Finite Group Databasebeta

← Group #85604

Character table — Group #85604

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70
size1111111122222222222244444444444444446666888888888888888888888888121212121212
order122244444444444444443366666612121212121212124444121212121212121212121212121212121212121212121212222444
χ11111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111−1−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+i321111−1−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+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32111111
χ311111111111111111111−1+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−i321111−1+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−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32111111
χ4111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-11-1-1
χ5111111111111-1-1-1-1-1-1-1-1−1−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+i321111−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i321-1-11-1-1
χ6111111111111-1-1-1-1-1-1-1-1−1+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−i321111−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i321-1-11-1-1
χ711111111-1-1-1-11111-1-1-1-111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-11-1-11-1
χ811111111-1-1-1-11111-1-1-1-1−1−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+i3211111+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32-11-1-11-1
χ911111111-1-1-1-11111-1-1-1-1−1+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−i3211111−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32-11-1-11-1
χ1011111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11-1-11
χ1111111111-1-1-1-1-1-1-1-11111−1−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+i3211111+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32-1-11-1-11
χ1211111111-1-1-1-1-1-1-1-11111−1+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−i3211111−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32-1-11-1-11
χ131111-1-1-1-111-1-111-1-111-1-111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-111-1-111-1-111-1-111-1-1-11
χ141111-1-1-1-111-1-111-1-111-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i3211-1-1−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i3211-1-1-11
χ151111-1-1-1-111-1-111-1-111-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i3211-1-1−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i3211-1-1-11
χ161111-1-1-1-111-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-11111-1-1-1-111-1-1111-11-11-1
χ171111-1-1-1-111-1-1-1-111-1-111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i3211-1-1−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321-11-11-1
