Finite Group Databasebeta

← Group #13155930

Character table — Group #13155930

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99
size112222222222222444444444444444444444448888888888881212121212121212121212121212121212121212242424242424242424242424242424242436367272727272727272108108
order1223334466666121233366666666612121212121212121212123666612121212121212444412121212121212121212121212121212812121212121212122424242424242424242666812242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111-111111111-1-1-1-1-1-1-1-1-1-11-111-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-11-111-1-1
χ41111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-11-1-1-11-1-111
χ511111111111111111111111111111111111111111111111111-1-11111111111111111111-1-1-1-1-1-1-1-11111111111-11-1-1-11-1-1-1-1
χ611111111111111111111111111111111111111111111111111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11111
χ711111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-11-111-1-1-1-111
χ811111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1
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χ1322222-122-1-12-12222-1-12-1-12-12-1-1-1-1-12-1-1-1-12222-12-1-1-12-1-1-1-1-1-1-2-222-1-1-1-12222-1-1-1-1-1-1-1-10-21-2111110000000000-2011000000
χ1422222-122-1-12-12222-1-12-1-12-12-1-1-1-1-12-1-1-1-12222-12-1-1-12-1-1-1-1-1-1-2-2-2-21111-2-2-2-2111111110-21-211111000000000020-1-1000000
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χ824-404-2-200−2i32i3-422−2323-2-210−2i32i32-10i3−i320003−3−3i3i0−2323010i3−i3-10003−3−3i3i00−2i2i−2ζ72ζ7−2ζ112ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2+ζ7−2ζ10ζ2−ζ7+2ζ10ζ2+ζ7+2ζ10−ζ2−ζ7−2ζ102ζ2+ζ10+ζ11−2ζ2−ζ10−ζ11−2ζ2−ζ10+ζ112ζ2+ζ10−ζ1100000000000000000000000000000
χ834-404-2-2002i3−2i3-42223−23-2-2102i3−2i32-10−i3i32000−33−3i3i023−23010−i3i3-1000−33−3i3i002i−2i2ζ11−2ζ112ζ7−2ζ7−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ112ζ2+ζ10−ζ11−2ζ2−ζ10+ζ11−2ζ2−ζ10−ζ112ζ2+ζ10+ζ11−ζ2−ζ7−2ζ10ζ2+ζ7+2ζ10ζ2−ζ7+2ζ10−ζ2+ζ7−2ζ1000000000000000000000000000000
χ844-404-2-2002i3−2i3-42223−23-2-2102i3−2i32-10−i3i32000−33−3i3i023−23010−i3i3-1000−33−3i3i00−2i2i−2ζ112ζ11−2ζ72ζ7ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−2ζ2−ζ10+ζ112ζ2+ζ10−ζ112ζ2+ζ10+ζ11−2ζ2−ζ10−ζ11ζ2+ζ7+2ζ10−ζ2−ζ7−2ζ10−ζ2+ζ7−2ζ10ζ2−ζ7+2ζ1000000000000000000000000000000
χ854-404-2-2002i3−2i3-422−2323-2-2102i3−2i32-10−i3i320003−33i−3i0−2323010−i3i3-10003−33i−3i002i−2i2ζ11−2ζ112ζ7−2ζ7ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−2ζ2−ζ10−ζ112ζ2+ζ10+ζ112ζ2+ζ10−ζ11−2ζ2−ζ10+ζ11ζ2−ζ7+2ζ10−ζ2+ζ7−2ζ10−ζ2−ζ7−2ζ10ζ2+ζ7+2ζ1000000000000000000000000000000
χ864-404-2-2002i3−2i3-422−2323-2-2102i3−2i32-10−i3i320003−33i−3i0−2323010−i3i3-10003−33i−3i00−2i2i−2ζ112ζ11−2ζ72ζ7−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ112ζ2+ζ10+ζ11−2ζ2−ζ10−ζ11−2ζ2−ζ10+ζ112ζ2+ζ10−ζ11−ζ2+ζ7−2ζ10ζ2−ζ7+2ζ10ζ2+ζ7+2ζ10−ζ2−ζ7−2ζ1000000000000000000000000000000
χ87888-4-4-488-4-4-4-4-4-4-4222-42222-4222-4-4-42222-422-4-12-1-1-1222-1-1-1-10000000000000000000000000000000000000000000000000
χ88888-4-4-4-8-8-4-4-4-4-444222-42222-4222444-2-2-2-24-2-24-12-1-1-1-2-2-211110000000000000000000000000000000000000000000000000
χ8988-8-4-4-48-844-4-4-4-4-42224-2-2224-2-22-44422-2-2-4224-1-211-1-22-2-1-1110000000000000000000000000000000000000000000000000
χ9088-8-4-4-4-8844-4-4-4442224-2-2224-2-224-4-4-2-2224-2-2-4-1-211-12-2211-1-10000000000000000000000000000000000000000000000000
χ918-80-48800004-8-800-4-480004-8000400000000000-4000400000000000000000000000000000000000000000000000000000000
χ928-80-48-400−4i34i344-800-42-402i3−2i3440−4i34i3-200000000000202i3−2i3-200000000000000000000000000000000000000000000000000000000
χ938-80-48-4004i3−4i344-800-42-40−2i32i34404i3−4i3-20000000000020−2i32i3-200000000000000000000000000000000000000000000000000000000
χ948-80-4-4800004-8443−432-4-4000-24000400043−43000−232302000-2000−2323000000000000000000000000000000000000000000000000000
χ958-80-4-4800004-84−43432-4-4000-240004000−434300023−2302000-200023−23000000000000000000000000000000000000000000000000000
χ968-80-4-4-400−4i34i344443−4322202i3−2i3-2-202i3−2i3-2000−23236i−6i0−23230-10−i3i310003−3−3i3i0000000000000000000000000000000000000000000000000
χ978-80-4-4-400−4i34i3444−434322202i3−2i3-2-202i3−2i3-200023−23−6i6i023−230-10−i3i31000−333i−3i0000000000000000000000000000000000000000000000000
χ988-80-4-4-4004i3−4i344443−432220−2i32i3-2-20−2i32i3-2000−2323−6i6i0−23230-10i3−i310003−33i−3i0000000000000000000000000000000000000000000000000
χ998-80-4-4-4004i3−4i3444−43432220−2i32i3-2-20−2i32i3-200023−236i−6i023−230-10i3−i31000−33−3i3i0000000000000000000000000000000000000000000000000

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