Finite Group Databasebeta

← Group #13155944

Character table — Group #13155944

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99
size112222222222222444444444444444444444448888888888881212121212121212121212121212121212121212242424242424242424242424242424242436367272727272727272108108
order1223334466612121212333666666661212121212121212121212123666661212121212122444121212121212121212121212121212126666812121212242424242424242424468121212242422
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-111-1-1
χ31111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-11-1-1-111-1-1-1-1
χ41111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11111-1-1-1-1-1-1-1-111-11-11-1-1-1-111
χ511111111111111111111111111111111111111111111111111-1-1111111111111111111-1-1-1-11-1-1-1-11111111111-11-11-1-1-1-1-1-1
χ611111111111111111111111111111111111111111111111111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-111-1-111
χ711111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-11-1-1-11111
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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χ10222222-2-2222-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2-2-2-2-2-200000000000000000000000000000000000000000000000-22
χ1122222-1222-12-1-122-1-122-1-12-1-1-122-12-1-1-1-1222-1-1-1-12-1-1-1-12-1-1-1-100222222-1-1-1-1-1-1-1-1-1-1-1-1000020000-1-122-1-1-1-1220-10-1000000
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χ1322222-1222-12-1-122-1-122-1-12-1-1-122-12-1-1-1-1222-1-1-1-12-1-1-1-12-1-1-1-100-2-2-2-2-2-2111111111111000020000-1-122-1-1-1-1-2-20101000000
χ1422222-1222-12-1-122-1-122-1-12-1-1-122-12-1-1-1-1222-1-1-1-12-1-1-1-12-1-1-1-100-2-2-2-2-2-21111111111110000-2000011-2-21111220-10-1000000
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χ3522-2-1222-2-1222211-12-1-2-121-211-1-1-2-2-1-11111222-1-2111-1-2-1-1-1112-20033−3−3000033−3−333−3−3-12-1-101-21100000000000000003−300
χ3622-2-1222-2-1222211-12-1-2-121-211-1-1-2-2-1-11111222-1-2111-1-2-1-1-1112-200−3−3330000−3−333−3−333-12-1-101-2110000000000000000−3300
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χ414444-2-2444-2-2-2-244-21-2-2-214-2-2-2-24-2-2-2-2-2-2-2-2-21111-21111-2111100000000000000000000000040000-2-2-2-21111000000000000
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χ5744-44-2-24-44-2-2-2-2-4-4-21-22-21-4222-2422-2-22222-2111-12-1-11-1-211-1-100000000000000000000000000000002i3−2i3−i3i3−i3i3000000000000
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χ814-40-24-20022-423−23−23231-2-20-1200-332000−333−3−2323023−23100-33-100−333−3002i−2iζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−iiζ2−2ζ7−ζ10−2ζ11−ζ2+2ζ7+ζ10+2ζ11−ζ2−2ζ7+ζ10−2ζ11ζ2+2ζ7−ζ10+2ζ11−ii00000000000000000000000000000
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χ834-40-24-20022-4−232323−231-2-20-1200-3320003−3−3323−230−2323100-33-1003−3−33002i−2i−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ii−ζ2−2ζ7+ζ10−2ζ11ζ2+2ζ7−ζ10+2ζ11ζ2−2ζ7−ζ10−2ζ11−ζ2+2ζ7+ζ10+2ζ11−ii00000000000000000000000000000
χ844-40-24-20022-4−232323−231-2-20-1200-3320003−3−3323−230−2323100-33-1003−3−3300−2i2iζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11i−iζ2+2ζ7−ζ10+2ζ11−ζ2−2ζ7+ζ10−2ζ11−ζ2+2ζ7+ζ10+2ζ11ζ2−2ζ7−ζ10−2ζ11i−i00000000000000000000000000000
χ854-40-24-20022-4−2323−23231-2-20-12003-320003−33−3−23230−23231003-3-1003−33−3002i−2iζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2−2ζ7+ζ10−2ζ11ζ2+2ζ7−ζ10+2ζ11−ii−iiζ2−2ζ7−ζ10−2ζ11−ζ2+2ζ7+ζ10+2ζ1100000000000000000000000000000
χ864-40-24-20022-4−2323−23231-2-20-12003-320003−33−3−23230−23231003-3-1003−33−300−2i2i−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2+2ζ7−ζ10+2ζ11−ζ2−2ζ7+ζ10−2ζ11i−ii−i−ζ2+2ζ7+ζ10+2ζ11ζ2−2ζ7−ζ10−2ζ1100000000000000000000000000000
χ87888-4-4-488-4-4-4-4-4-4-4222-422-4-4222-4-4-4222222-422-122-1-1-122-1-1-1-10000000000000000000000000000000000000000000000000
χ88888-4-4-4-8-8-4-4-44444222-422-4-4222444-2-2-2-2-2-24-2-2-122-1-1-1-2-211110000000000000000000000000000000000000000000000000
χ8988-8-4-4-48-8-4-4-4-4-44422242244-2-22-44422-2-2-2-2-422-1-2-211-1-22-1-1110000000000000000000000000000000000000000000000000
χ9088-8-4-4-4-88-4-4-444-4-422242244-2-224-4-4-2-222224-2-2-1-2-211-12-211-1-10000000000000000000000000000000000000000000000000
χ918-808-4800-8-8400008-4-40-8400004000000000000-4000040000000000000000000000000000000000000000000000000000000
χ928-808-4-400-84443−4300-42-404-20000400043−4300000−232320000-200−2323000000000000000000000000000000000000000000000000000
χ938-808-4-400-844−434300-42-404-200004000−43430000023−2320000-20023−23000000000000000000000000000000000000000000000000000
χ948-80-4-48004-840043−43-4-420440000-20000043−43−232300020000-20000−23230000000000000000000000000000000000000000000000000
χ958-80-4-48004-8400−4343-4-420440000-200000−434323−2300020000-2000023−230000000000000000000000000000000000000000000000000
χ968-80-4-4-40044443−4343−432220-2-2006-6-2000−2323−2323−23230−2323-100-331003−33−30000000000000000000000000000000000000000000000000
χ978-80-4-4-40044443−43−43432220-2-200-66-2000−232323−2323−230−2323-1003-31003−3−330000000000000000000000000000000000000000000000000
χ988-80-4-4-400444−434343−432220-2-200-66-200023−23−2323−2323023−23-1003-3100−333−30000000000000000000000000000000000000000000000000
χ998-80-4-4-400444−4343−43432220-2-2006-6-200023−2323−2323−23023−23-100-33100−33−330000000000000000000000000000000000000000000000000

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