Finite Group Databasebeta

← Group #13144491

Character table — Group #13144491

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size111111222222222444444444444666666666666666688812121212121212121212121212121212121212121212121224242424242424242424242424242424363636363636363636363636727272727272
order1233662226666662444661212121212123333666666666666412126666666612121212121212121212121212121212666612121212121212121212121222446666121212124412121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111-1-11111-1-1-1-11111111111111111-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1
χ411111111111111111-1-11111-1-1-1-11111111111111111-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111-1-111-1-1-1-111111111111111111111-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-111-1-11-111-1-1
χ6111111111111111-1-111-1-1-1-111111111111111111111-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-111-11-1-111
χ7111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11-11-111-1-111-1-1-11-1-111
χ8111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-11-11-1-111-1-1111-111-1-1
χ92222222222222222222222222222-1-1-122-1-1-1-1-1-12-1-1-122222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12-1-1-122-1-1-1-1-1-12-1-1-1000000000000000000
χ10222222222222222222222222222-12-1-1-1-122-1-1-1-1-12-1-1222-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-12-1-1-1-122-1-1-1-1-12-1-1000000000000000000
χ11222222222222222222222222222-1-12-1-1-1-1-122-1-1-1-12-1222-1-1-1-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-12-1-1-1-1-122-1-1-1-12-1000000000000000000
χ12222222222222222222222222222-1-1-12-1-1-1-1-1-122-1-1-12222-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-12-1-1-1-1-1-122-1-1-12000000000000000000
χ1322222222222222222-2-22222-2-2-2-22-1-1-122-1-1-1-1-1-12-1-1-1-2-2-222-1-1-1-1-1-1-2-2-2-21111111111112-1-1-1-2-21111112-1-1-1000000000000000000
χ1422222222222222222-2-22222-2-2-2-2-12-1-1-1-122-1-1-1-1-12-1-1-2-2-2-1-122-1-1-1-11111-2-2-2-211111111-12-1-111-2-21111-12-1-1000000000000000000
χ1522222222222222222-2-22222-2-2-2-2-1-12-1-1-1-1-122-1-1-1-12-1-2-2-2-1-1-1-122-1-111111111-2-2-2-21111-1-12-11111-2-211-1-12-1000000000000000000
χ1622222222222222222-2-22222-2-2-2-2-1-1-12-1-1-1-1-1-122-1-1-12-2-2-2-1-1-1-1-1-122111111111111-2-2-2-2-1-1-12111111-2-2-1-1-12000000000000000000
χ17222222222222222-2-222-2-2-2-222222-1-1-122-1-1-1-1-1-12-1-1-1-2-2-222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2111-2-2111111-2111000000000000000000
χ18222222222222222-2-222-2-2-2-22222-12-1-1-1-122-1-1-1-1-12-1-1-2-2-2-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-11-21111-2-211111-211000000000000000000
χ19222222222222222-2-222-2-2-2-22222-1-12-1-1-1-1-122-1-1-1-12-1-2-2-2-1-1-1-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-111-211111-2-21111-21000000000000000000
χ20222222222222222-2-222-2-2-2-22222-1-1-12-1-1-1-1-1-122-1-1-12-2-2-2-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-12222111-2111111-2-2111-2000000000000000000
χ21222222222222222-2-2-2-2-2-2-2-2-2-2-2-22-1-1-122-1-1-1-1-1-12-1-1-122222-1-1-1-1-1-1-2-2-2-2111111111111-211122-1-1-1-1-1-1-2111000000000000000000
χ22222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-12-1-1-1-122-1-1-1-1-12-1-1222-1-122-1-1-1-11111-2-2-2-2111111111-211-1-122-1-1-1-11-211000000000000000000
χ23222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-1-12-1-1-1-1-122-1-1-1-12-1222-1-1-1-122-1-111111111-2-2-2-2111111-21-1-1-1-122-1-111-21000000000000000000
χ24222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-1-1-12-1-1-1-1-1-122-1-1-12222-1-1-1-1-1-122111111111111-2-2-2-2111-2-1-1-1-1-1-122111-2000000000000000000
χ252222222-2-222-2-2-2-22-20022-2-200002222222222222222000-2-2-2-2-2-2-2-20000000000000000222200000000-2-2-2-2000000000000000000
