Finite Group Databasebeta

← Group #13161563

Character table — Group #13161563

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size111122222222222222444444444444444444444444448888888888888888888888888888888888888363636363636363636363636363636363636727272727272727272
order12223334466666666633333666666666666666121212121212412121212121212121212121212121212121212121212121212121212121212121212121224668888121224242424242424242446612121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11-1-111-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-11-1-1-1-1-111
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-11-1-111-1-1
χ511111111111111111111111111111111111111111111-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111111111111111-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-111-1-11111
χ711111111111111111111111111111111111111111111-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11-111111-1-1
χ811111111111111111111111111111111111111111111-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-111-1-111
χ92222222-2-222222222222222222222222222222-2-2-2-2-2-20000000-2-2-2-2-2-2-2-2-2-2000000000000000000002-2220000-2-200000000000000000
χ102222222-2-222222222222222222222222222222-2-2-2-2-2-20000000-2-2-2-2-2-2-2-2-2-200000000000000000000-22-2-200002200000000000000000
χ11222222-12222-122-1-1222-1-1-1-12-1-1-1-12-1-1-1-12-1-1-1-12-1-1222222-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-10000-1-100000000200-1-10000
χ12222222-12222-122-1-1222-1-1-1-12-1-1-1-12-1-1-1-12-1-1-1-12-1-1222222-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-21100001100000000-200110000
χ13222222-12222-122-1-1222-1-1-1-12-1-1-1-12-1-1-1-12-1-1-1-12-1-1222-2-2-211-2-222-1-1-1-1-1-1-1-1-2-2-2-2111111111111111122-1-10000-1-100000000-200110000
χ14222222-12222-122-1-1222-1-1-1-12-1-1-1-12-1-1-1-12-1-1-1-12-1-1222-2-2-211-2-222-1-1-1-1-1-1-1-1-2-2-2-21111111111111111-2-21100001100000000200-1-10000
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χ17222222-1-2-222-122-1-1222-1-1-1-12-1-1-1-12-1-1-1-12-1-1-1-1-211-2-2-2000i3−i300-2-2111111110000i3i3i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i32-2-1-100001100000000000i3−i30000
χ18222222-1-2-222-122-1-1222-1-1-1-12-1-1-1-12-1-1-1-12-1-1-1-1-211-2-2-2000i3−i300-2-2111111110000i3i3i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3-22110000-1-100000000000−i3i30000
χ1922222-12222-122-122-12-12-1-1-1-12-1-1-1-12-1-1-1-12-1-1-1222-12-12-1-12222-1-122-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-100000022000000-1-1-1-100200-1-100
χ2022222-12222-122-122-12-12-1-1-1-12-1-1-1-12-1-1-1-12-1-1-1222-12-12-1-12222-1-122-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1000000-2-2000000111100-2001100
χ2122222-12222-122-122-12-12-1-1-1-12-1-1-1-12-1-1-1-12-1-1-1222-12-1-211-2-2-2-2-1-122-1-1-1-1-1-11111-2-2111111-2-211111100000022000000-1-1-1-100-2001100
χ2222222-12222-122-122-12-12-1-1-1-12-1-1-1-12-1-1-1-12-1-1-1222-12-1-211-2-2-2-2-1-122-1-1-1-1-1-11111-2-2111111-2-2111111000000-2-2000000111100200-1-100
χ232222-12222-122-12222-1-1-12-1-1-1-12-1-1-1-12-1-1-1-12-1-1-1222-1222222-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-10000220000-1-1-1-100000200000-1-1
