Finite Group Databasebeta

← Group #13181513

Character table — Group #13181513

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162C163C164C165C166C167C168
size111122222222224444444444444444444444444444444444444444444444449999181818181818181818185454545454545454111122222222224444444444444444444444444444444444444444444444449999181818181818181818185454545454545454
order1244234666121212123333336666666666666666661212121212121212121212121212121212121212121212122244246666121212124444444422442646661212121266666666666666666666666612121212121212121212121212121212121212121212121222442466661212121244444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i11111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii11111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii
χ51111-11-1-1-1111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-111-1-111-1-11111-11-1-1-1111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-111-1-111-1-1
χ61111-11-1-1-1111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-111-1-1111111-11-1-1-1111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-111-1-111
χ71111-11-1-1-1111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111ii−i−i−i−iii1111-11-1-1-1111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111ii−i−i−i−iii
χ81111-11-1-1-1111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111−i−iiiii−i−i1111-11-1-1-1111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111−i−iiiii−i−i
χ911-1-111-1111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-11111-1-1-1-11-11-11-11-111-1-111-1111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-11111-1-1-1-11-11-11-11-1
χ1011-1-111-1111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-11111-1-1-1-1-11-11-11-1111-1-111-1111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-11111-1-1-1-1-11-11-11-11
χ1111-1-111-1111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11-1-1-1-11111i−ii−i−ii−ii11-1-111-1111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11-1-1-1-11111i−ii−i−ii−ii
χ1211-1-111-1111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11-1-1-1-11111−ii−iii−ii−i11-1-111-1111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11-1-1-1-11111−ii−iii−ii−i
χ1311-1-1-111-1-11-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1111-1-1-1-1111-1-111-1-1111-1-1-111-1-11-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1111-1-1-1-1111-1-111-1-11
χ1411-1-1-111-1-11-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1111-1-1-1-111-111-1-111-111-1-1-111-1-11-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1111-1-1-1-111-111-1-111-1
χ1511-1-1-111-1-11-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1111-1-1-11111-1-1i−i−ii−iii−i11-1-1-111-1-11-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1111-1-1-11111-1-1i−i−ii−iii−i
χ1611-1-1-111-1-11-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1111-1-1-11111-1-1−iii−ii−i−ii11-1-1-111-1-11-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1111-1-1-11111-1-1−iii−ii−i−ii
χ1722222-12-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-10000000022222-12-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-100000000
