Finite Group Databasebeta

← Group #13145732

Character table — Group #13145732

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162
size111122222222222222222222222222222244444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444363636363636363636363636363636363636363636363636363636363636363636363636
order1244222333444666666666121212121212121212121212333336666666666666666666666666666666666666666612121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212444444448888121212121212121212121212121212122424242424242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111-1-1111-1-1111111-1-1-1-1111111-1-1-1-1111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−i11-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1
χ611111-1-1111-1-1111111-1-1-1-1111111-1-1-1-1111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i−i−iii-1-111iiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111
χ711111-1-1111-1-1111111-1-1-1-1111111-1-1-1-1111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iiiii−i−i-1-111−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111
χ811111-1-1111-1-1111111-1-1-1-1111111-1-1-1-1111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii11-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1
χ91111-11-11111-1-1-1-111111-1-111111111-1-1-1-111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111111-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11-11-1i−ii−ii−ii−i11-1-111-1-1ii−i−iii−i−iii−i−iii−i−i
χ101111-11-11111-1-1-1-111111-1-111111111-1-1-1-111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111111-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11-11-1−ii−ii−ii−ii11-1-111-1-1−i−iii−i−iii−i−iii−i−iii
χ111111-11-11111-1-1-1-111111-1-111111111-1-1-1-111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111111-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-11-11i−ii−i−ii−ii-1-111-1-111ii−i−iii−i−i−i−iii−i−iii
χ121111-11-11111-1-1-1-111111-1-111111111-1-1-1-111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111111-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-11-11−ii−iii−ii−i-1-111-1-111−i−iii−i−iiiii−i−iii−i−i
χ131111-1-11111-11-1-1-1111-1-111111111-1-111-1-111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111i−i−ii1-1-11−iii−iii−i−i−i−iii11-1-1-1-111−i−iiiii−i−i
χ141111-1-11111-11-1-1-1111-1-111111111-1-111-1-111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111i−i−ii-111-1i−i−iiii−i−i−i−iii-1-11111-1-1ii−i−i−i−iii
χ151111-1-11111-11-1-1-1111-1-111111111-1-111-1-111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111−iii−i1-1-11i−i−ii−i−iiiii−i−i11-1-1-1-111ii−i−i−i−iii
χ161111-1-11111-11-1-1-1111-1-111111111-1-111-1-111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111−iii−i-111-1−iii−i−i−iiiii−i−i-1-11111-1-1−i−iiiii−i−i
χ17222222222-12222222-122-1-12222-1-122-1-1222-1-1-1-12-12-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12-1-1-1-12-12-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-100002222000000000000-1-1-1-1-1-1-1-100000000
χ18222222222-12222222-122-1-12222-1-122-1-1222-1-1-1-12-12-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12-1-1-1-12-12-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-10000-2-2-2-20000000000001111111100000000
χ1922222222-12222222-12-1-12222-1-122-1-12222-12-1-1-1-12222-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-12-1-1-1-12222-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1222200000000-1-1-1-1-1-1-1-10000000000000000
