Finite Group Databasebeta

← Group #13161821

Character table — Group #13161821

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162
size111122222222222222222222222222222244444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444363636363636363636363636363636363636363636363636363636363636363636363636
order124422233344466666666612121212121212121212121233333666666666666666666666666666666666666666661212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121222444444666688881212121212121212121212122424242424242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111-1-111111-1-1-1-1-1-1111111111-1-111-1-111111111-1-1-11-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-11-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-111-1-111-1-11111-1-1-1-111-1-11111-1-1-1-1
χ61111-1-111111-1-1-1-1-1-1111111111-1-111-1-111111111-1-1-11-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-11-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-11111
χ71111-1-111111-1-1-1-1-1-1111111111-1-111-1-111111111-1-1-11-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-11-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-1-1-111-1-1111111-1-1-1-1-1-111-1-1-1-11111
χ81111-1-111111-1-1-1-1-1-1111111111-1-111-1-111111111-1-1-11-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-11-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-11111-1-1-1-1-1-11111-1-1111111-1-1-1-1
χ911-1-11-1-111111-111-1-111-1-1111-1-1-1-1-1-111-1-111111-11-1-1-11-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111111111-11-11111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11-1-11i−ii−i11-1-1i−ii−iii−i−iii−i−i-1-111ii−i−iii−i−i
χ1011-1-11-1-111111-111-1-111-1-1111-1-1-1-1-1-111-1-111111-11-1-1-11-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111111111-11-11111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11-1-11−ii−ii11-1-1−ii−ii−i−iii−i−iii-1-111−i−iii−i−iii
χ1111-1-11-1-111111-111-1-111-1-1111-1-1-1-1-1-111-1-111111-11-1-1-11-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111111111-11-11111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-111-1i−ii−i-1-111−ii−iiii−i−iii−i−i11-1-1−i−iii−i−iii
χ1211-1-11-1-111111-111-1-111-1-1111-1-1-1-1-1-111-1-111111-11-1-1-11-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111111111-11-11111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-111-1−ii−ii-1-111i−ii−i−i−iii−i−iii11-1-1ii−i−iii−i−i
χ1311-1-1-11-11111-11-1-11111-1-1111-1-111-1-1-1-1-1-111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1i−i−ii1111i−i−iiii−i−i−i−iii-1-1-1-1ii−i−i−i−iii
χ1411-1-1-11-11111-11-1-11111-1-1111-1-111-1-1-1-1-1-111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1−iii−i1111−iii−i−i−iiiii−i−i-1-1-1-1−i−iiiii−i−i
χ1511-1-1-11-11111-11-1-11111-1-1111-1-111-1-1-1-1-1-111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111i−i−ii-1-1-1-1−iii−iii−i−i−i−iii1111−i−iiiii−i−i
χ1611-1-1-11-11111-11-1-11111-1-1111-1-111-1-1-1-1-1-111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111−iii−i-1-1-1-1i−i−ii−i−iiiii−i−i1111ii−i−i−i−iii
χ17222222222-122222-1-12222-1222222-1-1-1-1222-1-1-1-12222-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12-1-1-1-12222-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122220000-1-1-1-1000000000000-1-1-1-100000000
χ18222222222-122222-1-12222-1222222-1-1-1-1222-1-1-1-12222-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12-1-1-1-12222-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-200001111000000000000111100000000
