Finite Group Databasebeta

← Group #6857

Character table — Group #6857

Order 243.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35
size11111111199999999999999999999999999
order13333333333333333999999999999999999
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+3i32−3−3i32−3−3i32−3−3i3200000000000000ζ2+2ζ5ζ2−ζ5−2ζ2−ζ50002ζ+ζ4−ζ+ζ4−ζ−2ζ4000
χ13333−3+3i32−3+3i32−3+3i32−3−3i32−3−3i32−3−3i3200000000000000ζ2−ζ5−2ζ2−ζ5ζ2+2ζ5000−ζ+ζ4−ζ−2ζ42ζ+ζ4000
χ14333−3+3i32−3+3i32−3+3i32−3−3i32−3−3i32−3−3i3200000000000000−2ζ2−ζ5ζ2+2ζ5ζ2−ζ5000−ζ−2ζ42ζ+ζ4−ζ+ζ4000
χ15333−3−3i32−3−3i32−3−3i32−3+3i32−3+3i32−3+3i32000000000000002ζ+ζ4−ζ+ζ4−ζ−2ζ4000ζ2−ζ5−2ζ2−ζ5ζ2+2ζ5000
χ16333−3−3i32−3−3i32−3−3i32−3+3i32−3+3i32−3+3i3200000000000000−ζ+ζ4−ζ−2ζ42ζ+ζ4000−2ζ2−ζ5ζ2+2ζ5ζ2−ζ5000
χ17333−3−3i32−3−3i32−3−3i32−3+3i32−3+3i32−3+3i3200000000000000−ζ−2ζ42ζ+ζ4−ζ+ζ4000ζ2+2ζ5ζ2−ζ5−2ζ2−ζ5000
χ183−3+3i32−3−3i323−3+3i32−3−3i323−3+3i32−3−3i32000000000003+i32−3+i32−i3000000000i33−i32−3−i32
χ193−3+3i32−3−3i323−3+3i32−3−3i323−3+3i32−3−3i3200000000000−3+i32−i33+i320000000003−i32−3−i32i3
χ203−3+3i32−3−3i323−3+3i32−3−3i323−3+3i32−3−3i3200000000000−i33+i32−3+i32000000000−3−i32i33−i32
χ213−3+3i32−3−3i32−3+3i32−3−3i323−3−3i323−3+3i3200i33−i32−3−i323+i32−3+i32−i3000000000000000000
χ223−3+3i32−3−3i32−3+3i32−3−3i323−3−3i323−3+3i32003−i32−3−i32i3−3+i32−i33+i32000000000000000000
χ233−3+3i32−3−3i32−3+3i32−3−3i323−3−3i323−3+3i3200−3−i32i33−i32−i33+i32−3+i32000000000000000000
χ243−3+3i32−3−3i32−3−3i323−3+3i32−3+3i32−3−3i32300000000i33−i32−3−i320000003+i32−3+i32−i3000000
χ253−3+3i32−3−3i32−3−3i323−3+3i32−3+3i32−3−3i323000000003−i32−3−i32i3000000−3+i32−i33+i32000000
χ263−3+3i32−3−3i32−3−3i323−3+3i32−3+3i32−3−3i32300000000−3−i32i33−i32000000−i33+i32−3+i32000000
χ273−3−3i32−3+3i323−3−3i32−3+3i323−3−3i32−3+3i3200000000000i33−i32−3−i32000000000−3+i32−i33+i32
χ283−3−3i32−3+3i323−3−3i32−3+3i323−3−3i32−3+3i32000000000003−i32−3−i32i3000000000−i33+i32−3+i32
χ293−3−3i32−3+3i323−3−3i32−3+3i323−3−3i32−3+3i3200000000000−3−i32i33−i320000000003+i32−3+i32−i3
χ303−3−3i32−3+3i32−3+3i323−3−3i32−3−3i32−3+3i323000000003+i32−3+i32−i3000000−3−i32i33−i32000000
χ313−3−3i32−3+3i32−3+3i323−3−3i32−3−3i32−3+3i32300000000−3+i32−i33+i32000000i33−i32−3−i32000000
χ323−3−3i32−3+3i32−3+3i323−3−3i32−3−3i32−3+3i32300000000−i33+i32−3+i320000003−i32−3−i32i3000000
χ333−3−3i32−3+3i32−3−3i32−3+3i323−3+3i323−3−3i32003+i32−3+i32−i3−3−i32i33−i32000000000000000000
χ343−3−3i32−3+3i32−3−3i32−3+3i323−3+3i323−3−3i3200−3+i32−i33+i32i33−i32−3−i32000000000000000000
χ353−3−3i32−3+3i32−3−3i32−3+3i323−3+3i323−3−3i3200−i33+i32−3+i323−i32−3−i32i3000000000000000000

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