χ2022222222-12222222-12-1-12222-1-122-1-12222-12-1-1-1-12222-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-12-1-1-1-12222-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-2-2-2-200000000111111110000000000000000
χ212222222-122222-1-1-1222222-1-122222222-1-1-1-12-1-122-12-12-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-12-1-122-12-12-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-10000000022220000000000000000-1-1-1-1-1-1-1-1
χ222222222-122222-1-1-1222222-1-122222222-1-1-1-12-1-122-12-12-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-12-1-122-12-12-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-100000000-2-2-2-2000000000000000011111111
χ2322222-2-222-1-2-222222-1-2-2112222-1-1-2-211222-1-1-1-12-1-21-2-222-1-1-1-1-1-1-1-1-2-211111111-2-2111111112-1-1-1-12-1-21-2-222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-211111111-2-21111111100002i2i−2i−2i000000000000−i−i−i−iiiii00000000
χ2422222-2-222-1-2-222222-1-2-2112222-1-1-2-211222-1-1-1-12-1-21-2-222-1-1-1-1-1-1-1-1-2-211111111-2-2111111112-1-1-1-12-1-21-2-222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-211111111-2-2111111110000−2i−2i2i2i000000000000iiii−i−i−i−i00000000
χ2522222-2-22-12-2-22222-1211-2-222-1-12211-2-222-12-1-1-1-12-2-2-21-1-122-1-1-1-1-1-111-2-211111111-2-2111111-12-1-1-1-12-2-2-21-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-111-2-211111111-2-21111112i2i−2i−2i00000000−i−i−i−iiiii0000000000000000
χ2622222-2-22-12-2-22222-1211-2-222-1-12211-2-222-12-1-1-1-12-2-2-21-1-122-1-1-1-1-1-111-2-211111111-2-2111111-12-1-1-1-12-2-2-21-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-111-2-211111111-2-2111111−2i−2i2i2i00000000iiii−i−i−i−i0000000000000000
χ2722222-2-2-122-2-22-1-1-122-2-2-2-2-1-12222-2-2-2-2-1-1-1-12-1-1221-21-2-1-1-1-122-1-1-1-11111-2-211111111-2-21111-1-12-1-1221-21-2-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-11111-2-211111111-2-211110000000022-2-20000000000000000-1-1-1-11111
χ2822222-2-2-122-2-22-1-1-122-2-2-2-2-1-12222-2-2-2-2-1-1-1-12-1-1221-21-2-1-1-1-122-1-1-1-11111-2-211111111-2-21111-1-12-1-1221-21-2-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-11111-2-211111111-2-2111100000000-2-22200000000000000001111-1-1-1-1
χ292222-22-222-12-2-2-2-222-122112222-1-12211-2-22-1-1-1-1-212-1-2-2-2-21111111122-1-1-1-1-1-1-1-1-2-2111111112-1-1-1-1-212-1-2-222-1-1-1-1-1-1-1-1-2-21111111122-1-1-1-1-1-1-1-1-2-21111111100002i−2i2i−2i000000000000−i−iii−i−iii00000000
χ302222-22-222-12-2-2-2-222-122112222-1-12211-2-22-1-1-1-1-212-1-2-2-2-21111111122-1-1-1-1-1-1-1-1-2-2111111112-1-1-1-1-212-1-2-222-1-1-1-1-1-1-1-1-2-21111111122-1-1-1-1-1-1-1-1-2-2111111110000−2i2i−2i2i000000000000ii−i−iii−i−i00000000
χ312222-22-22-122-2-2-2-22-12-1-1-2-222-1-122-1-1-2-2-2-2-12-1-1-11-222-2111-2-2111111-1-122-1-1-1-1-1-111-2-2111111-12-1-1-11-222-21-1-122-1-1-1-1-1-111-2-2111111-1-122-1-1-1-1-1-111-2-21111112-22-200000000-1-111-1-1110000000000000000
χ322222-22-22-122-2-2-2-22-12-1-1-2-222-1-122-1-1-2-2-2-2-12-1-1-11-222-2111-2-2111111-1-122-1-1-1-1-1-111-2-2111111-12-1-1-11-222-21-1-122-1-1-1-1-1-111-2-2111111-1-122-1-1-1-1-1-111-2-2111111-22-220000000011-1-111-1-10000000000000000
χ332222-22-2-1222-2-211-12222-2-2-1-1222222-2-211-1-12-1-1-2-2-121-21111-2-21111-1-1-1-122-1-1-1-11111-2-21111-1-12-1-1-2-2-121-2-1-1-1-122-1-1-1-11111-2-21111-1-1-1-122-1-1-1-11111-2-21111000000002i−2i2i−2i0000000000000000−i−iii−i−iii