χ242222-12222-122-12222-1-1-12-1-1-1-12-1-1-1-12-1-1-1-12-1-1-1222-1222222-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-10000-2-20000111100000-20000011
χ252222-12222-122-12222-1-1-12-1-1-1-12-1-1-1-12-1-1-1-12-1-1-1222-12-2-2-2-2-211-1-1-1-122-1-1-1-1111111-2-2111111-2-211110000220000-1-1-1-100000-20000011
χ262222-12222-122-12222-1-1-12-1-1-1-12-1-1-1-12-1-1-1-12-1-1-1222-12-2-2-2-2-211-1-1-1-122-1-1-1-1111111-2-2111111-2-211110000-2-20000111100000200000-1-1
χ272-2-222222-2-2-2-22-2-222-222222-2-2-2-2-222222-2-2-2-2-222-22-2-200000002-22-22-222-2-2000000000000000000000000002i−2i0000002i2i−2i−2i000000000
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χ312-2-222-122-2-21-221-22-1-2-12-1-1-11-2111-12-1-1-11-211122-2-1-2103−30000-112-2-11-1-11133−3−3003−333−3−3003−333−3−30000002i−2i000000−i−iii00000−i3i300
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χ332-2-222-122-2-21-221-22-1-2-12-1-1-11-2111-12-1-1-11-211122-2-1-210−330000-112-2-11-1-111−3−33300−33−3−33300−33−3−3330000002i−2i000000−i−iii00000i3−i300
χ342-2-222-122-2-21-221-22-1-2-12-1-1-11-2111-12-1-1-11-211122-2-1-210−330000-112-2-11-1-111−3−33300−33−3−33300−33−3−333000000−2i2i000000ii−i−i00000−i3i300
χ352-2-22-122-221-2-2-1-2-2221-1-12-1-111-211-1-12-1-111-2111-22-2-12000003−31-11-1-2211-1-13−33−33−3003−33−33−3003−33−300002-20000-1-111000000000003−3
χ362-2-22-122-221-2-2-1-2-2221-1-12-1-111-211-1-12-1-111-2111-22-2-12000003−31-11-1-2211-1-13−33−33−3003−33−33−3003−33−30000-22000011-1-100000000000−33
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χ514444-2-24-4-4-2-24-2-244-2-21-2-2111-2-2111-2-2111-2-2112-4-42220000000-1-12222-1-1-1-13-3-3300003-3-3300003-3-33000000000000000000000000000
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χ834-4-44-24-24-42-42-2-42-242-21-2112-12-1-1-21-2112-12-1-1-2-2242-40000000-221-1-2211-1-100003i−3i003i−3i3i−3i−3i3i00−3i3i−3i3i000000000000000000000000000
χ844-4-44-24-24-42-42-2-42-242-21-2112-12-1-1-21-2112-12-1-1-2-2242-40000000-221-1-2211-1-10000−3i3i00−3i3i−3i3i3i−3i003i−3i3i−3i000000000000000000000000000
χ854-4-44-24-2-442-42-2-42-242-21-2112-12-1-1-21-2112-12-1-122-2-4-240000023−232-2-112-2-1-11123−2323−23−3300−33−33−3300−33−33000000000000000000000000000
χ864-4-44-24-2-442-42-2-42-242-21-2112-12-1-1-21-2112-12-1-122-2-4-2400000−23232-2-112-2-1-111−2323−23233−3003−33−33−3003−33−3000000000000000000000000000
χ874-4-44-2-244-422-4-22-44-221-2-211-122-1-11-2-211-122-1-1-24-4-222023−2300001-1-22-2211-1-1−3−3330023−23−3−3330023−23−3−333000000000000000000000000000
χ884-4-44-2-244-422-4-22-44-221-2-211-122-1-11-2-211-122-1-1-24-4-2220−232300001-1-22-2211-1-133−3−300−232333−3−300−232333−3−3000000000000000000000000000
χ894-4-44-2-24-4422-4-22-44-221-2-211-122-1-11-2-211-122-1-12-442-2-20000023−23-112-22-2-1-111−33−3323−2300−33−3323−2300−33−33000000000000000000000000000
χ904-4-44-2-24-4422-4-22-44-221-2-211-122-1-11-2-211-122-1-12-442-2-200000−2323-112-22-2-1-1113−33−3−2323003−33−3−2323003−33−3000000000000000000000000000
χ914-4-44-2-2-24-4222-222-2-22111−1−3i32−1+3i32-1-1-11+3i321−3i32111−1−3i32−1+3i32-1-1-11+3i321−3i32-2-22-222023−2300001-11-11-1−1−3i32−1+3i321+3i321−3i32−3−3333i−3i−33ζ14+2ζ22−2ζ14−ζ222ζ14+ζ22−ζ14−2ζ22−3i3i−33−2ζ14−ζ22ζ14+2ζ22−ζ14−2ζ222ζ14+ζ22000000000000000000000000000