χ1922222222-1222222222-1-1-12-1-1-1-122222222-12-1-1-12-12-122-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-12-1-1-122-1-122-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-10000222200000000-1-1-1-1-1-1-1-1000000000000
χ2022222222-1222222222-1-1-12-1-1-1-122222222-12-1-1-12-12-122-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-12-1-1-122-1-122-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-10000-2-2-2-20000000011111111000000000000
χ212222222-122222-1-122-122222222-1-12222-1-1-1-12-1-1-12-1222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-12-1-1-1-12222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-10000000000002222000000000000-1-1-1-1-1-1-1-1
χ222222222-122222-1-122-122222222-1-12222-1-1-1-12-1-1-12-1222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-12-1-1-1-12222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1000000000000-2-2-2-200000000000011111111
χ2322222-2-2222-2-2222-2-222-2-22-2-2222222-2-22222222-22-2-2-22-2-2-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-222222-2-2-22-22-2-2-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-22222222222000000000000000000000000000000000000
χ2422222-2-222-1-2-22221122-2-2-1-2-22222-1-111222-1-1-1-1-22-2-21-1-2-21111111122-1-1-1-1-1-1-1-1-2-2111111112-1-1-1-1-2-2-221-1-2-21111111122-1-1-1-1-1-1-1-1-2-21111111122-1-1-1-1-1-1-1-100000000−i3i3−i3i3000000000000−i3i3−i3i300000000
χ2522222-2-222-1-2-22221122-2-2-1-2-22222-1-111222-1-1-1-1-22-2-21-1-2-21111111122-1-1-1-1-1-1-1-1-2-2111111112-1-1-1-1-2-2-221-1-2-21111111122-1-1-1-1-1-1-1-1-2-21111111122-1-1-1-1-1-1-1-100000000i3−i3i3−i3000000000000i3−i3i3−i300000000
χ2622222-2-22-12-2-2222-2-22-111211-1-12222-2-222-12-1-1-1-2-1-21-2211-2-2111111-1-122-1-1-1-1-1-111-2-2111111-12-1-1-1-2-21-1-2211-2-2111111-1-122-1-1-1-1-1-111-2-2111111-1-122-1-1-1-1-1-100000000000000003−33−33−33−3000000000000
χ2722222-2-22-12-2-2222-2-22-111211-1-12222-2-222-12-1-1-1-2-1-21-2211-2-2111111-1-122-1-1-1-1-1-111-2-2111111-12-1-1-1-2-21-1-2211-2-2111111-1-122-1-1-1-1-1-111-2-2111111-1-122-1-1-1-1-1-10000000000000000−33−33−33−33000000000000
χ2822222-2-2-122-2-22-1-1-2-2-12-2-22-2-222-1-122-2-2-1-1-1-12-1-1121-2-221111-2-21111-1-1-1-122-1-1-1-11111-2-21111-1-12-1-111-22-221111-2-21111-1-1-1-122-1-1-1-11111-2-21111-1-1-1-122-1-1-1-10000000000000000000000000000−i3i3−i3i3−i3i3−i3i3
χ2922222-2-2-122-2-22-1-1-2-2-12-2-22-2-222-1-122-2-2-1-1-1-12-1-1121-2-221111-2-21111-1-1-1-122-1-1-1-11111-2-21111-1-12-1-111-22-221111-2-21111-1-1-1-122-1-1-1-11111-2-21111-1-1-1-122-1-1-1-10000000000000000000000000000i3−i3i3−i3i3−i3i3−i3
χ302222-22-2222-22-2-2-22222-2-22-2-222-2-222222222222-2-222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222222222222-222-2-2-2-2-2-2-2-2-2-2-2-2-222222222222222222222-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000
χ312222-22-222-1-22-2-2-2-1-122-2-2-1-2-222-2-2-1-1-1-1222-1-1-1-1-2-22211-2-211111111-2-21111111122-1-1-1-1-1-1-1-12-1-1-1-1-222-211-2-21111111122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-21111111100000000−i3i3i3−i3000000000000−i3i3i3−i300000000
χ322222-22-222-1-22-2-2-2-1-122-2-2-1-2-222-2-2-1-1-1-1222-1-1-1-1-2-22211-2-211111111-2-21111111122-1-1-1-1-1-1-1-12-1-1-1-1-222-211-2-21111111122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-21111111100000000i3−i3−i3i3000000000000i3−i3−i3i300000000
χ332222-22-22-12-22-2-2-2222-111211-1-1-2-2222222-12-1-1-1-212-1-2-211-2-211111111-2-2111111-1-122-1-1-1-1-1-1-12-1-1-1-22-11-2-211-2-2111111-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-111-2-211111100000000000000003−33−3−33−33000000000000