χ1822222-12-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-2111111110000000022222-12-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-21111111100000000
χ192222-2-1-211-1-1-11122-1-1-1-1-2-2-2-21111111122-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2111111112222-2-2-1-111-1-111000000002222-2-1-211-1-1-11122-1-1-1-1-2-2-2-21111111122-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2111111112222-2-2-1-111-1-11100000000
χ202222-2-1-211-1-1-11122-1-1-1-1-2-2-2-21111111122-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-211111111-2-2-2-22211-1-111-1-1000000002222-2-1-211-1-1-11122-1-1-1-1-2-2-2-21111111122-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-211111111-2-2-2-22211-1-111-1-100000000
χ2122-2-22-1-2-1-1-1111122-1-1-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-211111111-2-2-2-21111111122-2-22-2-1-1-1-111110000000022-2-22-1-2-1-1-1111122-1-1-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-211111111-2-2-2-21111111122-2-22-2-1-1-1-1111100000000
χ2222-2-22-1-2-1-1-1111122-1-1-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-211111111-2-2-2-211111111-2-222-221111-1-1-1-10000000022-2-22-1-2-1-1-1111122-1-1-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-211111111-2-2-2-211111111-2-222-221111-1-1-1-100000000
χ2322-2-2-2-1211-111-1-122-1-1-1-1-2-2-2-21111111122-1-1-1-1-2-2-2-2111111112222-1-1-1-1-1-1-1-122-2-2-22-1-11111-1-10000000022-2-2-2-1211-111-1-122-1-1-1-1-2-2-2-21111111122-1-1-1-1-2-2-2-2111111112222-1-1-1-1-1-1-1-122-2-2-22-1-11111-1-100000000
χ2422-2-2-2-1211-111-1-122-1-1-1-1-2-2-2-21111111122-1-1-1-1-2-2-2-2111111112222-1-1-1-1-1-1-1-1-2-2222-211-1-1-1-1110000000022-2-2-2-1211-111-1-122-1-1-1-1-2-2-2-21111111122-1-1-1-1-2-2-2-2111111112222-1-1-1-1-1-1-1-1-2-2222-211-1-1-1-11100000000
χ252-22i−2i02000-22i−2i00222222000000000000-2-2-2-2-2-22i2i−2i−2i2i2i2i2i−2i−2i−2i−2i0000000000002-22i−2i002-2002i−2i00000000002-22i−2i02000-22i−2i00222222000000000000-2-2-2-2-2-22i2i−2i−2i2i2i2i2i−2i−2i−2i−2i0000000000002-22i−2i002-2002i−2i0000000000
χ262-22i−2i02000-22i−2i00222222000000000000-2-2-2-2-2-22i2i−2i−2i2i2i2i2i−2i−2i−2i−2i000000000000-22−2i2i00-2200−2i2i00000000002-22i−2i02000-22i−2i00222222000000000000-2-2-2-2-2-22i2i−2i−2i2i2i2i2i−2i−2i−2i−2i000000000000-22−2i2i00-2200−2i2i0000000000
χ272-22i−2i0-10−i3i31−ii3−322-1-1-1-10000−i3−i3−i3−i3i3i3i3i3-2-211112i2i−2i−2i−i−i−i−iiiii00003333−3−3−3−32-22i−2i00-11−i3i3−ii3−3000000002-22i−2i0-10−i3i31−ii3−322-1-1-1-10000−i3−i3−i3−i3i3i3i3i3-2-211112i2i−2i−2i−i−i−i−iiiii00003333−3−3−3−32-22i−2i00-11−i3i3−ii3−300000000
χ282-22i−2i0-10−i3i31−ii3−322-1-1-1-10000−i3−i3−i3−i3i3i3i3i3-2-211112i2i−2i−2i−i−i−i−iiiii00003333−3−3−3−3-22−2i2i001-1i3−i3i−i−33000000002-22i−2i0-10−i3i31−ii3−322-1-1-1-10000−i3−i3−i3−i3i3i3i3i3-2-211112i2i−2i−2i−i−i−i−iiiii00003333−3−3−3−3-22−2i2i001-1i3−i3i−i−3300000000
χ292-22i−2i0-10i3−i31−ii−3322-1-1-1-10000i3i3i3i3−i3−i3−i3−i3-2-211112i2i−2i−2i−i−i−i−iiiii0000−3−3−3−333332-22i−2i00-11i3−i3−ii−33000000002-22i−2i0-10i3−i31−ii−3322-1-1-1-10000i3i3i3i3−i3−i3−i3−i3-2-211112i2i−2i−2i−i−i−i−iiiii0000−3−3−3−333332-22i−2i00-11i3−i3−ii−3300000000
