Finite Group Databasebeta

← Group #88708

Character table — Group #88708

Order 432.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112222222222333333336666666666666666666666666666181818181818181818181818
order1244234666121212123366121212126699912121818181818181818183636363636363636363636362244666612121212
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i321111−1−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
χ411111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-1-1-1-11+i321+i321−i321−i321+i321+i321−i321−i32
χ511111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i321111−1+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
χ611111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-1-1-1-11−i321−i321+i321+i321−i321−i321+i321+i32
χ71111-11-1-1-1111-1-111111111-1-1111-1-1-1-1-1-1-1-111111-1-111-1-111-1-11-11-11-11-11-11-1
χ81111-11-1-1-1111-1-111111111-1-1111-1-1-1-1-1-1-1-111111-1-111-1-111-1-1-11-11-11-11-11-11
χ91111-11-1-1-1111-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321−i321−1−i32−1+i321+i321−i32-1-11+i321+i321−i321−i321−1−i32−1+i3211-1-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321-11-1−1−i321+i32−1+i321−i32−1−i321+i32−1+i321−i32
χ101111-11-1-1-1111-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321−i321−1−i32−1+i321+i321−i32-1-11+i321+i321−i321−i321−1−i32−1+i3211-1-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32-11-111+i32−1−i321−i32−1+i321+i32−1−i321−i32−1+i32
χ111111-11-1-1-1111-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321+i321−1+i32−1−i321−i321+i32-1-11−i321−i321+i321+i321−1+i32−1−i3211-1-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321-11-1−1+i321−i32−1−i321+i32−1+i321−i32−1−i321+i32
χ121111-11-1-1-1111-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321+i321−1+i32−1−i321−i321+i32-1-11−i321−i321+i321+i321−1+i32−1−i3211-1-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32-11-111−i32−1+i321+i32−1−i321−i32−1+i321+i32−1−i32
χ1311-1-111-1111-1-1-1-11111-1-1-1-111111-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-111-11-1-11-11
χ1411-1-111-1111-1-1-1-11111-1-1-1-111111-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-111-11-1
χ1511-1-111-1111-1-1-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i321−1−i32−1+i321+i321−i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i321-1-11−1−i321+i32−1+i321−i321+i32−1−i321−i32−1+i32
χ1611-1-111-1111-1-1-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i321−1−i32−1+i321+i321−i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32-111-11+i32−1−i321−i32−1+i32−1−i321+i32−1+i321−i32
χ1711-1-111-1111-1-1-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i321−1+i32−1−i321−i321+i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i321-1-11−1+i321−i32−1−i321+i321−i32−1+i321+i32−1−i32
χ1811-1-111-1111-1-1-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i321−1+i32−1−i321−i321+i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32-111-11−i32−1+i321+i32−1−i32−1+i321−i32−1−i321+i32
χ1911-1-1-111-1-11-1-1111111-1-1-1-1-1-111111-1-1-1-1-1-1111-1-111-1-111-1-11111-1-11111-1-1-1-1
χ2011-1-1-111-1-11-1-1111111-1-1-1-1-1-111111-1-1-1-1-1-1111-1-111-1-111-1-111-1-111-1-1-1-11111