χ181111-1-1-1-111-1-1-1-111-1-111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i3211-1-1−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321-11-11-1
χ191111-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-111-1111-1-1
χ201111-1-1-1-1-1-11111-1-1-1-111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i3211-1-11+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32-1111-1-1
χ211111-1-1-1-1-1-11111-1-1-1-111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i3211-1-11−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32-1111-1-1
χ221111-1-1-1-1-1-111-1-11111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-111-1-11111-1-1-1-1-1111
χ231111-1-1-1-1-1-111-1-11111-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i3211-1-11+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32-1-1-1111
χ241111-1-1-1-1-1-111-1-11111-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i3211-1-11−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32-1-1-1111
χ2522-2-22i2i−2i−2i00000000000022-2-22-22-22i2i−2i−2i2i2i−2i−2i2-22i−2i000000000000000000000000000000
χ2622-2-22i2i−2i−2i000000000000−1−i3−1+i31+i31−i3−1−i31+i3−1+i31−i32ζ112ζ11−2ζ11−2ζ112ζ72ζ7−2ζ7−2ζ72-22i−2i000000000000000000000000000000
χ2722-2-22i2i−2i−2i000000000000−1+i3−1−i31−i31+i3−1+i31−i3−1−i31+i32ζ72ζ7−2ζ7−2ζ72ζ112ζ11−2ζ11−2ζ112-22i−2i000000000000000000000000000000
χ2822-2-2−2i−2i2i2i00000000000022-2-22-22-2−2i−2i2i2i−2i−2i2i2i2-2−2i2i000000000000000000000000000000
χ2922-2-2−2i−2i2i2i000000000000−1−i3−1+i31+i31−i3−1−i31+i3−1+i31−i3−2ζ11−2ζ112ζ112ζ11−2ζ7−2ζ72ζ72ζ72-2−2i2i000000000000000000000000000000
χ3022-2-2−2i−2i2i2i000000000000−1+i3−1−i31−i31+i3−1+i31−i3−1−i31+i3−2ζ7−2ζ72ζ72ζ7−2ζ11−2ζ112ζ112ζ112-2−2i2i000000000000000000000000000000
χ312-22-22i−2i2i−2i2i−2i2-22i−2i2-22-22i−2i-1-1111-11-1i−ii−ii−ii−i0000i−i1-1i−i1-11-1i−ii−i1-1i−i1-11-1i−i000000
χ322-22-22i−2i2i−2i2i−2i2-22i−2i2-22-22i−2i1+i321−i32−1−i32−1+i32−1−i321+i32−1+i321−i32ζ11−ζ11ζ11−ζ11ζ7−ζ7ζ7−ζ70000ζ11−ζ11−1−i321+i32ζ11−ζ11−1−i321+i32−1−i321+i32ζ11−ζ11ζ7−ζ7−1+i321−i32ζ7−ζ7−1+i321−i32−1+i321−i32ζ7−ζ7000000
χ332-22-22i−2i2i−2i2i−2i2-22i−2i2-22-22i−2i1−i321+i32−1+i32−1−i32−1+i321−i32−1−i321+i32ζ7−ζ7ζ7−ζ7ζ11−ζ11ζ11−ζ110000ζ7−ζ7−1+i321−i32ζ7−ζ7−1+i321−i32−1+i321−i32ζ7−ζ7ζ11−ζ11−1−i321+i32ζ11−ζ11−1−i321+i32−1−i321+i32ζ11−ζ11000000
χ342-22-22i−2i2i−2i2i−2i2-2−2i2i-22-22−2i2i-1-1111-11-1i−ii−ii−ii−i0000i−i1-1−ii-11-11−iii−i1-1−ii-11-11−ii000000
χ352-22-22i−2i2i−2i2i−2i2-2−2i2i-22-22−2i2i1+i321−i32−1−i32−1+i32−1−i321+i32−1+i321−i32ζ11−ζ11ζ11−ζ11ζ7−ζ7ζ7−ζ70000ζ11−ζ11−1−i321+i32−ζ11ζ111+i32−1−i321+i32−1−i32−ζ11ζ11ζ7−ζ7−1+i321−i32−ζ7ζ71−i32−1+i321−i32−1+i32−ζ7ζ7000000
