Finite Group Databasebeta

← Group #13159070

Character table — Group #13159070

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size11222222222222222444444444444444444444444444444888888888888888888888888888888888881212242424242424242424242424242424242436363636363636367272108108216
order1222233333666666633336666666666666666666666666646666666612121212121212121212121212121212121212121212121212122446666121212121212121212121212244412121212612244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111
χ511111111111111111111111111111111111111111111111-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1
χ611111111111111111111111111111111111111111111111-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11
χ711111111111111111111111111111111111111111111111-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-11
χ811111111111111111111111111111111111111111111111-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1111111-1-111-1
χ9222222222-1-1-12222-1-1-1-1-12222-1-1-1-1-1-12222-1-1-1-1-1-1-1-122222-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000002222-1-1-1-1-1-1000
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χ11222222222-1-1-12222-1-1-1-1-12222-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-2-1-1-1-1-1-1-1-111-2-2-2-2-2-2-2-21111111111111111000000000000000000022-2-21111-1-1000
χ12222222222-1-1-12222-1-1-1-1-12222-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-2-1-1-1-1-1-1-1-111-2-2-2-2-2-2-2-211111111111111110000000000000000000-2-222-1-1-1-111000
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χ5422-2-22-1-1-122-2-2-1-1-122-1-1-12-1-1-12-22-1-1-12111-2111111-2-2111-201-11-11-1-2200−33−333−300−33−33−33−333−33−30000-220111-2-1-1-123−33−3−33000000000000000
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χ9044-4-444-2-2-2-2224-2-2-2-2-21114-2-2-22-2-2111-422222-1-1-1-1-1-1-422202-2-11-11-110000−2323−2323−232300003−33−33−33−33−33−300000000000000000000000000000000
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χ9344-4-44-2-24-2-222-2-24-2-211-21-2-24-22-211-2122-42-1-1-1-122-1-122-420-11-112-2-110023−23−23230023−23−33−333−33−30000−33−3300000000000000000000000000000000
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χ9544-4-44-2-2-24-222-2-2-24-2111-2-2-2-242-2111-2222-4-1-1-1-1-1-122222-40-11-11-112-20023−2323−23−232300−33−33−33−333−33−3000000000000000000000000000000000000
χ9644-4-44-2-2-24-222-2-2-24-2111-2-2-2-242-2111-2222-4-1-1-1-1-1-122222-40-11-11-112-200−2323−232323−23003−33−33−33−3−33−33000000000000000000000000000000000000
χ974-40004444400-4-4-4-4-44444000000-4-4-4-40000000000000000000000000000000000000000000000000000000000000000000000002i−2i2i−2i2i−2i00000
χ984-40004444400-4-4-4-4-44444000000-4-4-4-4000000000000000000000000000000000000000000000000000000000000000000000000−2i2i−2i2i−2i2i00000
χ994-40004444-2−2i32i3-4-4-4-42-2-2-2-200000022220000−2i32i3−2i32i3−2i32i3−2i32i30000000000000000000000000000000000000000000000000000000000002i−2i2ζ11−2ζ112ζ7−2ζ700000
χ1004-40004444-2−2i32i3-4-4-4-42-2-2-2-200000022220000−2i32i3−2i32i3−2i32i3−2i32i3000000000000000000000000000000000000000000000000000000000000−2i2i−2ζ112ζ11−2ζ72ζ700000
χ1014-40004444-22i3−2i3-4-4-4-42-2-2-2-2000000222200002i3−2i32i3−2i32i3−2i32i3−2i30000000000000000000000000000000000000000000000000000000000002i−2i2ζ7−2ζ72ζ11−2ζ1100000
χ1024-40004444-22i3−2i3-4-4-4-42-2-2-2-2000000222200002i3−2i32i3−2i32i3−2i32i3−2i3000000000000000000000000000000000000000000000000000000000000−2i2i−2ζ72ζ7−2ζ112ζ1100000
χ1038-80008-4-4-4800-8444-88-4-4-4000000-844400000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1048-80008-4-4-4-4−4i34i3-84444-42220000004-2-2-20000−4i34i32i3−2i32i3−2i32i3−2i300000000000000000000000000000000000000000000000000000000000000000000000
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χ1068-8000-48-4-48004-844-8-48-4-40000004-84400000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1078-8000-48-4-4-4−4i34i34-84442-422000000-24-2-200002i3−2i3−4i34i32i3−2i32i3−2i300000000000000000000000000000000000000000000000000000000000000000000000
χ1088-8000-48-4-4-44i3−4i34-84442-422000000-24-2-20000−2i32i34i3−4i3−2i32i3−2i32i300000000000000000000000000000000000000000000000000000000000000000000000
χ1098-8000-4-48-480044-84-8-4-48-400000044-8400000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1108-8000-4-48-4-4−4i34i344-84422-42000000-2-24-200002i3−2i32i3−2i3−4i34i32i3−2i300000000000000000000000000000000000000000000000000000000000000000000000
χ1118-8000-4-48-4-44i3−4i344-84422-42000000-2-24-20000−2i32i3−2i32i34i3−4i3−2i32i300000000000000000000000000000000000000000000000000000000000000000000000
χ1128-8000-4-4-48800444-8-8-4-4-48000000444-800000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1138-8000-4-4-48-4−4i34i3444-84222-4000000-2-2-2400002i3−2i32i3−2i32i3−2i3−4i34i300000000000000000000000000000000000000000000000000000000000000000000000
χ1148-8000-4-4-48-44i3−4i3444-84222-4000000-2-2-240000−2i32i3−2i32i3−2i32i34i3−4i300000000000000000000000000000000000000000000000000000000000000000000000

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