χ342222-22-2-1222-2-211-12222-2-2-1-1222222-2-211-1-12-1-1-2-2-121-21111-2-21111-1-1-1-122-1-1-1-11111-2-21111-1-12-1-1-2-2-121-2-1-1-1-122-1-1-1-11111-2-21111-1-1-1-122-1-1-1-11111-2-2111100000000−2i2i−2i2i0000000000000000ii−i−iii−i−i
χ352222-2-2222-1-22-2-2-222-1-2-2-1-12222-1-1-2-2-1-1-2-22-1-1-1-1-21-2122-2-211111111-2-21111111122-1-1-1-1-1-1-1-12-1-1-1-1-21-212222-1-1-1-1-1-1-1-1-2-211111111-2-21111111122-1-1-1-1-1-1-1-100002-2-22000000000000-1-11111-1-100000000
χ362222-2-2222-1-22-2-2-222-1-2-2-1-12222-1-1-2-2-1-1-2-22-1-1-1-1-21-2122-2-211111111-2-21111111122-1-1-1-1-1-1-1-12-1-1-1-1-21-212222-1-1-1-1-1-1-1-1-2-211111111-2-21111111122-1-1-1-1-1-1-1-10000-222-200000000000011-1-1-1-11100000000
χ372222-2-222-12-22-2-2-22-12112222-1-1221122-2-2-12-1-1-11-2-2-22-111-2-211111111-2-2111111-1-122-1-1-1-1-1-1-12-1-1-11-2-2-22-1-1-122-1-1-1-1-1-111-2-211111111-2-2111111-1-122-1-1-1-1-1-12i−2i−2i2i00000000−i−iiiii−i−i0000000000000000
χ382222-2-222-12-22-2-2-22-12112222-1-1221122-2-2-12-1-1-11-2-2-22-111-2-211111111-2-2111111-1-122-1-1-1-1-1-1-12-1-1-11-2-2-22-1-1-122-1-1-1-1-1-111-2-211111111-2-2111111-1-122-1-1-1-1-1-1−2i2i2i−2i00000000ii−i−i−i−iii0000000000000000
χ392222-2-22-122-22-211-122-2-222-1-12222-2-22211-1-12-1-1-2-21-2-121111-2-211111111-2-21111-1-1-1-122-1-1-1-1-1-12-1-1-2-21-2-12-1-1-1-122-1-1-1-11111-2-211111111-2-21111-1-1-1-122-1-1-1-1000000002i−2i−2i2i0000000000000000−i−iiiii−i−i
χ402222-2-22-122-22-211-122-2-222-1-12222-2-22211-1-12-1-1-2-21-2-121111-2-211111111-2-21111-1-1-1-122-1-1-1-1-1-12-1-1-2-21-2-12-1-1-1-122-1-1-1-11111-2-211111111-2-21111-1-1-1-122-1-1-1-100000000−2i2i2i−2i0000000000000000ii−i−i−i−iii
χ4122-2-2222222-2-2-2222222222-2-2-2-2-2-2-2-2-2-2-2-22222222222222222222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000
χ4222-2-222222-1-2-2-22222-122-1-1-2-2-2-211-2-211-2-22-1-1-1-12-12-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12-1-1-1-1-21-21-2-2-2-211111111-2-211111111-2-211111111-2-21111111100000000000000000000−i3i3−i3i3−i3i3−i3i300000000
χ4322-2-222222-1-2-2-22222-122-1-1-2-2-2-211-2-211-2-22-1-1-1-12-12-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12-1-1-1-1-21-21-2-2-2-211111111-2-211111111-2-211111111-2-21111111100000000000000000000i3−i3i3−i3i3−i3i3−i300000000
χ4422-2-22222-12-2-2-2222-12-1-122-2-211-2-211-2-2-2-2-12-1-1-1-12222-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-12-1-1-11-2-2-2-2111-2-211111111-2-211111111-2-211111111-2-2111111000000000000−i3i3−i3i3−i3i3−i3i30000000000000000
χ4522-2-22222-12-2-2-2222-12-1-122-2-211-2-211-2-2-2-2-12-1-1-1-12222-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-12-1-1-11-2-2-2-2111-2-211111111-2-211111111-2-211111111-2-2111111000000000000i3−i3i3−i3i3−i3i3−i30000000000000000
χ4622-2-2222-122-2-2-2-1-1-122222211-2-2-2-2-2-2-2-211-1-12-1-122-12-12-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-12-1-1-2-21-21-21111-2-211111111-2-211111111-2-211111111-2-2111100000000000000000000000000003−33−33−33−3
χ4722-2-2222-122-2-2-2-1-1-122222211-2-2-2-2-2-2-2-211-1-12-1-122-12-12-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-12-1-1-2-21-21-21111-2-211111111-2-211111111-2-211111111-2-211110000000000000000000000000000−33−33−33−33
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.