Finite Group Databasebeta

← Group #11923215

Character table — Group #11923215

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11112222224444444444444444666666668888888888881212121212121212121212121616161616161616161616161616161624242424242424243636363648484848
order1222344666233466666666121212122244444433666666121212124444121212121212121266666612121212121212121212666612121212244412121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-1-1-111111111111111111-11-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111−1−i32−1+i32111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32111111111111−1−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+i321111−1−i32−1+i32−1−i32−1+i32
χ411111111111−1−i32−1+i32111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321111-1-1-1-11111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321-11-111111111−1−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+i321+i321+i321−i321−i321+i321+i321−i321−i32-1-1-1-11+i321−i321+i321−i32
χ511111111111−1+i32−1−i32111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32111111111111−1+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−i321111−1+i32−1−i32−1+i32−1−i32
χ611111111111−1+i32−1−i32111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321111-1-1-1-11111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321-11-111111111−1+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−i321−i321−i321+i321+i321−i321−i321+i321+i32-1-1-1-11−i321+i321−i321+i32
χ71111111111-111-1-1-111111111-1-111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111-1-111-1-111111111-111-1-1-1-1-1
χ81111111111-111-1-1-111111111-1-1-1-1-1-11111111111111111-11-1111-1-111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11-1-111111
χ91111111111-1−1−i32−1+i32-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211-1-111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1-1-111-1-111-1-11+i321−i321+i321+i321−i321−i321+i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32-111-11+i321−i321+i321−i32
χ101111111111-1−1−i32−1+i32-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211-1-1-1-1-1-11111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32-11-1111-1-111-1-11+i321−i321+i321+i321−i321−i321+i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321+i321+i321−i321−i321+i321+i321−i321−i321-1-11−1−i32−1+i32−1−i32−1+i32
χ111111111111-1−1+i32−1−i32-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211-1-111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1-1-111-1-111-1-11−i321+i321−i321−i321+i321+i321−i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32-111-11−i321+i321−i321+i32
χ121111111111-1−1+i32−1−i32-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211-1-1-1-1-1-11111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32-11-1111-1-111-1-11−i321+i321−i321−i321+i321+i321−i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321−i321−i321+i321+i321−i321−i321+i321+i321-1-11−1+i32−1−i32−1+i32−1−i32
χ1311111-1-1111111-111111111-1-1-1-111-1-111-1-111111111-1-1-1-1-111-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11-11-1-111
χ1411111-1-1111111-111111111-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-11-111-1-1
χ1511111-1-11111−1−i32−1+i32-111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-1-1-111-1-111-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32-111-1-1-1-1-11111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321−i321+i321+i321+i321+i321−i321−i321−i321−i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32-11-111+i321−i32−1−i32−1+i32