χ362-22-22i−2i2i−2i2i−2i2-2−2i2i-22-22−2i2i1−i321+i32−1+i32−1−i32−1+i321−i32−1−i321+i32ζ7−ζ7ζ7−ζ7ζ11−ζ11ζ11−ζ110000ζ7−ζ7−1+i321−i32−ζ7ζ71−i32−1+i321−i32−1+i32−ζ7ζ7ζ11−ζ11−1−i321+i32−ζ11ζ111+i32−1−i321+i32−1−i32−ζ11ζ11000000
χ372-22-22i−2i2i−2i−2i2i-222i−2i2-2-22−2i2i-1-1111-11-1i−ii−ii−ii−i0000−ii-11i−i1-1-11−ii−ii-11i−i1-1-11−ii000000
χ382-22-22i−2i2i−2i−2i2i-222i−2i2-2-22−2i2i1+i321−i32−1−i32−1+i32−1−i321+i32−1+i321−i32ζ11−ζ11ζ11−ζ11ζ7−ζ7ζ7−ζ70000−ζ11ζ111+i32−1−i32ζ11−ζ11−1−i321+i321+i32−1−i32−ζ11ζ11−ζ7ζ71−i32−1+i32ζ7−ζ7−1+i321−i321−i32−1+i32−ζ7ζ7000000
χ392-22-22i−2i2i−2i−2i2i-222i−2i2-2-22−2i2i1−i321+i32−1+i32−1−i32−1+i321−i32−1−i321+i32ζ7−ζ7ζ7−ζ7ζ11−ζ11ζ11−ζ110000−ζ7ζ71−i32−1+i32ζ7−ζ7−1+i321−i321−i32−1+i32−ζ7ζ7−ζ11ζ111+i32−1−i32ζ11−ζ11−1−i321+i321+i32−1−i32−ζ11ζ11000000
χ402-22-22i−2i2i−2i−2i2i-22−2i2i-222-22i−2i-1-1111-11-1i−ii−ii−ii−i0000−ii-11−ii-111-1i−i−ii-11−ii-111-1i−i000000
χ412-22-22i−2i2i−2i−2i2i-22−2i2i-222-22i−2i1+i321−i32−1−i32−1+i32−1−i321+i32−1+i321−i32ζ11−ζ11ζ11−ζ11ζ7−ζ7ζ7−ζ70000−ζ11ζ111+i32−1−i32−ζ11ζ111+i32−1−i32−1−i321+i32ζ11−ζ11−ζ7ζ71−i32−1+i32−ζ7ζ71−i32−1+i32−1+i321−i32ζ7−ζ7000000
χ422-22-22i−2i2i−2i−2i2i-22−2i2i-222-22i−2i1−i321+i32−1+i32−1−i32−1+i321−i32−1−i321+i32ζ7−ζ7ζ7−ζ7ζ11−ζ11ζ11−ζ110000−ζ7ζ71−i32−1+i32−ζ7ζ71−i32−1+i32−1+i321−i32ζ7−ζ7−ζ11ζ111+i32−1−i32−ζ11ζ111+i32−1−i32−1−i321+i32ζ11−ζ11000000
χ432-22-2−2i2i−2i2i2i−2i-222i−2i-222-2−2i2i-1-1111-11-1−ii−ii−ii−ii0000i−i-11i−i-111-1−iii−i-11i−i-111-1−ii000000
χ442-22-2−2i2i−2i2i2i−2i-222i−2i-222-2−2i2i1+i321−i32−1−i32−1+i32−1−i321+i32−1+i321−i32−ζ11ζ11−ζ11ζ11−ζ7ζ7−ζ7ζ70000ζ11−ζ111+i32−1−i32ζ11−ζ111+i32−1−i32−1−i321+i32−ζ11ζ11ζ7−ζ71−i32−1+i32ζ7−ζ71−i32−1+i32−1+i321−i32−ζ7ζ7000000
χ452-22-2−2i2i−2i2i2i−2i-222i−2i-222-2−2i2i1−i321+i32−1+i32−1−i32−1+i321−i32−1−i321+i32−ζ7ζ7−ζ7ζ7−ζ11ζ11−ζ11ζ110000ζ7−ζ71−i32−1+i32ζ7−ζ71−i32−1+i32−1+i321−i32−ζ7ζ7ζ11−ζ111+i32−1−i32ζ11−ζ111+i32−1−i32−1−i321+i32−ζ11ζ11000000
χ462-22-2−2i2i−2i2i2i−2i-22−2i2i2-2-222i−2i-1-1111-11-1−ii−ii−ii−ii0000i−i-11−ii1-1-11i−ii−i-11−ii1-1-11i−i000000
χ472-22-2−2i2i−2i2i2i−2i-22−2i2i2-2-222i−2i1+i321−i32−1−i32−1+i32−1−i321+i32−1+i321−i32−ζ11ζ11−ζ11ζ11−ζ7ζ7−ζ7ζ70000ζ11−ζ111+i32−1−i32−ζ11ζ11−1−i321+i321+i32−1−i32ζ11−ζ11ζ7−ζ71−i32−1+i32−ζ7ζ7−1+i321−i321−i32−1+i32ζ7−ζ7000000
χ482-22-2−2i2i−2i2i2i−2i-22−2i2i2-2-222i−2i1−i321+i32−1+i32−1−i32−1+i321−i32−1−i321+i32−ζ7ζ7−ζ7ζ7−ζ11ζ11−ζ11ζ110000ζ7−ζ71−i32−1+i32−ζ7ζ7−1+i321−i321−i32−1+i32ζ7−ζ7ζ11−ζ111+i32−1−i32−ζ11ζ11−1−i321+i321+i32−1−i32ζ11−ζ11000000
χ492-22-2−2i2i−2i2i−2i2i2-22i−2i-22-222i−2i-1-1111-11-1−ii−ii−ii−ii0000−ii1-1i−i-11-11i−i−ii1-1i−i-11-11i−i000000