χ2111-1-1-111-1-11-1-111−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i321+i321−i321−1−i32−1+i32−1−i32−1+i32-1-11+i321+i321−i321−i321−1−i32−1+i32-1-1111+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i3211-1-1−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32
χ2211-1-1-111-1-11-1-111−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i321+i321−i321−1−i32−1+i32−1−i32−1+i32-1-11+i321+i321−i321−i321−1−i32−1+i32-1-1111+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32-1-1111+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32
χ2311-1-1-111-1-11-1-111−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i321−i321+i321−1+i32−1−i32−1+i32−1−i32-1-11−i321−i321+i321+i321−1+i32−1−i32-1-1111−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i3211-1-1−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32
χ2411-1-1-111-1-11-1-111−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i321−i321+i321−1+i32−1−i32−1+i32−1−i32-1-11−i321−i321+i321+i321−1+i32−1−i32-1-1111−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32-1-1111−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32
χ25222222222222222222222222-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ2622222222222222−1−i3−1+i3−1−i3−1+i3−1−i3−1−i3−1+i3−1+i3−1−i3−1+i3-11+i321−i32−1−i3−1+i3-1-11+i321+i321−i321−i32-11+i321−i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32000000000000
χ2722222222222222−1+i3−1−i3−1+i3−1−i3−1+i3−1+i3−1−i3−1−i3−1+i3−1−i3-11−i321+i32−1+i3−1−i3-1-11−i321−i321+i321+i32-11−i321+i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32000000000000
χ282222-22-2-2-2222-2-222222222-2-2-1-1-1-2-2111111-1-1-1-1-111-1-111-1-111000000000000
χ292222-22-2-2-2222-2-2−1−i3−1+i3−1−i3−1+i3−1−i3−1−i3−1+i3−1+i31+i31−i3-11+i321−i321+i31−i311−1−i32−1−i32−1+i32−1+i32-11+i321−i32-1-1111+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32000000000000
χ302222-22-2-2-2222-2-2−1+i3−1−i3−1+i3−1−i3−1+i3−1+i3−1−i3−1−i31−i31+i3-11−i321+i321−i31+i311−1+i32−1+i32−1−i32−1−i32-11−i321+i32-1-1111−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32000000000000
χ3122-2-222-2222-2-2-2-22222-2-2-2-222-1-1-1-2-2-1-1-1-1-1-1-1-1-1111111111111000000000000
χ3222-2-222-2222-2-2-2-2−1−i3−1+i3−1−i3−1+i31+i31+i31−i31−i3−1−i3−1+i3-11+i321−i321+i31−i3-1-11+i321+i321−i321−i32-11+i321−i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32000000000000
χ3322-2-222-2222-2-2-2-2−1+i3−1−i3−1+i3−1−i31−i31−i31+i31+i3−1+i3−1−i3-11−i321+i321−i31+i3-1-11−i321−i321+i321+i32-11−i321+i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32000000000000
χ3422-2-2-222-2-22-2-2222222-2-2-2-2-2-2-1-1-122111111-1-1-111-1-111-1-111-1-1000000000000
χ3522-2-2-222-2-22-2-222−1−i3−1+i3−1−i3−1+i31+i31+i31−i31−i31+i31−i3-11+i321−i32−1−i3−1+i311−1−i32−1−i32−1+i32−1+i32-11+i321−i3211-1-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32000000000000
χ3622-2-2-222-2-22-2-222−1+i3−1−i3−1+i3−1−i31−i31−i31+i31+i31−i31+i3-11−i321+i32−1+i3−1−i311−1+i32−1+i32−1−i32−1−i32-11−i321+i3211-1-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32000000000000
χ372-22i−2i02000-22i−2i0022-2-22i−2i2i−2i0022200000000-2-2-22i−2i002i−2i002i−2i00000000000000