χ302-22i−2i0-10i3−i31−ii−3322-1-1-1-10000i3i3i3i3−i3−i3−i3−i3-2-211112i2i−2i−2i−i−i−i−iiiii0000−3−3−3−33333-22−2i2i001-1−i3i3i−i3−3000000002-22i−2i0-10i3−i31−ii−3322-1-1-1-10000i3i3i3i3−i3−i3−i3−i3-2-211112i2i−2i−2i−i−i−i−iiiii0000−3−3−3−33333-22−2i2i001-1−i3i3i−i3−300000000
χ312-2−2i2i02000-2−2i2i00222222000000000000-2-2-2-2-2-2−2i−2i2i2i−2i−2i−2i−2i2i2i2i2i0000000000002-2−2i2i002-200−2i2i00000000002-2−2i2i02000-2−2i2i00222222000000000000-2-2-2-2-2-2−2i−2i2i2i−2i−2i−2i−2i2i2i2i2i0000000000002-2−2i2i002-200−2i2i0000000000
χ322-2−2i2i02000-2−2i2i00222222000000000000-2-2-2-2-2-2−2i−2i2i2i−2i−2i−2i−2i2i2i2i2i000000000000-222i−2i00-22002i−2i00000000002-2−2i2i02000-2−2i2i00222222000000000000-2-2-2-2-2-2−2i−2i2i2i−2i−2i−2i−2i2i2i2i2i000000000000-222i−2i00-22002i−2i0000000000
χ332-2−2i2i0-10−i3i31i−i−3322-1-1-1-10000−i3−i3−i3−i3i3i3i3i3-2-21111−2i−2i2i2iiiii−i−i−i−i0000−3−3−3−333332-2−2i2i00-11−i3i3i−i−33000000002-2−2i2i0-10−i3i31i−i−3322-1-1-1-10000−i3−i3−i3−i3i3i3i3i3-2-21111−2i−2i2i2iiiii−i−i−i−i0000−3−3−3−333332-2−2i2i00-11−i3i3i−i−3300000000
χ342-2−2i2i0-10−i3i31i−i−3322-1-1-1-10000−i3−i3−i3−i3i3i3i3i3-2-21111−2i−2i2i2iiiii−i−i−i−i0000−3−3−3−33333-222i−2i001-1i3−i3−ii3−3000000002-2−2i2i0-10−i3i31i−i−3322-1-1-1-10000−i3−i3−i3−i3i3i3i3i3-2-21111−2i−2i2i2iiiii−i−i−i−i0000−3−3−3−33333-222i−2i001-1i3−i3−ii3−300000000
χ352-2−2i2i0-10i3−i31i−i3−322-1-1-1-10000i3i3i3i3−i3−i3−i3−i3-2-21111−2i−2i2i2iiiii−i−i−i−i00003333−3−3−3−32-2−2i2i00-11i3−i3i−i3−3000000002-2−2i2i0-10i3−i31i−i3−322-1-1-1-10000i3i3i3i3−i3−i3−i3−i3-2-21111−2i−2i2i2iiiii−i−i−i−i00003333−3−3−3−32-2−2i2i00-11i3−i3i−i3−300000000
χ362-2−2i2i0-10i3−i31i−i3−322-1-1-1-10000i3i3i3i3−i3−i3−i3−i3-2-21111−2i−2i2i2iiiii−i−i−i−i00003333−3−3−3−3-222i−2i001-1−i3i3−ii−33000000002-2−2i2i0-10i3−i31i−i3−322-1-1-1-10000i3i3i3i3−i3−i3−i3−i3-2-21111−2i−2i2i2iiiii−i−i−i−i00003333−3−3−3−3-222i−2i001-1−i3i3−ii−3300000000
χ37444444444444441-211-2-211-2-211-2-211-2-21-211-2-21-21-211-2-211-2-211-2-211-2-211-2-20000000000000000000000444444444444441-211-2-211-2-211-2-211-2-21-211-2-21-21-211-2-211-2-211-2-211-2-211-2-20000000000000000000000
χ3844444444444444-21-2-211-2-211-2-211-2-211-21-2-211-21-21-2-211-2-211-2-211-2-211-2-211000000000000000000000044444444444444-21-2-211-2-211-2-211-2-211-21-2-211-21-21-2-211-2-211-2-211-2-211-2-2110000000000000000000000
χ3944444-24-2-2-2-2-2-2-21-2−1−3i32−1+3i321111-2-2−1−3i32−1+3i3211−1−3i32−1+3i32111-2−1−3i32−1+3i32111-21-2−1−3i32−1+3i3211−1−3i32−1+3i321111-2-2−1−3i32−1+3i3211−1−3i32−1+3i3211000000000000000000000044444-24-2-2-2-2-2-2-21-2−1−3i32−1+3i321111-2-2−1−3i32−1+3i3211−1−3i32−1+3i32111-2−1−3i32−1+3i32111-21-2−1−3i32−1+3i3211−1−3i32−1+3i321111-2-2−1−3i32−1+3i3211−1−3i32−1+3i32110000000000000000000000
χ4044444-24-2-2-2-2-2-2-21-2−1+3i32−1−3i321111-2-2−1+3i32−1−3i3211−1+3i32−1−3i32111-2−1+3i32−1−3i32111-21-2−1+3i32−1−3i3211−1+3i32−1−3i321111-2-2−1+3i32−1−3i3211−1+3i32−1−3i3211000000000000000000000044444-24-2-2-2-2-2-2-21-2−1+3i32−1−3i321111-2-2−1+3i32−1−3i3211−1+3i32−1−3i32111-2−1+3i32−1−3i32111-21-2−1+3i32−1−3i3211−1+3i32−1−3i321111-2-2−1+3i32−1−3i3211−1+3i32−1−3i32110000000000000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.