χ502-22-2−2i2i−2i2i−2i2i2-22i−2i-22-222i−2i1+i321−i32−1−i32−1+i32−1−i321+i32−1+i321−i32−ζ11ζ11−ζ11ζ11−ζ7ζ7−ζ7ζ70000−ζ11ζ11−1−i321+i32ζ11−ζ111+i32−1−i321+i32−1−i32ζ11−ζ11−ζ7ζ7−1+i321−i32ζ7−ζ71−i32−1+i321−i32−1+i32ζ7−ζ7000000
χ512-22-2−2i2i−2i2i−2i2i2-22i−2i-22-222i−2i1−i321+i32−1+i32−1−i32−1+i321−i32−1−i321+i32−ζ7ζ7−ζ7ζ7−ζ11ζ11−ζ11ζ110000−ζ7ζ7−1+i321−i32ζ7−ζ71−i32−1+i321−i32−1+i32ζ7−ζ7−ζ11ζ11−1−i321+i32ζ11−ζ111+i32−1−i321+i32−1−i32ζ11−ζ11000000
χ522-22-2−2i2i−2i2i−2i2i2-2−2i2i2-22-2−2i2i-1-1111-11-1−ii−ii−ii−ii0000−ii1-1−ii1-11-1−ii−ii1-1−ii1-11-1−ii000000
χ532-22-2−2i2i−2i2i−2i2i2-2−2i2i2-22-2−2i2i1+i321−i32−1−i32−1+i32−1−i321+i32−1+i321−i32−ζ11ζ11−ζ11ζ11−ζ7ζ7−ζ7ζ70000−ζ11ζ11−1−i321+i32−ζ11ζ11−1−i321+i32−1−i321+i32−ζ11ζ11−ζ7ζ7−1+i321−i32−ζ7ζ7−1+i321−i32−1+i321−i32−ζ7ζ7000000
χ542-22-2−2i2i−2i2i−2i2i2-2−2i2i2-22-2−2i2i1−i321+i32−1+i32−1−i32−1+i321−i32−1−i321+i32−ζ7ζ7−ζ7ζ7−ζ11ζ11−ζ11ζ110000−ζ7ζ7−1+i321−i32−ζ7ζ7−1+i321−i32−1+i321−i32−ζ7ζ7−ζ11ζ11−1−i321+i32−ζ11ζ11−1−i321+i32−1−i321+i32−ζ11ζ11000000
χ55333333333333333333330000000000000000-1-1-1-1000000000000000000000000-1-1-1-1-1-1
χ56333333333333-3-3-3-3-3-3-3-30000000000000000-1-1-1-1000000000000000000000000-111-111
χ5733333333-3-3-3-33333-3-3-3-30000000000000000-1-1-1-10000000000000000000000001-111-11
χ5833333333-3-3-3-3-3-3-3-333330000000000000000-1-1-1-100000000000000000000000011-111-1
χ593333-3-3-3-333-3-333-3-333-3-30000000000000000-1-111000000000000000000000000-1-1111-1
χ603333-3-3-3-333-3-3-3-333-3-3330000000000000000-1-111000000000000000000000000-11-11-11
χ613333-3-3-3-3-3-33333-3-3-3-3330000000000000000-1-1110000000000000000000000001-1-1-111
χ623333-3-3-3-3-3-333-3-33333-3-30000000000000000-1-111000000000000000000000000111-1-1-1
χ634-4-444-4-44000000000000-2-2-2-222222-2-222-2-220000000000000000000000000000000000
χ644-4-444-4-440000000000001+i31−i31+i31−i3−1−i3−1−i3−1+i3−1+i3−1−i31+i31+i3−1−i3−1+i31−i31−i3−1+i30000000000000000000000000000000000
χ654-4-444-4-440000000000001−i31+i31−i31+i3−1+i3−1+i3−1−i3−1−i3−1+i31−i31−i3−1+i3−1−i31+i31+i3−1−i30000000000000000000000000000000000
χ664-4-44-444-4000000000000-2-2-2-22222-222-2-222-20000000000000000000000000000000000
χ674-4-44-444-40000000000001+i31−i31+i31−i3−1−i3−1−i3−1+i3−1+i31+i3−1−i3−1−i31+i31−i3−1+i3−1+i31−i30000000000000000000000000000000000
χ684-4-44-444-40000000000001−i31+i31−i31+i3−1+i3−1+i3−1−i3−1−i31−i3−1+i3−1+i31−i31+i3−1−i3−1−i31+i30000000000000000000000000000000000
χ6966-6-66i6i−6i−6i0000000000000000000000000000-22−2i2i000000000000000000000000000000
χ7066-6-6−6i−6i6i6i0000000000000000000000000000-222i−2i000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.