Finite Group Databasebeta

← Group #13164652

Character table — Group #13164652

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size1122666666699121212121212121212121212121212121212121248484848545454545496969696144144144144
order1236222449182266612121818181818181818183636363636363366222449918186666
χ111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111−1+i32−1−i32−1+i32−1−i3211111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32
χ3111111111111111111111111111111111−1−i32−1+i32−1−i32−1+i3211111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32
χ411111111111-1-1111111111111111111111111-1-1-1-1-11111-1-1-1-1
χ511111111111-1-111111111111111111111−1+i32−1−i32−1+i32−1−i32-1-1-1-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32
χ611111111111-1-111111111111111111111−1−i32−1+i32−1−i32−1+i32-1-1-1-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32
χ7222222222-1-10022222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222200000-1-1-1-10000
χ8222222222-1-10022222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−1+i3−1−i3−1+i3−1−i3000001−i321+i321−i321+i320000
χ9222222222-1-10022222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−1−i3−1+i3−1−i3−1+i3000001+i321−i321+i321−i320000
χ1033333-1-1-1-133333-1-1-1-1333-1-1-1-1-1-1-1-1-1-1-1-100003-1-1-1-100000000
χ1133333-1-1-1-133-3-33-1-1-1-1333-1-1-1-1-1-1-1-1-1-1-1-10000-3111100000000
χ123333-13-1-1-13333-13-1-1-1-1-1-1333-1-1-1-1-1-1-1-1-10000-13-1-1-100000000
χ133333-13-1-1-133-3-3-13-1-1-1-1-1-1333-1-1-1-1-1-1-1-1-100001-311100000000
χ143333-1-13-1-13333-1-13-1-1-1-1-1-1-1-1333-1-1-1-1-1-10000-1-13-1-100000000
χ153333-1-13-1-133-3-3-1-13-1-1-1-1-1-1-1-1333-1-1-1-1-1-1000011-31100000000
χ163333-1-1-13-13333-1-1-13-1-1-1-1-1-1-1-1-1-1333-1-1-10000-1-1-13-100000000
χ173333-1-1-13-133-3-3-1-1-13-1-1-1-1-1-1-1-1-1-1333-1-1-10000111-3100000000
χ183333-1-1-1-133333-1-1-1-13-1-1-1-1-1-1-1-1-1-1-1-13330000-1-1-1-1300000000
χ193333-1-1-1-1333-3-3-1-1-1-13-1-1-1-1-1-1-1-1-1-1-1-133300001111-300000000
χ204-44-4000004-44-40000000000000000000011-1-10000011-1-11-11-1
χ214-44-4000004-44-400000000000000000000−1+i32−1−i321−i321+i3200000−1+i32−1−i321−i321+i32−1+i321−i32−1−i321+i32
χ224-44-4000004-44-400000000000000000000−1−i32−1+i321+i321−i3200000−1−i32−1+i321+i321−i32−1−i321+i32−1+i321−i32
χ234-44-4000004-4-440000000000000000000011-1-10000011-1-1-11-11
χ244-44-4000004-4-4400000000000000000000−1+i32−1−i321−i321+i3200000−1+i32−1−i321−i321+i321−i32−1+i321+i32−1−i32
χ254-44-4000004-4-4400000000000000000000−1−i32−1+i321+i321−i3200000−1−i32−1+i321+i321−i321+i32−1−i321−i32−1+i32
χ2666666-2-2-2-2-3-3006-2-2-2-2-3-3-311111111111100000000000000000