χ342222-22-22-12-22-2-2-2222-111211-1-1-2-2222222-12-1-1-1-212-1-2-211-2-211111111-2-2111111-1-122-1-1-1-1-1-1-12-1-1-1-22-11-2-211-2-2111111-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-111-2-21111110000000000000000−33−333−33−3000000000000
χ352222-22-2-122-22-21122-12-2-22-2-222112222-1-1-1-12-1-11-2-12-2-21111-2-211111111-2-21111-1-1-1-122-1-1-1-1-1-12-1-11-12-2-2-21111-2-21111-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-11111-2-211110000000000000000000000000000−i3i3−i3i3i3−i3i3−i3
χ362222-22-2-122-22-21122-12-2-22-2-222112222-1-1-1-12-1-11-2-12-2-21111-2-211111111-2-21111-1-1-1-122-1-1-1-1-1-12-1-11-12-2-2-21111-2-21111-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-11111-2-211110000000000000000000000000000i3−i3i3−i3−i3i3−i3i3
χ372222-2-2222-12-2-2-2-2112222-12222-2-2-1-111222-1-1-1-12-2-2-2-1122-1-1-1-1-1-1-1-1-2-211111111-2-2111111112-1-1-1-12-2-2-2-1122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-211111111-2-2111111112-22-20000-1-111000000000000-1-11100000000
χ382222-2-2222-12-2-2-2-2112222-12222-2-2-1-111222-1-1-1-12-2-2-2-1122-1-1-1-1-1-1-1-1-2-211111111-2-2111111112-1-1-1-12-2-2-2-1122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-211111111-2-211111111-22-22000011-1-100000000000011-1-100000000
χ392222-2-222-122-2-2-2-2-2-22-1-1-12-1-1-1-1-2-222-2-222-12-1-1-121-212-2-1-122-1-1-1-1-1-111-2-211111111-2-2111111-12-1-1-12-2112-2-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-111-2-211111111-2-2111111000022-2-200000000-1-1-1-11111000000000000
χ402222-2-222-122-2-2-2-2-2-22-1-1-12-1-1-1-1-2-222-2-222-12-1-1-121-212-2-1-122-1-1-1-1-1-111-2-211111111-2-2111111-12-1-1-12-2112-2-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-111-2-211111111-2-21111110000-2-222000000001111-1-1-1-1000000000000
χ412222-2-22-1222-2-211-2-2-1222222221122-2-2-1-1-1-12-1-1-1-21-22-2-1-1-1-122-1-1-1-11111-2-211111111-2-21111-1-12-1-1-11-2-22-2-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-11111-2-211111111-2-2111100000000000022-2-2000000000000-1-1-1-11111
χ422222-2-22-1222-2-211-2-2-1222222221122-2-2-1-1-1-12-1-1-1-21-22-2-1-1-1-122-1-1-1-11111-2-211111111-2-21111-1-12-1-1-11-2-22-2-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-11111-2-211111111-2-21111000000000000-2-2220000000000001111-1-1-1-1
χ4322-2-2222222-2-2-2222222222-2-2-2-2-2-2-2-2-2-2-2-22222222222222222222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000
χ4422-2-222222-1-2-2-222-1-12222-1-2-2-2-2-2-21111-2-22-1-1-1-12222-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12-1-1-1-1-2-2-2-211-2-211111111-2-211111111-2-211111111-2-21111111100000000−i3i3i3−i3000000000000i3−i3−i3i300000000
χ4522-2-222222-1-2-2-222-1-12222-1-2-2-2-2-2-21111-2-22-1-1-1-12222-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12-1-1-1-1-2-2-2-211-2-211111111-2-211111111-2-211111111-2-21111111100000000i3−i3−i3i3000000000000−i3i3i3−i300000000
χ4622-2-22222-12-2-2-222222-1-1-121111-2-2-2-2-2-2-2-2-12-1-1-12-12-122-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-12-1-1-1-2-211-2-211-2-211111111-2-211111111-2-211111111-2-21111110000000000000000−i3i3i3−i3−i3i3i3−i3000000000000
χ4722-2-22222-12-2-2-222222-1-1-121111-2-2-2-2-2-2-2-2-12-1-1-12-12-122-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-12-1-1-1-2-211-2-211-2-211111111-2-211111111-2-211111111-2-21111110000000000000000i3−i3−i3i3i3−i3−i3i3000000000000
χ4822-2-2222-122-2-2-2-1-122-12222-2-2-2-211-2-2-2-211-1-12-1-1-12-1222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-12-1-111-2-2-2-21111-2-211111111-2-211111111-2-211111111-2-2111100000000000000000000000000003−3−333−3−33
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.