Finite Group Databasebeta

← Group #13155945

Character table — Group #13155945

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99
size112222222222222444444444444444444444448888888888881212121212121212121212121212121212121212242424242424242424242424242424242436367272727272727272108108
order1223334466666121233366666666612121212121212121212123666612121212121212224412121212121212121212121212121212666666668242424242424242424468121212242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-11-1-1-111-1-1-1-1
χ31111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-11-1-1-111-1-1
χ41111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111-11-11-1-1-1-111
χ511111111111111111111111111111111111111111111111111-1-1111111111111111111-1-1-1-1-1-1-1-111111111111-11-11-1-1-1-1-1-1
χ611111111111111111111111111111111111111111111111111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11111
χ711111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-11-1-1-111-1-111
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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χ1322222-122222-12-1-1-1-12222-1-12-1-1-1-122-1-1-1-12-1-12-1-1-1-1-122-1-1-1-1-100-2-2-2-2-2-2111111111111000000002-1-122-1-1-1-1-2-20101000000
χ1422222-122222-12-1-1-1-12222-1-12-1-1-1-122-1-1-1-12-1-12-1-1-1-1-122-1-1-1-1-100-2-2-2-2-2-211111111111100000000-211-2-21111220-10-1000000
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χ824-404-2-200-4−2i32i322−2323-21-20−2i32i32-120i3−i30003−3−3i3i0−2323010i3−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
χ834-404-2-200-42i3−2i32223−23-21-202i3−2i32-120−i3i3000−33−3i3i023−23010−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
χ844-404-2-200-42i3−2i32223−23-21-202i3−2i32-120−i3i3000−33−3i3i023−23010−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
χ854-404-2-200-42i3−2i322−2323-21-202i3−2i32-120−i3i30003−33i−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
χ864-404-2-200-42i3−2i322−2323-21-202i3−2i32-120−i3i30003−33i−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
χ87888-4-4-488-4-4-4-4-4-4-4222-422222-422-4-4-42222-422-4-12-1-1-1222-1-1-1-10000000000000000000000000000000000000000000000000
χ88888-4-4-4-8-8-4-4-4-4-444222-422222-422444-2-2-2-24-2-24-12-1-1-1-2-2-211110000000000000000000000000000000000000000000000000
χ8988-8-4-4-48-8-444-4-4-4-42224-2-22224-2-24-4422-2-2-4224-1-211-12-2-2-1-1110000000000000000000000000000000000000000000000000
χ9088-8-4-4-4-88-444-4-4442224-2-22224-2-2-44-4-2-2224-2-2-4-1-211-1-22211-1-10000000000000000000000000000000000000000000000000
χ918-80-48800400-8-800-48-40004-8400000000000000-4000400000000000000000000000000000000000000000000000000000000
χ928-80-48-4004004-843−432-4-4000-24400000043−43000−232302000-2000−2323000000000000000000000000000000000000000000000000000
χ938-80-48-4004004-8−43432-4-4000-244000000−434300023−2302000-200023−23000000000000000000000000000000000000000000000000000
χ948-80-4-48004−4i34i3-8400-4-4202i3−2i344-20−4i34i300000000000202i3−2i3-200000000000000000000000000000000000000000000000000000000
χ958-80-4-480044i3−4i3-8400-4-420−2i32i344-204i3−4i30000000000020−2i32i3-200000000000000000000000000000000000000000000000000000000
χ968-80-4-4-4004−4i34i34443−4322202i3−2i3-2-2-202i3−2i3000−23236i−6i0−23230-10−i3i310003−3−3i3i0000000000000000000000000000000000000000000000000
χ978-80-4-4-4004−4i34i344−434322202i3−2i3-2-2-202i3−2i300023−23−6i6i023−230-10−i3i31000−333i−3i0000000000000000000000000000000000000000000000000
χ988-80-4-4-40044i3−4i34443−432220−2i32i3-2-2-20−2i32i3000−2323−6i6i0−23230-10i3−i310003−33i−3i0000000000000000000000000000000000000000000000000
χ998-80-4-4-40044i3−4i344−43432220−2i32i3-2-2-20−2i32i300023−236i−6i023−230-10i3−i31000−33−3i3i0000000000000000000000000000000000000000000000000

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