Finite Group Databasebeta

← Group #13147393

Character table — Group #13147393

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size1111112224441212121212121212121212121212121218181818181836363636363636363636363636363611111122244412121212121212121212121212121212181818181818363636363636363636363636363636
order12336626641212336666661212121212121212441212121248888121224242424242424242266662664121266666666121212121212121244121212124888812122424242424242424
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1ii−i−i-1-1iiii−i−i−i−i1111111111111111111111111111-1-1-1-1-1-1-1ii−i−i-1-1iiii−i−i−i−i
χ41111111111111111111111111111-1-1-1-1-1-1-1−i−iii-1-1−i−i−i−iiiii1111111111111111111111111111-1-1-1-1-1-1-1−i−iii-1-1−i−i−i−iiiii
χ5111111111-1-1-111111111-1-1-1-1-1-1-1-1111111-11-11-1-1-111-1-111-1-1111111111-1-1-111111111-1-1-1-1-1-1-1-1111111-11-11-1-1-111-1-111-1-1
χ6111111111-1-1-111111111-1-1-1-1-1-1-1-1111111-1-11-11-1-1-1-111-1-111111111111-1-1-111111111-1-1-1-1-1-1-1-1111111-1-11-11-1-1-1-111-1-111
χ7111111111-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11i−i−ii11ii−i−i−i−iii111111111-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11i−i−ii11ii−i−i−i−iii
χ8111111111-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11−iii−i11−i−iiiii−i−i111111111-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11−iii−i11−i−iiiii−i−i
χ9222222-2-2-200022-2-2-2-222000000002-222-2-2000000000000000222222-2-2-200022-2-2-2-222000000002-222-2-2000000000000000
χ10222222-2-2-200022-2-2-2-22200000000-22-2-222000000000000000222222-2-2-200022-2-2-2-22200000000-22-2-222000000000000000
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χ1433−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i323−3−3i32−3+3i320000000000000000-1-11+i321−i321+i321−i32-1-1-1-1-11+i321−i321−i321+i321−i321+i321−i321+i321−i321+i3233−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i323−3−3i32−3+3i320000000000000000-1-11+i321−i321+i321−i32-1-1-1-1-11+i321−i321−i321+i321−i321+i321−i321+i321−i321+i32
χ1533−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i32-33+3i323−3i32000000000000000011−1−i32−1+i32−1−i32−1+i32-1i−i−ii1+i321−i32ζ7ζ11−ζ7−ζ11−ζ7−ζ11ζ7ζ1133−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i32-33+3i323−3i32000000000000000011−1−i32−1+i32−1−i32−1+i32-1i−i−ii1+i321−i32ζ7ζ11−ζ7−ζ11−ζ7−ζ11ζ7ζ11
χ1633−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i32-33+3i323−3i32000000000000000011−1−i32−1+i32−1−i32−1+i32-1−iii−i1+i321−i32−ζ7−ζ11ζ7ζ11ζ7ζ11−ζ7−ζ1133−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i32-33+3i323−3i32000000000000000011−1−i32−1+i32−1−i32−1+i32-1−iii−i1+i321−i32−ζ7−ζ11ζ7ζ11ζ7ζ11−ζ7−ζ11
χ1733−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i32-33+3i323−3i320000000000000000-1-11+i321−i321+i321−i3211-11-1−1−i32−1+i32−1+i32−1−i321−i321+i32−1+i32−1−i321−i321+i3233−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i32-33+3i323−3i320000000000000000-1-11+i321−i321+i321−i3211-11-1−1−i32−1+i32−1+i32−1−i321−i321+i32−1+i32−1−i321−i321+i32
χ1833−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i32-33+3i323−3i320000000000000000-1-11+i321−i321+i321−i321-11-11−1−i32−1+i321−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i3233−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i32-33+3i323−3i320000000000000000-1-11+i321−i321+i321−i321-11-11−1−i32−1+i321−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i32
χ1933−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i323−3+3i32−3−3i32000000000000000011−1+i32−1−i32−1+i32−1−i321ii−i−i−1+i32−1−i32ζ11ζ7ζ11ζ7−ζ11−ζ7−ζ11−ζ733−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i323−3+3i32−3−3i32000000000000000011−1+i32−1−i32−1+i32−1−i321ii−i−i−1+i32−1−i32ζ11ζ7ζ11ζ7−ζ11−ζ7−ζ11−ζ7
χ2033−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i323−3+3i32−3−3i32000000000000000011−1+i32−1−i32−1+i32−1−i321−i−iii−1+i32−1−i32−ζ11−ζ7−ζ11−ζ7ζ11ζ7ζ11ζ733−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i323−3+3i32−3−3i32000000000000000011−1+i32−1−i32−1+i32−1−i321−i−iii−1+i32−1−i32−ζ11−ζ7−ζ11−ζ7ζ11ζ7ζ11ζ7
χ2133−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i323−3+3i32−3−3i320000000000000000-1-11−i321+i321−i321+i32-111111−i321+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3233−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i323−3+3i32−3−3i320000000000000000-1-11−i321+i321−i321+i32-111111−i321+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32
χ2233−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i323−3+3i32−3−3i320000000000000000-1-11−i321+i321−i321+i32-1-1-1-1-11−i321+i321+i321−i321+i321−i321+i321−i321+i321−i3233−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i323−3+3i32−3−3i320000000000000000-1-11−i321+i321−i321+i32-1-1-1-1-11−i321+i321+i321−i321+i321−i321+i321−i321+i321−i32