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χ272222222-2-222-2-2-2-22-20022-2-200002-1-1-122-1-1-1-1-1-12-1-1-1000-2-21111110000i3i3−i3−i3i3i3−i3−i3i3i3−i3−i32-1-1-100i3−i3i3−i3i3−i3-2111000000000000000000
χ282222222-2-222-2-2-2-22-20022-2-20000-12-1-1-1-122-1-1-1-1-12-1-100011-2-21111−i3−i3i3i30000−i3−i3i3i3i3i3−i3−i3-12-1-1−i3i300−i3i3i3−i31-211000000000000000000
χ292222222-2-222-2-2-2-22-20022-2-20000-12-1-1-1-122-1-1-1-1-12-1-100011-2-21111i3i3−i3−i30000i3i3−i3−i3−i3−i3i3i3-12-1-1i3−i300i3−i3−i3i31-211000000000000000000
χ302222222-2-222-2-2-2-22-20022-2-20000-1-12-1-1-1-1-122-1-1-1-12-10001111-2-211−i3−i3i3i3i3i3−i3−i30000−i3−i3i3i3-1-12-1−i3i3i3−i300−i3i311-21000000000000000000
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χ372222222-2-222-2-2-2-2-2200-2-2220000-12-1-1-1-122-1-1-1-1-12-1-100011-2-21111−i3−i3i3i30000−i3−i3i3i3i3i3−i3−i31-211i3−i300i3−i3−i3i3-12-1-1000000000000000000
χ382222222-2-222-2-2-2-2-2200-2-2220000-12-1-1-1-122-1-1-1-1-12-1-100011-2-21111i3i3−i3−i30000i3i3−i3−i3−i3−i3i3i31-211−i3i300−i3i3i3−i3-12-1-1000000000000000000
χ392222222-2-222-2-2-2-2-2200-2-2220000-1-12-1-1-1-1-122-1-1-1-12-10001111-2-211−i3−i3i3i3i3i3−i3−i30000−i3−i3i3i311-21i3−i3−i3i300i3−i3-1-12-1000000000000000000
χ402222222-2-222-2-2-2-2-2200-2-2220000-1-12-1-1-1-1-122-1-1-1-12-10001111-2-211i3i3−i3−i3−i3−i3i3i30000i3i3−i3−i311-21−i3i3i3−i300−i3i3-1-12-1000000000000000000
χ412222222-2-222-2-2-2-2-2200-2-2220000-1-1-12-1-1-1-1-1-122-1-1-12000111111-2-2−i3−i3i3i3−i3−i3i3i3i3i3−i3−i30000111-2i3−i3i3−i3−i3i300-1-1-12000000000000000000
χ422222222-2-222-2-2-2-2-2200-2-2220000-1-1-12-1-1-1-1-1-122-1-1-12000111111-2-2i3i3−i3−i3i3i3−i3−i3−i3−i3i3i30000111-2−i3i3−i3i3i3−i300-1-1-12000000000000000000
χ43222222-22-2-2-222-2-20000000000002222-2-2-2-2-2-2-2-222220002-22-22-22-200000000000000000000000000000000020-2002200-2-2000000
χ44222222-22-2-2-222-2-20000000000002222-2-2-2-2-2-2-2-222220002-22-22-22-2000000000000000000000000000000000-20200-2-20022000000
χ45222222-2-22-2-2-2-2220000000000002222-2-2-2-2-2-2-2-22222000-22-22-22-220000000000000000000000000000000020-202200-2-200000000
χ46222222-2-22-2-2-2-2220000000000002222-2-2-2-2-2-2-2-22222000-22-22-22-2200000000000000000000000000000000-2020-2-2002200000000
χ4733−3−3i32−3+3i32−3−3i32−3+3i32333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i323333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i3200000000000000003−3−3i32−3+3i3200000000000000000000000000000000000000001111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211−1−i32−1+i32−1−i32−1+i32
χ4833−3−3i32−3+3i32−3−3i32−3+3i32333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i323333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i3200000000000000003−3−3i32−3+3i320000000000000000000000000000000000000000-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i32-1-11+i321−i321+i321−i32
χ4933−3−3i32−3+3i32−3−3i32−3+3i32333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233-3-3−3−3i32−3+3i32−3−3i32−3+3i323+3i323+3i323−3i323−3i320000000000000000-33+3i323−3i3200000000000000000000000000000000000000001111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-11+i321−i321+i321−i32
χ5033−3−3i32−3+3i32−3−3i32−3+3i32333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233-3-3−3−3i32−3+3i32−3−3i32−3+3i323+3i323+3i323−3i323−3i320000000000000000-33+3i323−3i320000000000000000000000000000000000000000-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i3211−1−i32−1+i32−1−i32−1+i32
χ5133−3−3i32−3+3i32−3−3i32−3+3i32333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-3-3333+3i323−3i323+3i323−3i32−3−3i32−3−3i32−3+3i32−3+3i320000000000000000-33+3i323−3i3200000000000000000000000000000000000000001-11-1−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i321-1−1−i32−1+i321+i321−i32