χ382-22i−2i02000-22i−2i0022-2-22i−2i2i−2i00-1-1-100−i3i3−i3i3−i3i3111−ii3−3−ii3−3−ii3−3000000000000
χ392-22i−2i02000-22i−2i0022-2-22i−2i2i−2i00-1-1-100i3−i3i3−i3i3−i3111−ii−33−ii−33−ii−33000000000000
χ402-22i−2i02000-22i−2i00−1−i3−1+i31+i31−i32ζ11−2ζ112ζ7−2ζ7002−1−i3−1+i300000000-21+i31−i32i−2i002ζ11−2ζ11002ζ7−2ζ700000000000000
χ412-22i−2i02000-22i−2i00−1−i3−1+i31+i31−i32ζ11−2ζ112ζ7−2ζ700-11+i321−i3200−i3i3−3+i323−i323+i32−3−i321−1−i32−1+i32−ii3−3−ζ11ζ112ζ7+ζ11−2ζ7−ζ11−ζ7ζ7−ζ7−2ζ11ζ7+2ζ11000000000000
χ422-22i−2i02000-22i−2i00−1−i3−1+i31+i31−i32ζ11−2ζ112ζ7−2ζ700-11+i321−i3200i3−i33−i32−3+i32−3−i323+i321−1−i32−1+i32−ii−33−ζ11ζ11−2ζ7−ζ112ζ7+ζ11−ζ7ζ7ζ7+2ζ11−ζ7−2ζ11000000000000
χ432-22i−2i02000-22i−2i00−1+i3−1−i31−i31+i32ζ7−2ζ72ζ11−2ζ11002−1+i3−1−i300000000-21−i31+i32i−2i002ζ7−2ζ7002ζ11−2ζ1100000000000000
χ442-22i−2i02000-22i−2i00−1+i3−1−i31−i31+i32ζ7−2ζ72ζ11−2ζ1100-11−i321+i3200−i3i33+i32−3−i32−3+i323−i321−1+i32−1−i32−ii3−3−ζ7ζ7−ζ7−2ζ11ζ7+2ζ11−ζ11ζ112ζ7+ζ11−2ζ7−ζ11000000000000
χ452-22i−2i02000-22i−2i00−1+i3−1−i31−i31+i32ζ7−2ζ72ζ11−2ζ1100-11−i321+i3200i3−i3−3−i323+i323−i32−3+i321−1+i32−1−i32−ii−33−ζ7ζ7ζ7+2ζ11−ζ7−2ζ11−ζ11ζ11−2ζ7−ζ112ζ7+ζ11000000000000
χ462-2−2i2i02000-2−2i2i0022-2-2−2i2i−2i2i0022200000000-2-2-2−2i2i00−2i2i00−2i2i00000000000000
χ472-2−2i2i02000-2−2i2i0022-2-2−2i2i−2i2i00-1-1-100−i3i3−i3i3−i3i3111i−i−33i−i−33i−i−33000000000000
χ482-2−2i2i02000-2−2i2i0022-2-2−2i2i−2i2i00-1-1-100i3−i3i3−i3i3−i3111i−i3−3i−i3−3i−i3−3000000000000
χ492-2−2i2i02000-2−2i2i00−1−i3−1+i31+i31−i3−2ζ112ζ11−2ζ72ζ7002−1−i3−1+i300000000-21+i31−i3−2i2i00−2ζ112ζ1100−2ζ72ζ700000000000000
χ502-2−2i2i02000-2−2i2i00−1−i3−1+i31+i31−i3−2ζ112ζ11−2ζ72ζ700-11+i321−i3200−i3i3−3+i323−i323+i32−3−i321−1−i32−1+i32i−i−33ζ11−ζ11−2ζ7−ζ112ζ7+ζ11ζ7−ζ7ζ7+2ζ11−ζ7−2ζ11000000000000
χ512-2−2i2i02000-2−2i2i00−1−i3−1+i31+i31−i3−2ζ112ζ11−2ζ72ζ700-11+i321−i3200i3−i33−i32−3+i32−3−i323+i321−1−i32−1+i32i−i3−3ζ11−ζ112ζ7+ζ11−2ζ7−ζ11ζ7−ζ7−ζ7−2ζ11ζ7+2ζ11000000000000
χ522-2−2i2i02000-2−2i2i00−1+i3−1−i31−i31+i3−2ζ72ζ7−2ζ112ζ11002−1+i3−1−i300000000-21−i31+i3−2i2i00−2ζ72ζ700−2ζ112ζ1100000000000000
χ532-2−2i2i02000-2−2i2i00−1+i3−1−i31−i31+i3−2ζ72ζ7−2ζ112ζ1100-11−i321+i3200−i3i33+i32−3−i32−3+i323−i321−1+i32−1−i32i−i−33ζ7−ζ7ζ7+2ζ11−ζ7−2ζ11ζ11−ζ11−2ζ7−ζ112ζ7+ζ11000000000000
χ542-2−2i2i02000-2−2i2i00−1+i3−1−i31−i31+i3−2ζ72ζ7−2ζ112ζ1100-11−i321+i3200i3−i3−3−i323+i323−i32−3+i321−1+i32−1−i32i−i3−3ζ7−ζ7−ζ7−2ζ11ζ7+2ζ11ζ11−ζ112ζ7+ζ11−2ζ7−ζ11000000000000
χ5566666-36-3-3-3-3-3-3-3000000000000000000000000000000000000000000000000
χ566666-6-3-633-3-3-333000000000000000000000000000000000000000000000000
χ5766-6-66-3-6-3-3-33333000000000000000000000000000000000000000000000000
χ5866-6-6-6-3633-333-3-3000000000000000000000000000000000000000000000000
χ596-66i−6i0-30−3i33i33−3i3i33−33000000000000000000000000000000000000000000000000
χ606-66i−6i0-303i3−3i33−3i3i−3333000000000000000000000000000000000000000000000000
χ616-6−6i6i0-30−3i33i333i−3i−3333000000000000000000000000000000000000000000000000
χ626-6−6i6i0-303i3−3i333i−3i33−33000000000000000000000000000000000000000000000000

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