χ276666-26-2-2-2-3-300-26-2-2-2111-3-3-311111111100000000000000000
χ286666-2-26-2-2-3-300-2-26-2-2111111-3-3-311111100000000000000000
χ296666-2-2-26-2-3-300-2-2-26-2111111111-3-3-311100000000000000000
χ306666-2-2-2-26-3-300-2-2-2-26111111111111-3-3-300000000000000000
χ3166-3-3666660000-3-3-3-3-300000000000000000000000000000000
χ3266-3-36-2-2-2-20000-311110002ζ+2ζ82ζ2+2ζ72ζ4+2ζ52ζ+2ζ82ζ2+2ζ72ζ4+2ζ52ζ+2ζ82ζ2+2ζ72ζ4+2ζ52ζ+2ζ82ζ2+2ζ72ζ4+2ζ500000000000000000
χ3366-3-36-2-2-2-20000-311110002ζ2+2ζ72ζ4+2ζ52ζ+2ζ82ζ2+2ζ72ζ4+2ζ52ζ+2ζ82ζ2+2ζ72ζ4+2ζ52ζ+2ζ82ζ2+2ζ72ζ4+2ζ52ζ+2ζ800000000000000000
χ3466-3-36-2-2-2-20000-311110002ζ4+2ζ52ζ+2ζ82ζ2+2ζ72ζ4+2ζ52ζ+2ζ82ζ2+2ζ72ζ4+2ζ52ζ+2ζ82ζ2+2ζ72ζ4+2ζ52ζ+2ζ82ζ2+2ζ700000000000000000
χ3566-3-3-26-2-2-200001-31112ζ+2ζ82ζ2+2ζ72ζ4+2ζ50002ζ+2ζ82ζ2+2ζ72ζ4+2ζ52ζ2+2ζ72ζ4+2ζ52ζ+2ζ82ζ4+2ζ52ζ+2ζ82ζ2+2ζ700000000000000000
χ3666-3-3-26-2-2-200001-31112ζ2+2ζ72ζ4+2ζ52ζ+2ζ80002ζ2+2ζ72ζ4+2ζ52ζ+2ζ82ζ4+2ζ52ζ+2ζ82ζ2+2ζ72ζ+2ζ82ζ2+2ζ72ζ4+2ζ500000000000000000
χ3766-3-3-26-2-2-200001-31112ζ4+2ζ52ζ+2ζ82ζ2+2ζ70002ζ4+2ζ52ζ+2ζ82ζ2+2ζ72ζ+2ζ82ζ2+2ζ72ζ4+2ζ52ζ2+2ζ72ζ4+2ζ52ζ+2ζ800000000000000000
χ3866-3-3-2-26-2-2000011-3112ζ+2ζ82ζ2+2ζ72ζ4+2ζ52ζ+2ζ82ζ2+2ζ72ζ4+2ζ50002ζ4+2ζ52ζ+2ζ82ζ2+2ζ72ζ2+2ζ72ζ4+2ζ52ζ+2ζ800000000000000000
χ3966-3-3-2-26-2-2000011-3112ζ2+2ζ72ζ4+2ζ52ζ+2ζ82ζ2+2ζ72ζ4+2ζ52ζ+2ζ80002ζ+2ζ82ζ2+2ζ72ζ4+2ζ52ζ4+2ζ52ζ+2ζ82ζ2+2ζ700000000000000000
χ4066-3-3-2-26-2-2000011-3112ζ4+2ζ52ζ+2ζ82ζ2+2ζ72ζ4+2ζ52ζ+2ζ82ζ2+2ζ70002ζ2+2ζ72ζ4+2ζ52ζ+2ζ82ζ+2ζ82ζ2+2ζ72ζ4+2ζ500000000000000000
χ4166-3-3-2-2-26-20000111-312ζ+2ζ82ζ2+2ζ72ζ4+2ζ52ζ2+2ζ72ζ4+2ζ52ζ+2ζ82ζ4+2ζ52ζ+2ζ82ζ2+2ζ70002ζ+2ζ82ζ2+2ζ72ζ4+2ζ500000000000000000
χ4266-3-3-2-2-26-20000111-312ζ2+2ζ72ζ4+2ζ52ζ+2ζ82ζ4+2ζ52ζ+2ζ82ζ2+2ζ72ζ+2ζ82ζ2+2ζ72ζ4+2ζ50002ζ2+2ζ72ζ4+2ζ52ζ+2ζ800000000000000000
χ4366-3-3-2-2-26-20000111-312ζ4+2ζ52ζ+2ζ82ζ2+2ζ72ζ+2ζ82ζ2+2ζ72ζ4+2ζ52ζ2+2ζ72ζ4+2ζ52ζ+2ζ80002ζ4+2ζ52ζ+2ζ82ζ2+2ζ700000000000000000
χ4466-3-3-2-2-2-2600001111-32ζ+2ζ82ζ2+2ζ72ζ4+2ζ52ζ4+2ζ52ζ+2ζ82ζ2+2ζ72ζ2+2ζ72ζ4+2ζ52ζ+2ζ82ζ+2ζ82ζ2+2ζ72ζ4+2ζ500000000000000000000
χ4566-3-3-2-2-2-2600001111-32ζ2+2ζ72ζ4+2ζ52ζ+2ζ82ζ+2ζ82ζ2+2ζ72ζ4+2ζ52ζ4+2ζ52ζ+2ζ82ζ2+2ζ72ζ2+2ζ72ζ4+2ζ52ζ+2ζ800000000000000000000
χ4666-3-3-2-2-2-2600001111-32ζ4+2ζ52ζ+2ζ82ζ2+2ζ72ζ2+2ζ72ζ4+2ζ52ζ+2ζ82ζ+2ζ82ζ2+2ζ72ζ4+2ζ52ζ4+2ζ52ζ+2ζ82ζ2+2ζ700000000000000000000
χ478-88-800000-44000000000000000000000022-2-200000-1-1110000
χ488-88-800000-440000000000000000000000−1+i3−1−i31−i31+i3000001−i321+i32−1+i32−1−i320000
χ498-88-800000-440000000000000000000000−1−i3−1+i31+i31−i3000001+i321−i32−1−i32−1+i320000
χ5024-24-12120000000000000000000000000000000000000000000000

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