χ2333−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i32-33−3i323+3i32000000000000000011−1+i32−1−i32−1+i32−1−i32-1i−i−ii1−i321+i32ζ11ζ7−ζ11−ζ7−ζ11−ζ7ζ11ζ733−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i32-33−3i323+3i32000000000000000011−1+i32−1−i32−1+i32−1−i32-1i−i−ii1−i321+i32ζ11ζ7−ζ11−ζ7−ζ11−ζ7ζ11ζ7
χ2433−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i32-33−3i323+3i32000000000000000011−1+i32−1−i32−1+i32−1−i32-1−iii−i1−i321+i32−ζ11−ζ7ζ11ζ7ζ11ζ7−ζ11−ζ733−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i32-33−3i323+3i32000000000000000011−1+i32−1−i32−1+i32−1−i32-1−iii−i1−i321+i32−ζ11−ζ7ζ11ζ7ζ11ζ7−ζ11−ζ7
χ2533−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i32-33−3i323+3i320000000000000000-1-11−i321+i321−i321+i3211-11-1−1+i32−1−i32−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i3233−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i32-33−3i323+3i320000000000000000-1-11−i321+i321−i321+i3211-11-1−1+i32−1−i32−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i32
χ2633−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i32-33−3i323+3i320000000000000000-1-11−i321+i321−i321+i321-11-11−1+i32−1−i321+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i3233−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i32-33−3i323+3i320000000000000000-1-11−i321+i321−i321+i321-11-11−1+i32−1−i321+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i32
χ274444444444441-211-2-21-21111-2-2-2-20000000000000000000004444444444441-211-2-21-21111-2-2-2-2000000000000000000000
χ28444444444444-21-2-211-21-2-2-2-21111000000000000000000000444444444444-21-2-211-21-2-2-2-21111000000000000000000000
χ29444444444-4-4-41-211-2-21-2-1-1-1-12222000000000000000000000444444444-4-4-41-211-2-21-2-1-1-1-12222000000000000000000000
χ30444444444-4-4-4-21-2-211-212222-1-1-1-1000000000000000000000444444444-4-4-4-21-2-211-212222-1-1-1-1000000000000000000000
χ31444444-4-4-40001-2-1-1221-233-3-30000000000000000000000000444444-4-4-40001-2-1-1221-233-3-30000000000000000000000000
χ32444444-4-4-40001-2-1-1221-2-3-3330000000000000000000000000444444-4-4-40001-2-1-1221-2-3-3330000000000000000000000000
χ33444444-4-4-4000-2122-1-1-21000033-3-3000000000000000000000444444-4-4-4000-2122-1-1-21000033-3-3000000000000000000000
χ34444444-4-4-4000-2122-1-1-210000-3-333000000000000000000000444444-4-4-4000-2122-1-1-210000-3-333000000000000000000000
χ354-444-4-40000001-23-300-123−33−30023−230000000000000000000004-444-4-40000001-23-300-123−33−30023−23000000000000000000000
χ364-444-4-40000001-23-300-12−33−3300−23230000000000000000000004-444-4-40000001-23-300-12−33−3300−2323000000000000000000000
χ374-444-4-40000001-2-3300-123−3−3323−23000000000000000000000004-444-4-40000001-2-3300-123−3−3323−2300000000000000000000000
χ384-444-4-40000001-2-3300-12−333−3−2323000000000000000000000004-444-4-40000001-2-3300-12−333−3−232300000000000000000000000
χ394-444-4-4000000440000-4-4000000000000000000000000000004-444-4-4000000440000-4-400000000000000000000000000000
χ404-444-4-4000000-21003-32-10023−233−3−330000000000000000000004-444-4-4000000-21003-32-10023−233−3−33000000000000000000000
χ414-444-4-4000000-21003-32-100−2323−333−30000000000000000000004-444-4-4000000-21003-32-100−2323−333−3000000000000000000000
χ424-444-4-4000000-2100-332-123−2300−33−330000000000000000000004-444-4-4000000-2100-332-123−2300−33−33000000000000000000000
χ434-444-4-4000000-2100-332-1−2323003−33−30000000000000000000004-444-4-4000000-2100-332-1−2323003−33−3000000000000000000000
χ4466−3−3i3−3+3i3−3−3i3−3+3i3-63+3i33−3i300000000000000000002-2−1−i3−1+i31+i31−i300000000000000066−3−3i3−3+3i3−3−3i3−3+3i3-63+3i33−3i300000000000000000002-2−1−i3−1+i31+i31−i3000000000000000
χ4566−3−3i3−3+3i3−3−3i3−3+3i3-63+3i33−3i30000000000000000000-221+i31−i3−1−i3−1+i300000000000000066−3−3i3−3+3i3−3−3i3−3+3i3-63+3i33−3i30000000000000000000-221+i31−i3−1−i3−1+i3000000000000000
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χ5111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111
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χ531111111111111111111111111111-1-1-1-1-1-1-1−i−iii-1-1−i−i−i−iiiii-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111ii−i−i11iiii−i−i−i−i
χ54111111111-1-1-111111111-1-1-1-1-1-1-1-1111111-11-11-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11-11-1111-1-111-1-111
χ55111111111-1-1-111111111-1-1-1-1-1-1-1-1111111-1-11-11-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-11-11111-1-111-1-1
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χ58222222-2-2-200022-2-2-2-222000000002-222-2-2000000000000000-2-2-2-2-2-2222000-2-22222-2-200000000-22-2-222000000000000000
χ59222222-2-2-200022-2-2-2-22200000000-22-2-222000000000000000-2-2-2-2-2-2222000-2-22222-2-2000000002-222-2-2000000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.