χ5233−3−3i32−3+3i32−3−3i32−3+3i32333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-3-3333+3i323−3i323+3i323−3i32−3−3i32−3−3i32−3+3i32−3+3i320000000000000000-33+3i323−3i320000000000000000000000000000000000000000-11-111+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i32-111+i321−i32−1−i32−1+i32
χ5333−3−3i32−3+3i32−3−3i32−3+3i32333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-3-3-3-33+3i323−3i323+3i323−3i323+3i323+3i323−3i323−3i3200000000000000003−3−3i32−3+3i3200000000000000000000000000000000000000001-11-1−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i32-111+i321−i32−1−i32−1+i32
χ5433−3−3i32−3+3i32−3−3i32−3+3i32333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-3-3-3-33+3i323−3i323+3i323−3i323+3i323+3i323−3i323−3i3200000000000000003−3−3i32−3+3i320000000000000000000000000000000000000000-11-111+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i321-1−1−i32−1+i321+i321−i32
χ5533−3+3i32−3−3i32−3+3i32−3−3i32333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i323333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32−3−3i3200000000000000003−3+3i32−3−3i3200000000000000000000000000000000000000001111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211−1+i32−1−i32−1+i32−1−i32
χ5633−3+3i32−3−3i32−3+3i32−3−3i32333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i323333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32−3−3i3200000000000000003−3+3i32−3−3i320000000000000000000000000000000000000000-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i32-1-11−i321+i321−i321+i32
χ5733−3+3i32−3−3i32−3+3i32−3−3i32333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i3233-3-3−3+3i32−3−3i32−3+3i32−3−3i323−3i323−3i323+3i323+3i320000000000000000-33−3i323+3i3200000000000000000000000000000000000000001111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-11−i321+i321−i321+i32
χ5833−3+3i32−3−3i32−3+3i32−3−3i32333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i3233-3-3−3+3i32−3−3i32−3+3i32−3−3i323−3i323−3i323+3i323+3i320000000000000000-33−3i323+3i320000000000000000000000000000000000000000-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i3211−1+i32−1−i32−1+i32−1−i32
χ5933−3+3i32−3−3i32−3+3i32−3−3i32333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32-3-3333−3i323+3i323−3i323+3i32−3+3i32−3+3i32−3−3i32−3−3i320000000000000000-33−3i323+3i3200000000000000000000000000000000000000001-11-1−1+i32−1−i321−i321+i32−1+i32−1−i321−i321+i321-1−1+i32−1−i321−i321+i32
χ6033−3+3i32−3−3i32−3+3i32−3−3i32333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32-3-3333−3i323+3i323−3i323+3i32−3+3i32−3+3i32−3−3i32−3−3i320000000000000000-33−3i323+3i320000000000000000000000000000000000000000-11-111−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i32-111−i321+i32−1+i32−1−i32
χ6133−3+3i32−3−3i32−3+3i32−3−3i32333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32-3-3-3-33−3i323+3i323−3i323+3i323−3i323−3i323+3i323+3i3200000000000000003−3+3i32−3−3i3200000000000000000000000000000000000000001-11-1−1+i32−1−i321−i321+i32−1+i32−1−i321−i321+i32-111−i321+i32−1+i32−1−i32
χ6233−3+3i32−3−3i32−3+3i32−3−3i32333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32-3-3-3-33−3i323+3i323−3i323+3i323−3i323−3i323+3i323+3i3200000000000000003−3+3i32−3−3i320000000000000000000000000000000000000000-11-111−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i321-1−1+i32−1−i321−i321+i32
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χ10212-12−6−6i3−6+6i36+6i36−6i300000000000−6i6i0000−6ζ116ζ11−6ζ76ζ700000000000000000000000000000000000000000000000000000000000000000000000000000
χ10312-12−6+6i3−6−6i36−6i36+6i3000000000006i−6i00006ζ7−6ζ76ζ11−6ζ1100000000000000000000000000000000000000000000000000000000000000000000000000000
χ10412-12−6+6i3−6−6i36−6i36+6i300000000000−6i6i0000−6ζ76ζ7−6ζ116ζ1100000000000000000000000000000000000000000000000000000000000000000000000000000

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