ5000−2ζ−ζ4ζ+2ζ4ζ−ζ4000
χ17333−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i3200000000000000−ζ2−2ζ52ζ2+ζ5−ζ2+ζ5000ζ+2ζ4ζ−ζ4−2ζ−ζ4000
χ183−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i3200000000000ζ+2ζ4ζ−ζ4−2ζ−ζ40000000002ζ2+ζ5−ζ2+ζ5−ζ2−2ζ5
χ193−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i3200000000000ζ−ζ4−2ζ−ζ4ζ+2ζ4000000000−ζ2+ζ5−ζ2−2ζ52ζ2+ζ5
χ203−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i3200000000000−2ζ−ζ4ζ+2ζ4ζ−ζ4000000000−ζ2−2ζ52ζ2+ζ5−ζ2+ζ5
χ213−3+3i32−3−3i32−3+3i32−3−3i32−3−3i3233−3+3i32000000003+i32−3+i32−i3000000i33−i32−3−i32000000
χ223−3+3i32−3−3i32−3+3i32−3−3i32−3−3i3233−3+3i3200000000−3+i32−i33+i320000003−i32−3−i32i3000000
χ233−3+3i32−3−3i32−3+3i32−3−3i32−3−3i3233−3+3i3200000000−i33+i32−3+i32000000−3−i32i33−i32000000
χ243−3+3i32−3−3i32−3−3i32−3+3i323−3+3i32−3−3i323003+i32−3+i32−i3i33−i32−3−i32000000000000000000
χ253−3+3i32−3−3i32−3−3i32−3+3i323−3+3i32−3−3i32300−3+i32−i33+i323−i32−3−i32i3000000000000000000
χ263−3+3i32−3−3i32−3−3i32−3+3i323−3+3i32−3−3i32300−i33+i32−3+i32−3−i32i33−i32000000000000000000
χ273−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32000000000002ζ2+ζ5−ζ2+ζ5−ζ2−2ζ5000000000ζ−ζ4−2ζ−ζ4ζ+2ζ4
χ283−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i3200000000000−ζ2+ζ5−ζ2−2ζ52ζ2+ζ5000000000−2ζ−ζ4ζ+2ζ4ζ−ζ4
χ293−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i3200000000000−ζ2−2ζ52ζ2+ζ5−ζ2+ζ5000000000ζ+2ζ4ζ−ζ4−2ζ−ζ4
χ303−3−3i32−3+3i32−3+3i32−3−3i323−3−3i32−3+3i32300i33−i32−3−i32−3+i32−i33+i32000000000000000000
χ313−3−3i32−3+3i32−3+3i32−3−3i323−3−3i32−3+3i323003−i32−3−i32i3−i33+i32−3+i32000000000000000000
χ323−3−3i32−3+3i32−3+3i32−3−3i323−3−3i32−3+3i32300−3−i32i33−i323+i32−3+i32−i3000000000000000000
χ333−3−3i32−3+3i32−3−3i32−3+3i32−3+3i3233−3−3i3200000000i33−i32−3−i32000000−3+i32−i33+i32000000
χ343−3−3i32−3+3i32−3−3i32−3+3i32−3+3i3233−3−3i32000000003−i32−3−i32i3000000−i33+i32−3+i32000000
χ353−3−3i32−3+3i32−3−3i32−3+3i32−3+3i3233−3−3i3200000000−3−i32i33−i320000003+i32−3+i32−i3000000

Here ζ is a primitive root of unity of order 9 (ζ9 = 1); i = ζ2.