χ924-4-44-2-2-24-4222-222-2-22111−1−3i32−1+3i32-1-1-11+3i321−3i32111−1−3i32−1+3i32-1-1-11+3i321−3i32-2-22-2220−232300001-11-11-1−1−3i32−1+3i321+3i321−3i3233−3−3−3i3i3−3−ζ14−2ζ222ζ14+ζ22−2ζ14−ζ22ζ14+2ζ223i−3i3−32ζ14+ζ22−ζ14−2ζ22ζ14+2ζ22−2ζ14−ζ22000000000000000000000000000
χ934-4-44-2-2-24-4222-222-2-22111−1+3i32−1−3i32-1-1-11−3i321+3i32111−1+3i32−1−3i32-1-1-11−3i321+3i32-2-22-222023−2300001-11-11-1−1+3i32−1−3i321−3i321+3i32−3−333−3i3i−33−2ζ14−ζ22ζ14+2ζ22−ζ14−2ζ222ζ14+ζ223i−3i−33ζ14+2ζ22−2ζ14−ζ222ζ14+ζ22−ζ14−2ζ22000000000000000000000000000
χ944-4-44-2-2-24-4222-222-2-22111−1+3i32−1−3i32-1-1-11−3i321+3i32111−1+3i32−1−3i32-1-1-11−3i321+3i32-2-22-2220−232300001-11-11-1−1+3i32−1−3i321−3i321+3i3233−3−33i−3i3−32ζ14+ζ22−ζ14−2ζ22ζ14+2ζ22−2ζ14−ζ22−3i3i3−3−ζ14−2ζ222ζ14+ζ22−2ζ14−ζ22ζ14+2ζ22000000000000000000000000000
χ954-4-44-2-2-2-44222-222-2-22111−1−3i32−1+3i32-1-1-11+3i321−3i32111−1−3i32−1+3i32-1-1-11+3i321−3i3222-22-2-20000023−23-11-11-111+3i321−3i32−1−3i32−1+3i32−33−33−333i−3iζ14+2ζ222ζ14+ζ22−2ζ14−ζ22−ζ14−2ζ22−33−3i3i−2ζ14−ζ22−ζ14−2ζ22ζ14+2ζ222ζ14+ζ22000000000000000000000000000
χ964-4-44-2-2-2-44222-222-2-22111−1−3i32−1+3i32-1-1-11+3i321−3i32111−1−3i32−1+3i32-1-1-11+3i321−3i3222-22-2-200000−2323-11-11-111+3i321−3i32−1−3i32−1+3i323−33−33−3−3i3i−ζ14−2ζ22−2ζ14−ζ222ζ14+ζ22ζ14+2ζ223−33i−3i2ζ14+ζ22ζ14+2ζ22−ζ14−2ζ22−2ζ14−ζ22000000000000000000000000000
χ974-4-44-2-2-2-44222-222-2-22111−1+3i32−1−3i32-1-1-11−3i321+3i32111−1+3i32−1−3i32-1-1-11−3i321+3i3222-22-2-20000023−23-11-11-111−3i321+3i32−1+3i32−1−3i32−33−33−33−3i3i−2ζ14−ζ22−ζ14−2ζ22ζ14+2ζ222ζ14+ζ22−333i−3iζ14+2ζ222ζ14+ζ22−2ζ14−ζ22−ζ14−2ζ22000000000000000000000000000
χ984-4-44-2-2-2-44222-222-2-22111−1+3i32−1−3i32-1-1-11−3i321+3i32111−1+3i32−1−3i32-1-1-11−3i321+3i3222-22-2-200000−2323-11-11-111−3i321+3i32−1+3i32−1−3i323−33−33−33i−3i2ζ14+ζ22ζ14+2ζ22−ζ14−2ζ22−2ζ14−ζ223−3−3i3i−ζ14−2ζ22−2ζ14−ζ222ζ14+ζ22ζ14+2ζ22000000000000000000000000000
χ9988-8-88-4-4008-4-4-84444-8-4-4222-4-422244-2-2-244-2-2-20000000000000000000000000000000000000000000000000000000000000000000000
χ10088-8-8-48-400-48-44-844-84-42-422-42-4224-24-2-24-24-2-20000000000000000000000000000000000000000000000000000000000000000000000
χ10188-8-8-4-4800-4-4844-8-8442-4-4222-4-422-244-2-2-244-2-20000000000000000000000000000000000000000000000000000000000000000000000
χ10288-8-8-4-4-400-4-4-4444444222−1−3i3−1+3i3222−1−3i3−1+3i3-2-2-21+3i31−3i3-2-2-21+3i31−3i30000000000000000000000000000000000000000000000000000000000000000000000
χ10388-8-8-4-4-400-4-4-4444444222−1+3i3−1−3i3222−1+3i3−1−3i3-2-2-21−3i31+3i3-2-2-21−3i31+3i30000000000000000000000000000000000000000000000000000000000000000000000
χ1048-88-88-4-400-844-8-4-4448-4-422244-2-2-244-2-2-2-4-42220000000000000000000000000000000000000000000000000000000000000000000000
χ1058-88-8-48-4004-8448-44-8-4-42-4224-24-2-24-24-2-2-42-4220000000000000000000000000000000000000000000000000000000000000000000000
χ1068-88-8-4-480044-84-48-84-42-4-422-244-2-2-244-2-22-4-4220000000000000000000000000000000000000000000000000000000000000000000000
χ1078-88-8-4-4-4004444-4-444-4222−1−3i3−1+3i3-2-2-21+3i31−3i3-2-2-21+3i31−3i3222−1−3i3−1+3i30000000000000000000000000000000000000000000000000000000000000000000000
χ1088-88-8-4-4-4004444-4-444-4222−1+3i3−1−3i3-2-2-21−3i31+3i3-2-2-21−3i31+3i3222−1+3i3−1−3i30000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.