χ1611111-1-11111−1−i32−1+i32-111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-1-1-1-1-11111-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32-1-111-1-1-1-11111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321−i321+i321+i321+i321+i321−i321−i321−i321−i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i321-11-1−1−i32−1+i321+i321−i32
χ1711111-1-11111−1+i32−1−i32-111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-1-1-111-1-111-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32-111-1-1-1-1-11111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321+i321−i321−i321−i321−i321+i321+i321+i321+i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32-11-111−i321+i32−1+i32−1−i32
χ1811111-1-11111−1+i32−1−i32-111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-1-1-1-1-11111-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32-1-111-1-1-1-11111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321+i321−i321−i321−i321−i321+i321+i321+i321+i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i321-11-1−1+i32−1−i321−i321+i32
χ1911111-1-1111-1111-1-1111111-1-11111-1-111-1-111111111-1-1-1-11-1-11-1-11111-1-1-1-1-1-1-1-111-1-111-1-1111111-1-1-1-111-1-111-1-1
χ2011111-1-1111-1111-1-1111111-1-111-1-11111-1-111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-11111-1-111-1-111
χ2111111-1-1111-1−1−i32−1+i321-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-11111-1-111-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i321-1-11-1-11111-1-11+i321−i321+i321+i321−i321−i32−1−i32−1+i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i3211-1-1−1−i32−1+i321+i321−i32
χ2211111-1-1111-1−1−i32−1+i321-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-111-1-11111-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i3211-1-1-1-11111-1-11+i321−i321+i321+i321−i321−i32−1−i32−1+i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32-1-1111+i321−i32−1−i32−1+i32
χ2311111-1-1111-1−1+i32−1−i321-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-11111-1-111-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i321-1-11-1-11111-1-11−i321+i321−i321−i321+i321+i32−1+i32−1−i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i3211-1-1−1+i32−1−i321−i321+i32
χ2411111-1-1111-1−1+i32−1−i321-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-111-1-11111-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i3211-1-1-1-11111-1-11−i321+i321−i321−i321+i321+i32−1+i32−1−i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32-1-1111−i321+i32−1+i32−1−i32
χ252222-122-1-1-12222-1-1222222-1-1-1-100002222-1-1-1-1-1-1-1-122222020-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-1-1-1-1-10000000000000000
χ262222-122-1-1-12−1−i3−1+i32-1-1−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3-1-1-1-1000022221+i321−i321+i321−i321+i321+i321−i321−i32−1−i3−1−i3−1+i3−1+i32020-1-1-1-1-1-1-1-1−1−i3−1+i31+i321+i321−i321−i32−1−i3−1+i31+i321+i321+i321+i321−i321−i321−i321−i320000000000000000
χ272222-122-1-1-12−1+i3−1−i32-1-1−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3-1-1-1-1000022221−i321+i321−i321+i321−i321−i321+i321+i32−1+i3−1+i3−1−i3−1−i32020-1-1-1-1-1-1-1-1−1+i3−1−i31−i321−i321+i321+i32−1+i3−1−i31−i321−i321−i321−i321+i321+i321+i321+i320000000000000000
χ282222-122-1-1-1-222-211222222-1-11100002222-1-1-1-1-1-1-1-12222-20-20-1-111-1-111-2-21111-2-2-1-111-1-1110000000000000000
χ292222-122-1-1-1-2−1−i3−1+i3-211−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3-1-111000022221+i321−i321+i321−i321+i321+i321−i321−i32−1−i3−1−i3−1+i3−1+i3-20-20-1-111-1-1111+i31−i3−1−i32−1−i32−1+i32−1+i321+i31−i31+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i320000000000000000
χ302222-122-1-1-1-2−1+i3−1−i3-211−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3-1-111000022221−i321+i321−i321+i321−i321−i321+i321+i32−1+i3−1+i3−1−i3−1−i3-20-20-1-111-1-1111−i31+i3−1+i32−1+i32−1−i32−1−i321−i31+i31−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i320000000000000000
χ312222-1-2-2-1-1-1222-2-1-12222221111000022-2-2-1-1-1-1-1-1-1-1-2-2-2-2-20201111-1-1-1-122-1-1-1-1-2-2111111110000000000000000
χ322222-1-2-2-1-1-12−1−i3−1+i3-2-1-1−1−i3−1+i3−1−i3−1+i3−1−i3−1+i31111000022-2-21+i321−i321+i321−i321+i321+i321−i321−i321+i31+i31−i31−i3-20201111-1-1-1-1−1−i3−1+i31+i321+i321−i321−i321+i31−i3−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i320000000000000000
χ332222-1-2-2-1-1-12−1+i3−1−i3-2-1-1−1+i3−1−i3−1+i3−1−i3−1+i3−1−i31111000022-2-21−i321+i321−i321+i321−i321−i321+i321+i321−i31−i31+i31+i3-20201111-1-1-1-1−1+i3−1−i31−i321−i321+i321+i321−i31+i3−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i320000000000000000
χ342222-1-2-2-1-1-1-22221122222211-1-1000022-2-2-1-1-1-1-1-1-1-1-2-2-2-220-2011-1-1-1-111-2-211112211-1-111-1-10000000000000000
χ352222-1-2-2-1-1-1-2−1−i3−1+i3211−1−i3−1+i3−1−i3−1+i3−1−i3−1+i311-1-1000022-2-21+i321−i321+i321−i321+i321+i321−i321−i321+i31+i31−i31−i320-2011-1-1-1-1111+i31−i3−1−i32−1−i32−1+i32−1+i32−1−i3−1+i3−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i320000000000000000
χ362222-1-2-2-1-1-1-2−1+i3−1−i3211−1+i3−1−i3−1+i3−1−i3−1+i3−1−i311-1-1000022-2-21−i321+i321−i321+i321−i321−i321+i321+i321−i31−i31+i31+i320-2011-1-1-1-1111−i31+i3−1+i32−1+i32−1−i32−1−i32−1+i3−1−i3−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i320000000000000000
χ372-22-222i−2i-2-22022000-2-222-2-22i−2i0000002-22i−2i2222-2-2-2-22i−2i2i−2i00002i−2i002-200000000002i−2i002i−2i000000000000000000
χ382-22-222i−2i-2-220−1−i3−1+i30001+i31−i3−1−i3−1+i31+i31−i32i−2i0000002-22i−2i−1−i3−1+i3−1−i3−1+i31+i31+i31−i31−i32ζ11−2ζ112ζ7−2ζ700002i−2i002-200000000002ζ11−2ζ11002ζ7−2ζ7000000000000000000
χ392-22-222i−2i-2-220−1+i3−1−i30001−i31+i3−1+i3−1−i31−i31+i32i−2i0000002-22i−2i−1+i3−1−i3−1+i3−1−i31−i31−i31+i31+i32ζ7−2ζ72ζ11−2ζ1100002i−2i002-200000000002ζ7−2ζ7002ζ11−2ζ11000000000000000000
χ402-22-22−2i2i-2-22022000-2-222-2-2−2i2i0000002-2−2i2i2222-2-2-2-2−2i2i−2i2i0000−2i2i002-20000000000−2i2i00−2i2i000000000000000000
χ412-22-22−2i2i-2-220−1−i3−1+i30001+i31−i3−1−i3−1+i31+i31−i3−2i2i0000002-2−2i2i−1−i3−1+i3−1−i3−1+i31+i31+i31−i31−i3−2ζ112ζ11−2ζ72ζ70000−2i2i002-20000000000−2ζ112ζ1100−2ζ72ζ7000000000000000000
χ422-22-22−2i2i-2-220−1+i3−1−i30001−i31+i3−1+i3−1−i31−i31+i3−2i2i0000002-2−2i2i−1+i3−1−i3−1+i3−1−i31−i31−i31+i31+i3−2ζ72ζ7−2ζ112ζ110000−2i2i002-20000000000−2ζ72ζ700−2ζ112ζ11000000000000000000
χ432-22-2-12i−2i11-10220−i3i3-2-222-2-2−ii3−300002-22i−2i-1-1-1-111112i−2i2i−2i0000−ii3−3-11−i3i300−i3i3−i3i300−ii3−3−ii3−30000000000000000
χ442-22-2-12i−2i11-10220i3−i3-2-222-2-2−ii−3300002-22i−2i-1-1-1-111112i−2i2i−2i0000−ii−33-11i3−i300i3−i3i3−i300−ii−33−ii−330000000000000000
χ452-22-2-12i−2i11-10−1−i3−1+i30−i3i31+i31−i3−1−i3−1+i31+i31−i3−ii3−300002-22i−2i1+i321−i321+i321−i32−1−i32−1−i32−1+i32−1+i322ζ11−2ζ112ζ7−2ζ70000−ii3−3-11−i3i300−3+i323−i323+i32−3−i3200−ζ11ζ112ζ7+ζ11−2ζ7−ζ11−ζ7ζ7−ζ7−2ζ11ζ7+2ζ110000000000000000
χ462-22-2-12i−2i11-10−1−i3−1+i30i3−i31+i31−i3−1−i3−1+i31+i31−i3−ii−3300002-22i−2i1+i321−i321+i321−i32−1−i32−1−i32−1+i32−1+i322ζ11−2ζ112ζ7−2ζ70000−ii−33-11i3−i3003−i32−3+i32−3−i323+i3200−ζ11ζ11−2ζ7−ζ112ζ7+ζ11−ζ7ζ7ζ7+2ζ11−ζ7−2ζ110000000000000000
χ472-22-2-12i−2i11-10−1+i3−1−i30−i3i31−i31+i3−1+i3−1−i31−i31+i3−ii3−300002-22i−2i1−i321+i321−i321+i32−1+i32−1+i32−1−i32−1−i322ζ7−2ζ72ζ11−2ζ110000−ii3−3-11−i3i3003+i32−3−i32−3+i323−i3200−ζ7ζ7−ζ7−2ζ11ζ7+2ζ11−ζ11ζ112ζ7+ζ11−2ζ7−ζ110000000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.